Magneto-Optical Investigations of Multiferroic Hybrid ... · 3.2 Ferroelectric domains in BaTiO ......

TECHNISCHE

UNIVERSITAT

MUNCHEN

WALTHER - MEISSNER -

INSTITUT FUR TIEF -

TEMPERATURFORSCHUNG

BAYERISCHE

AKADEMIE DER

WISSENSCHAFTEN

Magneto-Optical Investigations of

Multiferroic Hybrid Structures

Diploma Thesis

Matthias Brasse

Advisor: Prof. Dr. Rudolf Gross

Munich, October 2009

http://www.tum.de/

http://www.wmi.badw.de/

http://www.badw.de/

http://www.tum.de/

http://www.wmi.badw.de/

http://www.badw.de/

Abstract

Multiferroic hybrid structures, which hold the promise of an electric field control of fer-

romagnetism, are investigated by means of the magneto-optical Kerr effect.

As part of this thesis, a magneto-optical Kerr setup allowing spatially resolved Kerr

imaging has been established. This setup is presented, characterized and its capabilities

in large scale magnetic domain imaging are demonstrated.

The studied multiferroic hybrid structures consist of a ferromagnetic thin film and a

ferroelectric substrate and have mostly been prepared during this thesis. Nickel and iron-

cobalt have been chosen as ferromagnetic constituent and either piezoelectric actuators

based on lead circonate ceramics or barium titanate single crystals serve as ferroelectric

substrate. In these hybrid structures magnetization control by means of electric fields

is achieved by making use of the piezoelectric and the magnetoelastic effect. In all pre-

pared samples the mechanical strain dependence of the magnetic hysteresis is studied

extensively. On top of that, differences in the evolution of the magnetic microstructure

in dependence of the applied strain are observed and pointed out. In the piezoelectric

actuator based samples it is found that the strain coupling is strongly affected by the

used fabrication technique and by the choice of the ferromagnetic constituents. However,

in both, the actuator based hybrids as well as the barium titanate composites, magne-

toelastic coupling unambiguously influences the anisotropy of the attached ferromagnetic

thin film. Moreover, magneto-optical experiments are successfully performed regarding

electric field induced magnetization switching. Magnetization control by means of electric

fields is therefore established for all investigated samples.

In addition, experiments aiming at local magnetization control have been performed.

Local strain control is achieved by a modification of the actuator based hybrid struc-

tures and allows to control the magnetization orientation selectively. Applying the

magneto-optical Kerr technique, local magnetization switching is confirmed. Addition-

ally, magnetotransport measurements are applied to correlate the observed domain struc-

ture with anisotropic magnetoresistance data. Good agreement between both experiments

is achieved. Finally a novel sample design consisting of patterned nickel electrodes on

piezoelectric substrates is proposed and investigated. First experiments prove that local

strain and magnetization control in these samples is also possible.

Taken together, these results show that an electric field control of ferromagnetism is

possible via the elastic channel both on macroscopic (mm) as well as on microscopic (µm)

length scale.

I

Contents

Abstract I

1 Introduction 1

2 Theoretical Basics 5

2.1 Ferroics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Ferroelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Multiferroics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Piezoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Magnetoelastic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Magneto-Optical Kerr Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2 Microscopic Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.3 Macroscopic Description . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.4 Quantitative Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.5 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Materials 21

3.1 Ferromagnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.2 Iron-Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Piezoelectric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Lead Zirconate Titanate . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.2 Barium Titanate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.3 Lithium Niobate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Magneto-Optical Kerr Effect with Spatial Resolution 27

4.1 The Existing Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Kerr Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.4 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.5 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

III

IV Contents

4.5.1 CCD Noise and Signal-to-Noise Ratio . . . . . . . . . . . . . . . . . . 34

4.5.2 Magneto-Optical Contrast . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.5.3 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.6 Imaging of Thin Ferromagnetic Films . . . . . . . . . . . . . . . . . . . . . . 39

4.7 Quantitative Kerr Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Magneto-Optics on Ferromagnetic/Ferroelectric Hybrids 45

5.1 Ferromagnetic Thin Films on Piezoelectric Actuators . . . . . . . . . . . . . 45

5.1.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.1.2 Strain Control of the Magnetic Anisotropy . . . . . . . . . . . . . . . 47

5.1.3 Voltage Dependence of the Magnetic Hysteresis . . . . . . . . . . . . 49

5.1.4 Domain Evolution at Constant Strain . . . . . . . . . . . . . . . . . . 52

5.1.5 Strain Induced Birefringence . . . . . . . . . . . . . . . . . . . . . . . 58

5.1.6 Extraction of the Magnetic Contribution to Birefringence . . . . . . 61

5.1.7 Strain Induced Magnetization Switching . . . . . . . . . . . . . . . . 62

5.2 Ferromagnetic Thin Films on BaTiO3 Substrates . . . . . . . . . . . . . . . . 64

5.2.1 Sample Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2.2 M(H) Measurements at Constant Strain . . . . . . . . . . . . . . . . 66

5.2.3 Magnetization Switching at Constant Magnetic Field . . . . . . . . . 68

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6 Local Magnetization Control 71

6.1 Ferromagnets on Piezoelectric Actuators . . . . . . . . . . . . . . . . . . . . . 71


6.1.2 Local Polarization Control . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.1.3 Local Strain Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.1.4 Local Magnetization Switching . . . . . . . . . . . . . . . . . . . . . . 76

6.1.5 Magnetotransport Measurements . . . . . . . . . . . . . . . . . . . . . 79

6.2 Patterned Ni Electrodes on Piezoelectric Substrates . . . . . . . . . . . . . . 88


6.2.2 Polarization and Strain Control . . . . . . . . . . . . . . . . . . . . . . 90

6.2.3 Strain Induced Shift of the Coercive Field . . . . . . . . . . . . . . . 94

6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7 Conclusion and Outlook 97

Bibliography 101

List of Figures

2.1 Hysteresis of ferromagnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Multiferroics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Hysteresis of piezoelectric materials . . . . . . . . . . . . . . . . . . . . . . . . 11

2.5 Phenomenology of the magneto-optical Kerr effect . . . . . . . . . . . . . . . 13

2.6 Microscopic origin of the magneto-optical Kerr effect . . . . . . . . . . . . . 14

2.7 Geometry of the Kerr effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.8 Calculation of the MOKE signal . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1 Cubic and tetragonal unit cells of BaTiO3 . . . . . . . . . . . . . . . . . . . . 23

3.2 Ferroelectric domains in BaTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Kerr effect schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 Photograph of the established Kerr setup . . . . . . . . . . . . . . . . . . . . 29

4.3 Photograph of LED and focusing lens . . . . . . . . . . . . . . . . . . . . . . 30

4.4 Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.5 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.6 Magneto optical contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.7 Contrast with /4 plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.8 Sensitivity per pixel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.9 Domains Co . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.10 Domain evolution in CrO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.11 Quantitative Kerr microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1 Ferromagnet on piezoelectric actuator . . . . . . . . . . . . . . . . . . . . . . 46

5.2 Strain induced anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.3 Voltage dependent hysteresis of Ni and Fe50Co50 . . . . . . . . . . . . . . . . 50

5.4 Voltage dependent hysteresis of Ni . . . . . . . . . . . . . . . . . . . . . . . . 52

5.5 Domain evolution in Fe50Co50 on piezoelectric actuator . . . . . . . . . . . . 53

5.6 Inhomogenous strain distibution . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.7 Domain evolution in Ni at Vp = −30V . . . . . . . . . . . . . . . . . . . . . . . 55

5.8 Domain evolution in Ni at Vp = +30V . . . . . . . . . . . . . . . . . . . . . . . 56

5.9 Domains in Ni on actuator at Vp = 0V . . . . . . . . . . . . . . . . . . . . . . 57

5.10 Illustration of the actuator deformation . . . . . . . . . . . . . . . . . . . . . 58

V

VI List of Figures

5.11 Reference measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.12 Strain induced birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.13 Extraction of magnetic contribution to birefringence . . . . . . . . . . . . . . 61

5.14 Magnetization switching in Fe50Co50 cemented onto actuator . . . . . . . . 62

5.15 Magnetization switching in Ni evaporated onto actuator . . . . . . . . . . . 64

5.16 Ni on BaTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.17 Hysteresis curves of Ni on BaTiO3 for different applied voltages . . . . . . . 67

5.18 Domain evolution in Ni on BaTiO3 at E = +400 V/mm . . . . . . . . . . . . 67

5.19 Domain evolution in Ni on BaTiO3 at E = −60 V/mm . . . . . . . . . . . . . 68

5.20 Magnetization switching in Ni on BaTiO3 at 0H = 7.3 mT . . . . . . . . . 69

5.21 Magnetization switching in Ni on BaTiO3 at 0H = 8.0 mT . . . . . . . . . 69

6.1 Sample preparation for local magnetization control . . . . . . . . . . . . . . 72

6.2 Polarisation of single PZT monolayers . . . . . . . . . . . . . . . . . . . . . . 73

6.3 Local strain generation in evaporated samples . . . . . . . . . . . . . . . . . 74

6.4 Local strain generation in cemented samples . . . . . . . . . . . . . . . . . . 75

6.5 Local magnetization control in FeCo . . . . . . . . . . . . . . . . . . . . . . . 76

6.6 Local magnetization switching in Ni . . . . . . . . . . . . . . . . . . . . . . . 77

6.7 Local magnetization switching in Ni for different contact schemes . . . . . . 79

6.8 Sample preparation for magnetotransport measurements . . . . . . . . . . . 80

6.9 Magnetotransport at different applied voltages . . . . . . . . . . . . . . . . . 82

6.10 Local magnetization control and MTR . . . . . . . . . . . . . . . . . . . . . . 84

6.11 Magnetotransport and local magnetization control . . . . . . . . . . . . . . . 85

6.12 Correlation of magnetotransport and MOKE . . . . . . . . . . . . . . . . . . 86

6.13 Ni on PZT plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.14 Ni electrodes on BaTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.15 Polarization and strain control in Ni/PZT composites . . . . . . . . . . . . . 92

6.16 Strain control on PZT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.17 Strain induced coercivity shift in Ni on PZT . . . . . . . . . . . . . . . . . . 94

List of Tables

2.1 Overview of effects in multiferroic material systems . . . . . . . . . . . . . . 10

3.1 Magnetoeleastic constants of Ni and Fe50Co50 . . . . . . . . . . . . . . . . . . 22

3.2 Piezoelectric coefficients of PZT, BaTiO3 and LiNbO3 . . . . . . . . . . . . 23

5.1 Overview of prepared samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.1 Overview of prepared samples for local magnetization control. . . . . . . . . 90

VII

Chapter 1

Introduction

I was led some time ago to think it very likely, that if a beam of plane-

polarized light were reflected under proper conditions from the surface of

intensely magnetized iron, it would have its plane of polarization turned

through a sensible angle in the process of reflection.

(John Kerr, 1877)

This is the very first sentence of John Kerr’s publication on the discovery of the ro-

tation of the plane of polarization by reflection from a magnetic surface [1]. At that

time, John Kerr could not foresee the impact of his findings onto the research regarding

magnetic media. As of today, we know that his discovery paved the way to modern

magneto-optic experiments. The magneto-optical Kerr effect (MOKE), named after his

discoverer, became a powerful tool for probing surfaces of bulk ferromagnets or magnetic

thin films. Reasons for the success of magneto-optical methods are that they allow a fast

and non-destructive investigation of ferromagnetic samples and thus are widely used for

their characterization. Nowadays, Kerr signals can be recorded even on the time scale of

femtoseconds by applying pump-probe experiments and thus give information about mag-

netization dynamics [2, 3]. In addition, the magneto-optical Kerr effect allows the direct

observation of magnetic domains [4]. The introduction of the digital difference technique

in which non-magnetic background is digitally subtracted, together with the CCD camera

revolution represented important stimuli for the magneto-optical Kerr technique, since

from then on processes in the magnetic microstructure could be investigated vigorously

[5, 6, 7, 8]. In comparison to other domain observation methods like magnetic force mi-

croscopy (MFM), scanning electron microscopy (SEM) or tunneling electron microscopy

(TEM), the MOKE technique is the only one that allows direct evaluation of the mag-

netization vector. Moreover, in terms of the necessary financial investment it generally

beats its counterparts as well. As a consequence of these advantages, the magneto-optical

Kerr effect is today’s standard technique in domain imaging applications.

The significance of the magnetic substructure in research and applications has risen

steadily and plays an important role in the development of modern spintronic or mag-

1

2 Chapter 1 Introduction

netoelectronic devices. In contrast to conventional electronic devices, which utilize only

the charge degree of freedom, spintronic devices also take advantage of the electron spin

degree of freedom and thus represent a unification of electric and magnetic properties.

In the history of magnetism and the field of spintronics research and also regarding tech-

nological applications the discovery of the giant magneto resistance (GMR) by A. Fert

and P. Grunberg [9, 10] and of the tunneling magneto resistance (TMR) by M. Julliere

[11] have certainly represented mile-stones. Today’s hard disk drives reading heads and

magnetic sensor technology most often rely on one of those effects.

However, the scalability of magnetoelectronic devices to smaller dimensions turned out

to be the critical endeavor for future relevance in technology. Today’s nanofabrication

techniques allow to structure nanoscale systems, but the critical point is to control the

magnetic microstructure. In most applications, the magnetization of ferromagnets is

controlled by means of magnetic fields. Although magnetic fields are the natural way to

control the magnetization orientation, in small scale systems they need to be of sufficient

strength to achieve the desired magnetization control. Large magnetic fields implicate

stray fields which finally prevent ultimate scaling to state of the art nanodevices. More-

over, power consumption rises with the magnetic field strength.

As a consequence, the search for other possibilities of magnetization control began.

Electric fields are a promising alternative, because they are easy to implement on even

nanometer length scales, power efficient and fully switchable. To allow for magnetization

control, efficient coupling between the electric field and the ferromagnetic order parameter

is essential. Therefore, multifunctional material systems enabling magnetization control

by means of electric fields have been under vigorous research and numerous schemes have

been reported. One promising approach is the usage of intrinsic multiferroic materials

that unite electric and magnetic phases and thus allow a direct magnetization control by

electric fields [12, 13, 14, 15, 16]. In addition, heterostructures in which magnetic and

electric phases share a common interface also yield a promising alternative [17]. Last,

the establishment of multifunctional ferromagnetic and ferroelectric hybrid structures

represent another approach to aim for an electric field control of the magnetization [18,

19, 20, 21, 22]. All the above proposals rely on efficient coupling of the ferrolectric and

ferromagnetic phases, which is generally achieved with the so-called magnetoelectric or

magnetoelastic effects. More important, these approaches in principle facilitate scaling

to smaller dimensions.

From this matter of fact, the central motivation for this work arose. Multiferroic hybrid

structures have been prepared and studied in the framework of this thesis. The investi-

gation has concentrated upon magnetization control by means of electrically-controlled

mechanical strain. Moreover, the scalability and the possibility of local magnetization

control in the prepared samples was analyzed. The main instrument of characterization

was a magneto-optical Kerr setup that allows spatially resolved magnetic domain imag-

ing. As part of this thesis, an existing MOKE setup has been extended and has proven

to be a very valuable method in the observation of magnetic microstructure as already

3

mentioned above.

The outline of this thesis is the following:

Chapter 2 briefly reviews and summarizes the characteristics of ferroic systems, in

particular ferromagnetism and ferroelectricity. Then the concept of multiferroics is in-

troduced and the piezoelectric and magnetoelastic effects are reviewed in the context of

multiferroic systems. Finally the physical principles regarding the magneto-optical Kerr

effect are introduced.

Basic properties of the materials used for this thesis are presented in Chapter 3. Nickel

and iron-cobalt serve as ferromagnetic constituents, whereas lead zirconate titanate, bar-

ium titanate and lithium niobate are reviewed as the piezoelectric parts of the multiferroic

hybrid structures.

In Chapter 4 the magneto-optical Kerr setup established during this thesis is presented.

First, the setup and its components are described before its characterization in terms of

resolution, sensitivity and contrast is presented. Finally imaging experiments on thin

ferromagnetic films are shown to demonstrate the capabilities of the new low resolution

Kerr microscope.

Experiments on ferromagnetic/ferroelectric hybrid structures are presented in Chap-

ter 5. Hybrid structures consisting of piezoelectric actuators and ferromagnetic thin films

as well as composites made of barium titanate and nickel thin films are discussed. Both

types of samples are studied regarding their capabilities in magnetoelastic coupling and

magnetization control by means of electric fields.

Chapter 6 deals with the scalability of hybrid structures allowing electric field controlled

magnetization switching. The possibility of local magnetization control in hybrids based

on piezoelectric actuators is discussed. Moreover a novel approach for local magnetization

control is presented, in which micron size patterned ferromagnetic electrodes are strained

by piezoelectric substrates.

Finally, in Chapter 7 a brief conclusion is given and ideas for future applications and

experiments are proposed.

Chapter 2

Theoretical Basics

In this chapter the theoretical background, that is of relevance for this work, is re-

viewed. At first, basics of ferromagnetism and ferroelectricity as ferroic systems are

discussed. Then, characteristics of systems uniting ferromagnetic and ferroelectric prop-

erties, so-called multiferroics, are introduced. At last, the physical principles underlying

the magneto-optic sample characterization on the basis of the Kerr effect are reviewed.

2.1 Ferroics

Ferroics is the generic name given to the study of ferromagnets, ferroelectrics and ferro-

elastics. All ferroic materials have in common that they exhibit spontaneous long range

order characterized by an order parameter X ∈ M,P,", where M is the magnetization

in ferromagnets, P the polarization in ferroelectrics and " the strain in ferroelastics. It is

important to note, that this ordering is spontaneous which means that it occurs in absence

of external fields. Moreover, ferroics undergo a phase transition from a state with no order

(X = 0) above a critical temperature Tc to a state with long range order (X ≠ 0) below

Tc. The critical temperature Tc is referred to as Curie temperature. The application

of external fields Y ∈ H,E,1 results in a response of the order parameter. In linear

approximation the response is governed by X = Y, where denotes the susceptibility

tensor.

For the scope of this thesis, especially ferromagnetism and ferroelectricity are of im-

portance. Therefore a short review of both is given in the following.

2.1.1 Ferromagnetism

The order parameter in ferromagnets is the magnetization M, which is defined as the

quantity of magnetic moment per unit volume V [23]

M =1

V∑

j

j (2.1)

1H denotes a magnetic field, E an electric field and mechanical stress

5

6 Chapter 2 Theoretical Basics

The microscopic origin of the magnetic moment is the coupling of the classical orbital

angular momentum L of an electron with its spin S. In ferromagnets, magnetic moments

strongly interact with each other. This interaction is caused by the quantum mechanical

exchange mechanism, which is primarily responsible for the ordering of magnetic moments

in ferromagnets.

As mentioned above, the magnetization responds to external magnetic fields as de-

scribed in linear approximation by [24]

M = MH, (2.2)

where M denotes the magnetic susceptibility. In this work, magnetic fields will be

described by the magnetic induction B, which is related to M by

B = 0(H +M), (2.3)

where 0 = 4 × 10−7 VsAm denotes the vacuum-permeability.

Apart from those basic principles, ferromagnetism involves many fundamental con-

cepts. For the framework of this thesis, the concept of magnetic hysteresis, domain

formation and magnetic anisotropy are of importance and thus they are summarized

briefly.

Domains

A magnetic domain describes a region within a ferromagnet which has a uniform mag-

netization [25]. In absence of external fields, a ferromagnet is generally composed of

numerous domains with different magnetization orientations. Domains with different

magnetization orientations are separated by domain walls. The formation of magnetic

domains is energetically favorable compared to a single domain state. In the resulting

domain pattern the magneto-static stray field energy is balanced against the energy of

the domain walls, anisotropy and the term arising from the exchange mechanism [26].

In bulk ferromagnets, generally two types of domain walls exist: Bloch and Neel walls

[27]. The difference between both wall types is the mode of rotation of the magnetization

vector within the domain wall. If the rotation of the magnetization vector is within the

domain wall plane (perpendicular to the domain wall plane), the domain wall is referred

to as a Neel wall (Bloch wall).

In thin ferromagnetic films many different domain configurations and domain wall

types are present. An extensive study can be found in [5]. Generally, the domain wall

structure is strongly influenced by the film thickness. In particular, for thin films with

in plane anisotropy Neel type walls are preferred, since the magnetization rotates within

the domain plane and thus minimizes the demagnetization energy term (see below).

2.1 Ferroics 7

H

M

Mr

Hc

Ms

Figure 2.1: Illustration of a ferromagnetic hysteresis curve.

Hysteresis

One general feature of ferromagnetic substances is that the magnetization responds hys-

teretic upon the application of external magnetic fields [23] as depicted in Fig. 2.1. In the

demagnetized state at zero magnetic field the ferromagnet consist of domains and exhibits

no net magnetization. Increasing the field, domains which are energetically favored grow

at the expense of unfavorable domains. For large external magnetic fields (H >>Hc), the

magnetization is saturated and the ferromagnet is in a single domain state. Decreasing

the external field to H = 0 the macroscopic magnetization is reduced to the remanent

magnetization Mr. This behavior is due to the formation of domains in order to minimize

the free energy of the ferromagnet. At the coercive field H = −Hc, the macroscopic mag-

netization has diminished to zero as a consequence of domain formation. The individual

domains still exhibit a magnetization, however the average over all domains results in

M = 0. A further decrease of the magnetic field yields a uniform magnetic state again.

Magnetic Anisotropies

The direction of the external magnetic field H and the magnetization M do not necessarily

coincide in a ferromaget. The reason therefore are anisotropies, which can be induced

by intrinsic properties of the material, like shape or crystal structure, or by extrinsic

contributions like stresses. In order to determine the orientation of the magnetization

a free energy model was introduced [28, 29], which accounts for all intrinsic anisotropy

contributions in the following form:

Ftot = Fstat + Fdemag + Faniso (2.4)

In this approach Fstat denotes the Zeeman energy, Fdemag stands for the demagnetization

term and Faniso represents crystalline anisotropies. In equilibrium, the magnetization

always resides in local minimum of the free energy density. The minima (maxima) in the


z

y

H

M

x

Figure 2.2: Coordinate system relative to the sample [30].

free energy correspond to magnetically easy (hard) directions.

A coordinate system has been introduced [30] to describe the orientation of both M

and H with respect to the sample (cf. Fig. 2.2). Thus the following parametrization in

polar coordinates is achieved:

M = (M,Θ,Φ) (2.5)

H = (H,, ) (2.6)

Capital Greek letters describe the orientation of the magnetization and lower case

letters the orientation of the external magnetic field. In terms of this parametrization

the contributions to the free energy density can be expressed as follows:

• The Zeeman term Fstat describes the magnetostatic energy of the magnetization M

in an external magnetic field H. It is given by [31]

Fstat = −0H ⋅M. (2.7)

In terms of the parametrization above it becomes

Fstat = −0HM(sin Θ sin Φ sin sin + cos Θ cos + sin Θ cos Φ sin cos) (2.8)

Without consideration of further contributions to the free energy, the magnetization

would always be aligned parallel to the external magnetic field.

• The demagnetization term Fdemag takes the anisotropy arising from the sample

shape and geometry into account and is therefore often denoted as shape anisotropy.

For thin films, which is appropriate for all samples used in this thesis, it yields [32]:

2.2 Multiferroics 9

Fdemag =0

2M2 sin2 Θ cos2 Φ (2.9)

Usually, the shape anisotropy causes the magnetization to lie within the film plane

of the ferromagnetic sample since a magnetically hard axis perpendicular to the

film surface is induced.

• The crystalline anisotropy Faniso arises from the crystal structure of the ferromag-

netic sample. However, in this thesis only polycrystalline thin films have been

prepared. In this case, no net crystalline anisotropies are present [19] and thus this

energy term can be omitted.

All in all, in polycrystalline thin ferromagnetic films two intrinsic contributions to the

free energy are present, the Zeeman energy and the demagnetization term. Consequently,

considering ideal growth conditions the ferromagnetic thin film is fully isotropic in the

film plane but exhibits a magnetically hard axis out-of-plane.

2.1.2 Ferroelectricity

In ferroelectric materials the order parameter is the polarization P. The response of the

polarization upon the application of an electric Field is governed by

P = 0EE, (2.10)

where 0 = 8.85 × 10−12 AsVm denotes the permittivity of free space and E the electri-

cal susceptibility. Ferroelectric materials exhibit a spontaneous polarization below the

Curie temperature. In accordance to ferromagnets, their polarization can be reversed

by external electric fields and it also shows a hysteretic behavior. Another similarity

to ferromagnetism is the fact that domain formation also plays an important role in

ferroelectricity (cf. Chapter 3).

2.2 Multiferroics

So far, ferroelectrics and ferromagnets have been introduced as examples of ferroic ma-

terials. They both have in common that they exhibit spontaneous long range order.

Materials that unite more than one ferroic order parameter simultaneously are called

multiferroics. In Fig. 2.3 the relationship between the individual order parameters M, P

and " and the corresponding fields H, E and is represented by different colors. How-

ever, in multiferroic materials there are also cross-links, since each field may influence all

order parameters and the resulting effects are listed in Tab. 2.1.

For the framework of this thesis, the magnetoelastic and the piezoelectric effect are of

importance and therefore their main properties are reviewed briefly.


E

P

M

H

N S

M

P+ – + –

+ – + –

ε

ε

σ

Figure 2.3: Relation between the different ferroic order parameters and the external fields in multiferroic

systems [12].

Y→X EffectH→ P magnetoelectric effectE→M converse magnetoelectric effectH→ " magnetostrictive effect →M magnetoelastic effect → P piezoelectric effectE→ " inverse piezoelectric effect

Table 2.1: Overview of effects in multiferroic material systems. The external field Y induces a response

of the order parameter X in multiferroics.

2.2.1 Piezoelectric Effect

Piezoelectricity is the ability of some materials to generate an electric field or electric

potential in response to an applied mechanical stress [33]. Materials exhibiting the direct

piezoelectric effect also show the inverse piezoelectric effect, which describes the defor-

mation of the piezoelectric material upon the application of external electric fields. It is

important to note, that all ferroelectric materials show piezoelectricity, however, there

are piezoelectric materials, like e.g. quartz, which do not exhibit ferroelectricity. For

the scope of this thesis, especially the inverse piezoelectric effect is of importance. The

resulting elastic strain " can be correlated with the applied electric field E by [33, 34]

" = dpE − sE, (2.11)

where sE stands for the coefficient of elasticity (inverse of the Young’s modulus), de-

notes the mechanical stress and dp is the piezoelectric strain coefficient. The piezoelectric

effect is fundamental for the functioning of piezoelectric actuators and other piezoelec-

tric materials, which will be introduced in Chapter 3. In essence, one has to distinguish

between the longitudinal (d33-effect) and the transversal (d31-effect) mode of the piezo-

2.2 Multiferroics 11

electric substrate. The longitudinal mode describes the deformation of the piezoelectric

material parallel to the external field, whereas the transversal mode describes the defor-

mation perpendicular to it. The two effects can be expressed as [35]:

"3 = d33E3 − sE333 (2.12)

"⊥ = d31E3 − sE11⊥. (2.13)

As piezoelectric materials are generally also ferroelectric, the strain response to the

electric field is non-linear but hysteretic [36, 37]. The resulting hysteresis curve for the

mechanical strain is schematically depicted in Fig. 2.4. Due to its shape the hysteresis

curve is also denoted as butterfly curve. The origin of the hysteresis is the inverse piezo-

electric effect together with the switching and movement of ferroelectric domain walls

[36]. The minima in the hysteresis curve correspond to the ferroelectric coercive field

indicating the polarization reversal [36]. As a consequence of the hysteretic behavior, the

resulting strain at a certain electric field is not uniquely defined but depends upon the

field history. Moreover, also at vanishing electric field piezoelectric materials generally

exhibit remanent strain. For the matter of application, piezoelectric materials are usu-

ally used in a semi-bipolar field regime which comprises only the positive or the negative

hysteresis branch.

ε

E

Figure 2.4: Strain-field hysteresis of piezoelectric materials.

2.2.2 Magnetoelastic Effect

The magnetoelastic effect, also known as converse magnetostrictive effect, describes the

effect of stress onto the magnetization of a ferromagnet [31]. The applied stress induces

strains within the ferromagnet. In presence of strains, the free energy approach introduced


in Eq. (2.4) has to include the energy contribution Fmagel arising from magnetoelastic

coupling. Consequently the free energy Ftot of a polycrystalline ferromagnet under applied

stress is given by

Ftot = Fstat + Fdemag + Fmagel. (2.14)

Considering only strains along the x, y and z directions, shear strains can be neglected

in polycrystalline samples, since they average out. Thus the resulting strain is purely

uniaxial and is manifested in the magnetoelastic contribution Fmagel as [31, 34]

Fmagel =Kmagel,x sin2 Θ sin2 Φ +Kmagel,y cos2 Θ +Kmagel,z sin2 Θ cos2 Φ (2.15)

with

Kmagel,i =3

2(c12 − c11)"i, i ∈ x,y, z . (2.16)

In this equation denotes the magnetostrictive constant, c11, c12 represent the elastic

moduli of the ferromagnet and "i stands for the strains along the corresponding directions

in Voigt notation [38].

Strains can arise for instance from the lattice mismatch between substrate and thin film.

However, in this thesis strain will be induced on purpose with the help of piezoelectric

substrates. Thus, considering the principles presented above it has to be emphasized

that the magnetoelastic effect in principle opens the avenue for strain control of the

magnetization orientation.

2.3 Magneto-Optical Kerr Effect

The interaction of light with solids depends primarily on the electronic structure of the

solids. Magneto-optical effects come into play if the interaction additionally depends on

the magnetic state of the material. The most prominent magneto-optical effects are the

Faraday and the Kerr effect. Generally they differ in the manner of the observation. If

the magneto-optical effect is observed in transmission, it is denoted as Faraday effect.

Contrarily, the Kerr effect describes magneto-optical effects observed in reflection. In the

framework of this thesis a magneto-optical Kerr setup was extended and then used for

characterization of ferromagnetic samples. Therefore a short review of phenomenology,

origin and quantitative description of the magneto-optical Kerr effect (MOKE) will be

given in the following.

2.3.1 Phenomenology

The magneto-optical Kerr effect is based on the interaction of polarized light with a

magnetized sample and was first observed in 1877 [1]. The phenomenology of the Kerr

2.3 Magneto-Optical Kerr Effect 13

fk

Mtan(hk)=b/a

sample

EiErincident

lightreflectedlightb

aθ1

Figure 2.5: Phenomenology of the magneto-optical Kerr effect. Upon reflection off a magnetized sample

the polarization plane of the incident light (angle of incidence 1) is rotated by an angle 'k.

The state of polarization changes from linearly polarized to elliptically polarized, which is

characterized by the ellipticity k.

effect is pointed out with the help of Fig. 2.5. If you regard a linearly polarized light

beam, it undergoes two transformations upon the reflection off a magnetized sample.

First, its plane of polarization is rotated by the so-called Kerr angle 'k. In addition,

the state of polarization changes from linearly polarized to elliptically polarized. The

new state of polarization can be characterized by the ellipticity k which is defined as

the inverse tangent of the ratio of the principle ellipse axes tan k = b/a. All in all, both

transformations are combined to the complex Kerr angle Ψk with [39]

Ψk = 'k + ik (2.17)

The complex Kerr rotation depends upon the magnetization of the sample as will be

demonstrated in following. Therefore the magneto-optical effect constitutes a perfect

measure of the magnetization and is widely used for characterization of ferromagnetic

samples and domain observation.

2.3.2 Microscopic Origin

In order to understand the microscopic origin of the magneto-optical Kerr effect, quantum

mechanics has to be applied. In the following a simple explanation for the interaction

of light with a 3d ferromagnet based on quantum mechanical transition rules is given

[40]. An extensive treatment of this problem can be found in [41, 42]. Let us consider

optical transitions between a doubly degenerate dxz,yz level (l = 2, ml = ±1) and a pz level

above the Fermi energy. Due to the exchange mechanism in ferromagnets, the d levels for

spin-up and spin-down electrons are separated by the exchange energy EEx (cf. Fig. 2.6).

Moreover, the spin-orbit coupling lifts the degeneracy of the dxz,yz level for both spin

directions. They split into a d(x+iy)z level with ml = +1 and a d(x−iy)z level with ml = −1.

Optical transitions have to satisfy the selection rules for electric dipolar transitions. For


d↑xz d↑

yzd↑

(x+iy)z

d↑(x-iy)z

p↑z

d↓yzd↓

xz

d↓(x-iy)z

d↓(x+iy)z

p↓z

++--

-

S.O.

S.O.

E

absorption spectrum +

↓

↓↑

↑

ESO

ESO

EEx

EF

Figure 2.6: Microscopic origin of the magneto-optical Kerr effect in ferromagnets. The d energy levels

split due to exchange mechanism (EEx) and the spin-orbit coupling (ESO). On the left, the

optical dipole transitions for right- (+) and left- (-) circularly polarized light are depicted.

The corresponding absorption spectra versus photon energy are sketched on the right.

circularly polarized light they are given by [43]

Δl = ±1 Δm = ±1. (2.18)

The resulting transitions and the absorption spectra are depicted in Fig. 2.6. For

right-circularly (+) polarized light transitions from d(x−iy)z to pz are allowed, whereas left-

circularly (-) polarized light can excite electrons from d(x+iy)z to pz. During the transition,

the spin is conserved. Evidently, the absorption spectra is different for left- and right-

circularly polarized light. Thus, linearly polarized light, which is a superposition of

(+) and (-) circularly polarized light, is transformed into elliptically polarized light. In

addition, it can be shown that the different absorption behavior for (+) and (-) circularly

polarized light causes a phase shift between the two components [40]. This phase shift is

the origin of the Kerr rotation.

Of course, the absorption spectra drawn in Fig. 2.6 are exaggerated and in reality the

absorption curves for (+) and (-) are broader and they overlap. However, with the help

of this simple picture it is pointed out that the Kerr effect in ferromagnets arise from the

simultaneous occurrence of exchange splitting and spin-orbit coupling.

2.3.3 Macroscopic Description

Macroscopically the interaction of light with solids is determined by the complex index

of refraction n = nR+ inI. The index of refraction is connected with the dielectric tensor "


and the permeability tensor by n2 = " ⋅ . In the optical regime, the permeability tensor

can be set equal to one [44] and thus the index of refraction yields:

n2 = " (2.19)

For isotropic media and in absence of external fields, the diagonal elements of " are

identical and the off-diagonal elements are zero [44]. If the media is magnetized, how-

ever, the dielectric tensor yields asymmetric off-diagonal elements. Classically, " can be

calculated assuming a Lorentz-oscillator model [39, 45]. For a cubic material neglecting

higher order terms it is given by [5, 39]

" = "

⎛⎜⎜⎝

1 −iQmz iQmy

iQmz 1 −iQmx

−iQmy iQmx 1

⎞⎟⎟⎠

, mi =Mi

∣M∣, i ∈ x,y, z (2.20)

where mi denotes the projections of the components of M along the x, y and z direction

(direction cosines). " is the dielectric constant in absence of a magnetization. The

material constant Q is the so-called Voigt or magneto-optical constant.

Inserting " into Eq. (2.19) yields the index of refraction. The calculation involves

Maxwell’s equations with proper boundary conditions and can be found in [42, 46]. Two

solutions, n(+) and n(−), are obtained for right- and left-circularly polarized light, respec-

tively. In linear approximation they are given by [47]

n(±) ≈√"(1 ±

1

2Qk ⋅m) , (2.21)

where k is the unit vector along the propagation direction of the dielectric displacement

vector D. Exhibiting two different indices of refraction, the material is birefringent in

presence of a magnetization.

From this matter of fact, two consequences can be deduced. First, birefringence usually

results in different propagation velocities for (+) and (-) circularly polarized light [44] in

the medium. This effect is called linear magnetic birefringence and it causes the charac-

teristic rotation of the polarization plane of the incident light [47]. Second, the indices of

refraction are complex (Q is generally complex) and thus the media absorbs electromag-

netic radiation. However, usually the imaginary parts of n(+) and n(−) differ [47] which

results in a different absorption behavior for (+) and (-) polarized light. Hence, linearly

polarized light is transformed into an elliptical state of polarization. This transformation

is denoted as magnetic dichroism.

As the magneto-optical Kerr effect arises from the interaction of light with a magnetic

material, its information depth is restricted by the penetration depth of light in the probed

medium. In metals, information depths of about 20 nm have been reported [48, 49]. As a

consequence, magnetic properties of surfaces of bulk samples as well as of thin films can

be investigated by the Kerr effect.


M M

M

polar longitudinal transversal

(a) (b) (c)

Figure 2.7: Illustration of the Kerr effect geometries with respect to the plane of incidence. (a) The

magnetization is oriented perpendicular to the sample surface which is referred to as the

polar Kerr effect. (b) The magnetization is parallel to the the sample surface and parallel to

the plane of incidence causing the longitudinal Kerr effect. (c) In the transversal geometry

the magnetization is within the film plane but perpendicular to the plane of incidence.

2.3.4 Quantitative Formulation

So far, qualitative aspects of the Kerr effect have been discussed. This section is dedicated

to the presentation of quantitative expressions for the complex Kerr rotation Ψk. At

first, one distinguishes between three different effects depending on the orientation of

the magnetization with respect to the sample surface and the plane of incidence. The

resulting geometries are depicted in Fig. 2.7. The polar effect is characterized by an

out-of-plane magnetization direction (cf. Fig. 2.7(a)). In the longitudinal geometry the

magnetization is oriented within the film plane and parallel to the plane of incidence as

displayed in Fig. 2.7(b). In contrast, if the magnetization is oriented perpendicular to

the plane of incidence in Fig. 2.7(c), the transversal Kerr effect occurs.

For the following analysis, the electric field of the incident and reflected light is split

into two components E = Ess+Epp. Es denotes the component perpendicular to the plane

of incidence (s-polarized), Ep denotes the component parallel to the plane of incidence

(p-polarized). The electric field after the reflection off the sample surface is denoted as

E′. Reflection of electromagnetic waves at surfaces and interfaces can be described by the

Fresnel coefficients, which are denoted rss, rsp, rps, rpp [44]. Therefore E′ can be calculated

with the help of the reflection matrix R as

(E′

s

E′

p

) = (rss rsp

rps rpp)(

Es

Ep) . (2.22)

The complex Kerr rotation is determined by the amplitude ratio Ψk = E′

p/E′

s [50, 51].

For s-polarized light (Ep = 0) it simplifies to Ψsk = rps/rss, for p-polarized light (Es = 0) the

complex Kerr rotation yields Ψpk = rsp/rpp assuming small angles in both cases [42, 47].

The Fresnel coefficients occurring in this scattering matrix are tabulated [42, 52, 53].

However, for an individual analysis of the different Kerr effect geometries, it is more

convenient to express R in terms of rp, rl, rz, which denote the scattering matrices for the


polar, longitudinal and transversal geometry. Thus the reflection matrix can be rewritten

as [52, 53]

R =m2pr

p [Q/mp] +m2l r

l [Q/ml] +m2t t

t [Q/mt] . (2.23)

The square brackets imply that Q has to be replaced by Q/mi with (i ∈ p, l, t)

in the individual scattering matrices. mp, ml, mt again denote the projections of the

magnetization onto the corresponding axes and they yield m2p +m

2l +m

2t = 1.

For the polar Kerr effect the components of rp are given by [52, 53, 54]

rpss =

n1 cos 1 − n2 cos 2

n1 cos 1 + n2 cos 2

(2.24)

rppp =


n2 cos 1 + n1 cos 2

(2.25)

rpsp = r

pps =

in1n2Q cos 1

(n1 cos 1 + n2 cos 2)(n2 cos 1 + n1 cos 2), (2.26)

where n1 and n2 are the complex indices of refraction (for the magnetic material the

index of refraction is approximated by n2 ≈√" [42]) and 1, 2 denote the incident and

refracted angles according to the law of Snellius. Hence, the Kerr rotation arising from

the polar magnetization component can be calculated for s- and p-polarized light as

Ψs,polark =

rpps

rpss=

in1n2Q cos 1

(n2 cos 1 + n1 cos 2)(n1 cos 1 − n2 cos 2)(2.27)

Ψp,polark =

rpsp

rppp

=in1n2Q cos 1

(n1 cos 1 + n2 cos 2)(n2 cos 1 − n1 cos 2). (2.28)

Consequently, the largest Kerr rotation in both cases is obtained for 1 = 0°, which

corresponds to perpendicular light incidence.

For the longitudinal Kerr effect, the Fresnel coefficients of rl are tabulated as [50, 52, 53]

rlss =


n1 cos 1 + n2 cos 2

(2.29)

rlpp =


n2 cos 1 + n1 cos 2

(2.30)

rlsp = −r

lps =

in1n2Q cos 1 tan 2

(n1 cos 1 + n2 cos 2)(n2 cos 1 + n1 cos 2), (2.31)

and the Kerr rotation follows as


Ψs,longk =

rlps

rlss

= −in1n2Q cos 1 tan 2

(n2 cos 1 + n1 cos 2)(n1 cos 1 − n2 cos 2)(2.32)

Ψp,longk =

rlsp

rlss

=in1n2Q cos 1 tan 2

(n1 cos 1 + n2 cos 2)(n2 cos 1 − n1 cos 2). (2.33)

In contrast to the polar effect, the angle 2 appears in the denominator of the Kerr

rotation in the longitudinal geometry. As a consequence, at perpendicular light incidence

(1 = 2 = 0°), the Kerr rotation vanishes. The maximum Kerr rotation is obtained at an

angle of incidence 0° < 1° < 90°, depending on the angle of refraction 2. Comparing the

Kerr rotation of longitudinal and polar effect, the longitudinal Kerr rotation is smaller

by an order of magnitude than the polar one because of the additional tan 2 term in the

denominator.

At last, the Fresnel coefficients of the scattering matrix for the transversal geometry rt

are [52, 53, 54]

rtss =


n1 cos 1 + n2 cos 2

(2.34)

rtpp =


n2 cos 1 + n1 cos 2

+ i2n1n2Q cos 1 sin 2

(n2 cos 1 + n1 cos 2)2 (2.35)

rtsp = r

tps = 0. (2.36)

The off-diagonal elements of the scattering matrix for the transversal geometry are zero

and thus the transversal magnetization component does not cause a Kerr rotation of the

incident light. However, the amplitude of the p-polarized light upon reflection depends

on Q. Therefore the intensity change of p-polarized light in the transversal geometry is

a direct measure for the Voigt constant Q.

2.3.5 Detection

Having introduced the scattering matrices in the last paragraph, this section finally deals

with the detection of the magneto-optical Kerr effect. As already mentioned, the Kerr

effect induces a rotation of the polarization plane of the incident light and it also trans-

forms linearly polarized light into elliptically polarized light. In order to measure this

effect, one has to introduce simple polarization optics as depicted in Fig. 2.8. A polarizer

is placed into the illumination path before the sample to polarize the light linearly along

its transmission axes. The orientation of the polarizer is defined by the angle 'p with

respect to the plane of incidence. The reflected light is probed by an analyzer with the

orientation of the transmission axis defined by 'a. This setup allows to measure the real

Kerr rotation 'k only, the ellipticity k is not considered. Inserting a quarter-wave plate


Ml

Mt

s

p

yayp

polarizer analyzer

sample

Figure 2.8: Basic measurement principle and setup of the polarization components for MOKE. The

angles 'p and 'a define the transmission axis of the polarizer and analyzer with respect to

the plane of incidence.

results in a removal of the ellipticity and will be discussed in Chapter 4. The electric field

after transmission through the polarizer and incident upon the ferromagnetic film can be

expressed as

E = E0 sin'ps +E0 cos'pp. (2.37)

The interaction of the electric field with the ferromagnet is governed by the scattering

matrix introduced in Eq. (2.23). Assuming that the magnetization has only components

within the film plane Ml and Mt (cf. Section 2.1.1), the scattering matrix simplifies to

[55]

R =m2l r

l [Q/ml] +m2pt

t [Q/mt] . (2.38)

After the reflection off the sample surface the components of the electric field E′ are

given by [45, 55]

E′

s =m2l r

lspE0 cos'p + r

lssE0 sin'p (2.39)

E′

p = (m2tr

tpp +m

2l r

lpp)E0 cos'p +m

2l r

lpsE0 sin'p.

The reflected light travels to the analyzer where only the component parallel to the

analyzer transmission axis will pass. The electric field component E′′ along the analyzer

transmission axis can be calculated as

E′′ = E′

s sin'a +E′

p cos'a. (2.40)

Inserting the expressions obtained in Eq. (2.39), E′′ is finally determined as [45, 55]


E′′ = E0 m2l r

lps sin('p − 'a) + r

lss sin'p sin'a + (m2

trtpp +m

2l r

lpp) cos'p cos'a . (2.41)

The final intensity is the absolute value of the electric field calculated in Eq. (2.41) and

it is proportional to the measured signal at the detector. Analyzing the above expression,

it contains terms with the longitudinal magnetization component as well as with the

transversal magnetization component. However, if the orientation of the polarizer is

chosen such that it transmits s-polarized light only ('p = 90°), terms containing mt drop

out and the final intensity just depends on ml [45, 55]:

I/I0 = ∣rlss∣

2sin2'a + ∣m2

l rlps∣

2cos2'a + [rl

ssm2l r

l∗ps + r

l∗ssm

2l r

lps] sin'a cos'a. (2.42)

The ∗ in Eq. (2.42) denotes the complex conjugate.

In summary, the main result of the analysis above is that the resulting signal de-

pends only upon the longitudinal magnetization component if the polarizer angle is set

to 'p = 90°. Thus, using s-polarized incident light enables the measurement of the lon-

gitudinal magnetization component. In the experiments performed during this thesis

s-polarized incident light has been used exclusively.

Chapter 3

Materials

In the previous chapter the physical principles of ferromagnetism, ferroelectricity and

magneto-optic effects have been introduced. This chapter deals with the most relevant

properties concerning the materials that have been used in the framework of this thesis.

Firstly, nickel and iron cobalt will be introduced as the ferromagnetic constituents before

the basic properties of the piezoelectric materials lead zirconate titanate, barium titanate

and lithium niobate will be summarized.

3.1 Ferromagnetic Materials

The performance of the prepared hybrid structures is greatly influenced by the choice

of the ferromagnetic material. As the interplay between the ferroelectric phase and the

ferromagnetic phase is governed by the magnetoelastic coupling coefficient of the ferro-

magnet, this parameter is of great importance for successful magnetization control by

means of electric fields. The 3d-transition element nickel (Ni) and the binary alloy iron-

cobalt (Fe50Co50) have been chosen as the ferromagnetic constituents for the prepared

hybrid structures. In the following their most relevant physical properties, saturation

magnetization Ms, magnetostrictive constants 100, 110, and elastic moduli c11, c12

will be given. The magnetostrictive constants ijk describe the maximal elongation or

contraction = 23l/l of the ferromagnet in the direction [ijk] of the external magnetic

field upon magnetization from the demagnetized state to saturation [31] for cubic ma-

terials. For this thesis only polycrystalline ferromagnetic films have been prepared. In

this case, the magnetostrictive constant can be averaged as = 25100 +

35110 [31]. The

elastic moduli represent the stress per strain ratio cij =i"j

of the corresponding material

according to Hooke’s law [38].

3.1.1 Nickel

Nickel is a very common ferromagnet that most people have encountered in form of coins

in everyday life. It has a fairly high Curie temperature of TNi = 627 K [56] and crys-

tallizes in the face-centered-cubic (fcc) structure with room temperature lattice constant

21

22 Chapter 3 Materials

Material 100 × 106 110 × 106 × 106 c11 − c12 (1011 N/m2)

Ni −45.9 −24.3 −32.9 0.9Fe50Co50 119.3 41.3 72.5 1.2

Table 3.1: Magnetoelastic constants for bulk Ni taken from [59] and Fe50Co50 [31, 60] at room temper-

ature.

aNi = 3.524 A [57]. The bulk saturation magnetization of Ni is Ms = 411 kA/m [58]. Its

bulk magnetoelastic constants can be found in Tab. 3.1.

3.1.2 Iron-Cobalt

The equiatomic iron-cobalt alloy (Fe50Co50), also known as permendur, has been used as

ferromagnetic constituent apart from nickel. At room temperature, it crystallizes in the

body-centered-cubic (bcc) structure [61] with lattice parameter aFeCo = 2.849 A [62]. Due

to its large saturation magnetization of Ms = 1950 kA/m [26], permendur is often used

in transformers or generators when a high flux density is needed. Its Curie point is at

TNi ≈ 1200 K [63]. The magnetoelastic constants are given in Tab. 3.1.

3.2 Piezoelectric Materials

Apart from the ferromagnetic material, the piezoelectric constituent also plays a decisive

role for successful magnetization control in multifunctional hybrid structures. Therefore

three different possible candidates have been used in this thesis: lead zirconate titanate,

barium titanate, lithium niobate. Especially their converse piezoelectric response upon

the application of electric fields is of relevance for this work. In the following the used

materials will be introduced briefly.

3.2.1 Lead Zirconate Titanate

Lead zirconate titanate (Pb [ZrxTi1−x]O3, 0 < x < 1), abbreviated as PZT, is a ferro-

electric material which is commonly used in electroceramics or piezoelectric devices. For

x < 0.5, the ferroelectric phase crystallizes in the perovskite structure with a tetragonal

unit cell in analogy to barium titanate (cf. Fig. 3.1). For smaller portions of titanium

the rhombohedral unit cell predominates [64]. The Curie temperature ranges within

Tc(x = 0) = 500 K and Tc(x = 1) = 250 K also depending on the portion of titanium. The

ferroelectricity below the Curie point arises from the spontaneous displacement of the

Ti4+/Zr4+-ion out of the symmetry center of the unit cell.

In the framework of this thesis, two types of commercially available piezoelectric ac-

tuators made from PZT ceramics have been used. First, PSt 150/2×3/5 actuators [65]

3.2 Piezoelectric Materials 23

Material d31 (10−12 C/N) d33 (10−12 C/N)

PZT (PSt 150/2×3/5) −290 640PZT (PZT-5H) −274 593BaTiO3 −33.4 90LiNbO3 −0.9 6.0

Table 3.2: Piezoelectric coefficients of PZT ceramics (in PSt 150/2×3/5 stacked actuators [65] and PZT-

5H piezoelectric plates [66]), single crystal BaTiO3 [67] and single crystal LiNbO3 [68] at

room temperature.

T ≥ Tc T1 < T < Tc

Ba2+

O2-

Ti4+

Ps ≠ 0Ps = 0

cubic tetragonal

6 possibledirections of Ti4+

displacement

a a

a c

Figure 3.1: Illustration of the cubic and tetragonal unit cell of BaTiO3. The spontaneous polarization

is caused by the displacement of the Ti4+ ion [34].

built from stacks of PZT have been applied (cf. Chapter 5). In addition, PZT-5H piezo-

electric plates [66] have been used (cf. Chapter 6). The piezoelectric properties of the

ceramics employed in these particular actuators have been summarized in Tab. 3.2. In

the conventional mode of operation, both types of piezoelectric actuators rely on the d33-

and the d31-effect (cf. Chapter 2).

3.2.2 Barium Titanate

Barium titanate (BaTiO3) is a ferroelectric ceramic which is often used in dielectric

capacitors because of its relatively large relative permittivity of "/"0 ≈ 4100 [69] at room

temperature. It exhibits several crystalline phase transitions at distinct temperatures

[70]. Above the Curie temperature of Tc = 393 K [71] BaTiO3 is in the paraelectric

state with a cubic crystalline structure. Upon cooling below the Curie point it becomes

ferroelectric. At room temperature, the underlying crystal structure is tetragonal with

the corresponding lattice parameters a = b = 0.3993 nm and c = 0.4034 nm [72]. BaTiO3

24 Chapter 3 Materials

E=0

E>Ec

90° domain walls 180° domain wall

P

P=0c

c

a

(a)

(b)

Figure 3.2: (a) Schematic illustration of the multi-domain state in BaTiO3 in absence of an electric field.

The a-domains are tilted with respect to the orientation of the c-domains. (b) Application

of an electric field results in the formation of a single domain state [34, 73].

crystallizes in the perovskite structure with a unit cell as depicted in Fig. 3.1 for the

cubic and tetragonal phase. The ferroelectricity in the tetragonal phase results from the

displacement of the Ti4+-ion from its central position. BaTiO3 exhibits further phase

transitions at lower temperatures, but those are omitted since they are not of relevance

for the experiments in this thesis, which were all done at room temperature. Crystalline

BaTiO3 is chosen as substrate material because it has a relatively large piezoelectric

coefficient as given in Tab. 3.2.

The substructure of BaTiO3 in the tetragonal phase is dominated by ferroelectric do-

mains. The displacement of the Ti4+-ion out of the symmetry center can be along six

directions. As always two of these directions are equivalent by crystal symmetry, this

behavior gives rise to the formation of three sorts of domains at room temperature:

• c-domains with polar axis along (001)

• a1-domains with polar axis along (100)

• a2-domains with polar axis along (010)

In absence of external electric fields, the crystal resides in an equilibrium multidomain

state consisting of a- and c-domains as depicted in Fig. 3.2(a) [71]. The domains are

separated by 180° and 90° domain walls. Since the lattice parameters a and c are different,

the a-domains are tilted with respect to the orientation of the c-domains. Upon the

application of an external electric field with E > Ec the crystal enters a single domain

state as schematically depicted for the (001) direction in Fig. 3.2(b) [34, 73].

3.2 Piezoelectric Materials 25

3.2.3 Lithium Niobate

Lithium niobate (LiNbO3) is of central importance in integrated and guided wave optics

as well as in filter devices and resonators [74]. Below its ferroelectric Curie temperature

of Tc = 1483 K LiNbO3 crystallizes in a distorted hexagonal close-packed configuration

[74]. Table 3.2 lists the piezoelectric coefficient relevant for this thesis. In contrast to

PZT and BaTiO3, LiNbO3 is a pyroelectric material. Thus, the spontaneous polarization

cannot be reversed by external electric fields [75].

Chapter 4

Magneto-Optical Kerr Effect with

Spatial Resolution

The establishment of spatially resolved magneto-optical Kerr imaging was a substantial

aim of this thesis, since it offers a powerful tool to investigate magnetic microstructure.

Therefore an existing magneto-optical setup [45] was extended to allow for spatial reso-

lution. In the following an overview of the new Kerr imaging setup and its components

is given. Moreover, a characterization of the system’s resolution and sensitivity is shown.

At last the results of Kerr imaging on thin ferromagnetic (FM) films are presented and

the possibility of quantitative Kerr microscopy is discussed in brief.

4.1 The Existing Experimental Setup

In Fig. 4.1 a schematic drawing of a conventional Kerr setup can be seen. Such a system

has been built up at the WMI by M. Pelkner [45]. The basic features of this experimental

setup is reviewed in this section before turning to Kerr effect measurements with spatial

resolution. In the existing experimental configuration the longitudinal as well as the polar

Kerr effect can be recorded. The transverse Kerr effect, however, cannot be monitored

since the magnetic field cannot be applied perpendicular to the plane of incidence in

the current setup. For the purpose of this thesis the longitudinal configuration is usually

desired and therefore the angle of light incidence is chosen to be 40°, which is the maximum

angle allowed by the setup geometry and has proven to give the best results in terms of

sensitivity of all allowed incident angles [45]. The basic components of the conventional

Kerr setup are:

• Light source

As light source a AlGaInP semiconductor diode is used. It emits coherent light

with a characteristic wavelength of 670 nm and power of 7 mW.

• Polarizers

The polarizers are Glan-Thompson polarizers made of calcite. Glan Thompson

polarizers assure a very high extinction ratio of " = 10−6, which is fundamental

27

28 Chapter 4 Magneto-Optical Kerr Effect with Spatial Resolution

sample

electromagnet

polarizer analyzer

objective lens

focusing lens

light source detector

Figure 4.1: Experimental setup for basic Kerr effect measurements.

to achieve good contrast conditions in Kerr microscopy as will be discussed in

Section 4.5.2.

• Electromagnet

The electromagnet consists of two coils which are mounted onto an iron yoke and

connected in series. It allows the application of a magnetic field along one direction.

The power supply is a bipolar Bob 20-20 manufactured by Kepco.

• Hall probe

To measure the magnetic field a Hall probe of the type 475 DSP fabricated by

Lakeshore is used. An analog output enables to control the power supply of the

electromagnet and thus a very exact magnetic field adjustment is possible.

• Detector

Light detection is carried out by a Si - photo diode with integrated signal amplifi-

cation. The active area of the diode has a diameter of 2.5 mm.

4.2 Kerr Microscopy

In the original Kerr setup presented above, lenses were used to focus the laser light onto

the sample collimating the laser spot to a diameter of about 0.5 mm on the sample

surface. Thus the region probed was quite small and no information about the spatial

arrangement of magnetic domains was retrieved. But in addition to that, the magneto-

optical Kerr effect allows to go beyond and visualize magnetic domain structures with

microscopy techniques [76]. This can be achieved with a Kerr microscope. During this

4.2 Kerr Microscopy 29

LED

CCD camera

objective lens

analyzerquarter wave plate

polarizer

slit aperture

Hall probe

electromagnetsample holder

Figure 4.2: Photograph of the Kerr microscopy setup which was built up during this thesis.

thesis the existing experimental setup was partly redesigned and extended to enable

spatial resolution. Therefore some major modifications had to be made, as depicted in

Fig. 4.2.

Detector

At first the detector had to be exchanged and a Luca (S) EMCCD (Electron Multiplying

Charged Coupled Device) camera manufactured by Andor was installed. The camera

has 658 × 496 active pixels with a size of 10 µm × 10 µm resulting in an image area of

6.58 mm × 4.96 mm. Each pixel has a bit depth of 14 and the maximum read out rate

is 27 frames per second. The camera is fan-cooled and the active sensor is additionally

cooled by a Peltier element to reduce readout noise. It is connected via USB 2.0 and

can be controlled with LabVIEW during measurements. Long- and short-pass filters

are mounted onto the camera in order to absorb light of a wavelength < 600 nm and

> 665 nm, respectively. Thus, noise arising from stray light falling onto the camera

sensor is minimized.

Light source

Secondly the laser diode had to be replaced by a LED (Light Emitting Diode). The

problem with laser illumination in microscopy and imaging is its coherence resulting in

strong interference fringes and speckle. Even digital image subtraction cannot remove

this problem, since the necessary stability of all components is not given. Consequently a

high power LED, Luxeon LXHL-LD3C fabricated by Lumitronix is used. The electrical


lensLED

Figure 4.3: Photograph of the mounted LED and the focusing lens.

power is 3 W and the luminous flux is specified as 90 − 140 lm, which is equivalent to

a radiometric power of around 0.5 − 0.8 W. The LED emits red light with a dominant

wavelength of = 627 nm a spectral half-width of Δ = 20 nm. The angle of radiation

is 130°. To ensure thermal stability the LED is mounted onto an aluminum block (cf.

Fig. 4.3).

A focusing lens is directly placed and mounted on top of the diode to collimate the

light to a radiation angle of around 3°. In order to prevent the emission of stray light,

an aluminum tube covers the diode and lens. Replacing the laser diode with a LED is

advantageous, because it emits incoherent light. However, the collimation of the emitted

light in the current setup is not perfect and thus the light intensity is certainly lower com-

pared to laser illumination. However, further improvements in the illumination including

improved collimation are currently under way.

Slit aperture

Between LED and polarizer a slit aperture is placed in the illumination path (cf. Fig. 4.2).

A correct illumination aperture is important in Kerr microscopy, since too small apertures

result in disturbing diffraction fringes [5]. However, a large aperture causes light beams

to hit the polarizers at small angles which are not lying in the plane of incidence. The

consequence is an increased background intensity due to depolarization effects and thus

the magneto-optical contrast is reduced [5, 77]. Therefore, the slit aperture should be

oriented parallel to the plane of incidence for the longitudinal Kerr effect. The home-

built slit aperture integrated in the Kerr setup allows to adjust the slit size for optimal

illumination and contrast conditions.

4.3 Image Processing 31

Quarter wave plate

A rotatable achromatic quarter wave plate manufactured by Thorlabs is placed between

the sample and the analyzer in the illumination path. The wavelength bandwidth goes

from 450 nm to 800 nm. The ellipticity of the reflected light can be removed by proper

adjustment of the wave plate which finally improves the imaging contrast (cf. Section 4.5).

LabVIEW measurement program

The imaging experiments are automated with LabVIEW measurement software. The

central LabVIEW program developed in the framework of this thesis “MOKELuca.vi”

synchronizes all measurement devices and contains the camera readout and data handling.

Moreover, programs for image post-processing, e.g. contrast enhancement, have been

implemented.

Adjustment procedure

The proper adjustment of all components is of great importance for good contrast con-

ditions. At first the slit aperture should be placed properly in order to assure a homoge-

neous illumination of the sample. Moreover a good focus of the sample onto the camera

is necessary and is achieved by careful adjustment of lens and camera positions. The

objective lens can be tilted to reduce the image distortion arising from the oblique light

incidence [5]. The polarizer is placed such that the transmission axis is perpendicular to

the plane of incidence (s-polarized) to be sensitive only on the longitudinal component

of the magnetization as discussed in Chapter 2. The quarter wave plate and the analyzer

are then iteratively adjusted to achieve extinction before opening the analyzer by the

desired angle (cf. Section 4.5).

4.3 Image Processing

Digital image processing and contrast enhancement techniques are a substantial tool to

visualize magnetic domains. The detection of magnetic microstructure in a recorded

raw image without digital image processing is difficult (cf. Fig. 4.4(a)). At first, the

probed material has to exhibit an as large as possible Kerr rotation in order to obtain

strong contrast between domains of opposite magnetization direction. Moreover surface

imperfections and irregularities can produce a non-magnetic contrast which is then su-

perimposed with the desired magnetic contrast. At last, the illumination should be very

homogeneous within the field of view to assure good visibility. In sum, these issues impede

direct detection of magnetic domains.

In order to reduce those problems the technique of difference imaging was proposed

[7, 8, 78]. The standard procedure is to subtract two images digitally to obtain a resulting

image containing only contrast of magnetic origin. Therefore, an image of the sample


1 mm

(a) (b)

Figure 4.4: Domain pattern of a polycrystalline Co thin film before (a) and after digital contrast en-

hancement (b).

in a magnetically saturated state is acquired and stored in memory as reference. Then

this reference image is subtracted from images taken at other magnetic field strengths.

Ideally the resulting difference image contains only contrast which is truly of magnetic

origin.

In Fig. 4.4 a real image and a difference image of the same domain pattern are de-

picted. On the one hand a very weak domain pattern can be seen in the real image (cf.

Fig. 4.4(a)). The contrast between the domains of opposite magnetization is very weak.

The illumination of the sample is also not perfectly homogeneous and small speckle exist.

On the other hand the difference image (cf. Fig. 4.4(b)) displays a very clear domain

pattern. The contrast between black and white domains has improved significantly. Fur-

thermore the imaging problems with speckle are reduced. The whole process of image

subtraction is done in real time in the LabVIEW measurement program in order to di-

rectly observe the domain structure. Finally the difference image is saved and can then

be edited by another LabVIEW program or a commercial image processing software for

further contrast enhancement. It should be mentioned that the time between the acqui-

sition of the reference image and the acquisition of the image with the desired domain

pattern should not be too large. Drift effects, caused for instance by thermal fluctuations,

can have a negative influence on the visibility of domains.

4.4 Resolution 33

a

D

sample lens camera

g b

Figure 4.5: Schematic drawing of the imaging setup.

4.4 Resolution

The resolution is a crucial quantity in imaging and microscopy experiments. Therefore,

a short estimation of the resolution of the established Kerr imaging setup is given. Here

the resolution depends primarily on the imaging components, the system geometry and

the quality of the detector. Simple wide angle objective lenses image the sample onto

the CCD camera as seen schematically in Fig. 4.5. In the thin lens approximation the

imaging can be described by [44]

1

f=

1

g+

1

b, (4.1)

where f is the focal width of the lens, g and b the distance from sample to lens and from

lens to detector, respectively. The achievable magnification is limited by the geometry of

the setup, since the minimum distance from object to lens is about 15 cm. Usually the

objective lens and CCD are adjusted to have transverse magnifications between one to

three. In this configuration decent contrast and brightness conditions are given. Then,

assuming a transverse magnification of three and considering the pixel size of 10 µm ×

10 µm, a nominal resolution of around 3 µm can be achieved. But so far the wave nature

of light and the phenomenon of diffraction was neglected. The diffraction-limited spatial

resolution of a microscope is governed by [44]

dmin = 0.61 ⋅

NA, (4.2)

where dmin is the minimum distance between two points on the sample that can be

resolved. NA is the numerical aperture which is defined as NA = n ⋅ sin with the index

of refraction n = 1 for air and the angle as defined in Fig. 4.5. Assuming a lens radius

of D2 = 1 cm and a working distance of g = 20 cm the numerical aperture is approximately

given by NA ≈ 5 ⋅ 10−2. Inserting the wavelength = 627 nm you obtain a minimum


distance of dmin ≈ 8 µm and thus a lower resolution than the nominal resolution calculated

above. This reveals that our experimental setup is limited by the achievable numerical

aperture. In reality the resolution is probably even worse, since this consideration holds

only true for ideal imaging. No interfering effects like aberrations in the tilted objective

lens have been taken into consideration. Thus the current setup is capable of doing low

resolution Kerr microscopy [5] with a magnification of order 1.

Higher resolutions could be achieved by using a microscope objective and an eyepiece

instead of the objective lens. Especially a smaller working distance allowing the usage of

microscope objectives should be accompanied by a major improvement in resolution. But

this feature was not realized during this thesis since a total redesign of the experimental

setup would have been necessary. We therefore refrained from aiming at huge spatial

resolution and rather focused on the modifications described above, as the typical samples

studied had lateral dimensions of the order of mm. State of the are high resolution Kerr

microscopes are usually based on conventional polarization microscopes and in principle

they can achieve resolutions up to the limit of optical microscopy [79].

4.5 Characterization

There are many parameters in image recording devices that influence the quality of light

detection and the resulting image. Specifically in Kerr microscopy a large contrast be-

tween domains of opposite magnetization direction (black and white domains) is neces-

sary to visualize domain patterns. Usually the limiting factor is noise. Therefore, a short

overview of noise sources and a characterization of the setup is given.

4.5.1 CCD Noise and Signal-to-Noise Ratio

At first some basics of CCD camera noise are reviewed. The signal-to-noise ratio S/N is

determined by the ratio of the generated signal electrons to the number of noise electrons.

The signal S depends upon the number of photons Np impacting onto a camera pixel

during the exposure time and upon the quantum efficiency of the device:

S = Np ⋅ (4.3)

Regarding noise in light detection, there are three major sources that contribute to the

system noise [80]:

• Dark noise Ndark arises from thermally generated charges in the sensor. This noise

component can be reduced by cooling down the light sensor. Our CCD camera is

cooled to −20° C and the nominal dark current is 0.5 e−

s⋅pixel .

• Readout noise Nreadout is an inherent property of the sensor and originates from

the process of amplification and conversion of photoelectrons into a voltage. The

readout noise is specified to be between 1 and 15 e−

s⋅pixel at maximum frame rate.

4.5 Characterization 35

• Photon noise or shot noise Nphoton results from the inherent statistical variation in

the arrival rate of photons incident on the CCD and it follows the Poisson statistics.

Therefore, photon noise can be quantified as Nphoton =√Np ⋅ .

Taking everything into consideration the signal-to-noise ratio can be expressed as fol-

lows [80]:

S

N=

Np ⋅ √N2

photon +N2readout +N

2dark

(4.4)

A comparison of the noise contributions reveals, that shot noise dominates over dark

noise and readout noise.

Dark noise can be estimated as follows: The full well capacity of our CCD camera,

which is the number of electrons that can be held in one potential well of one pixel,

is given by 26000 electrons. Thus the number of counts arising from the nominal dark

current of 0.5 e−

s⋅pixel can be estimated by

Ndark ≈0.5 e−

s⋅pixel

26000 e−

214 counts

≈ 0.03counts

pixel ⋅ s(4.5)

where the dynamic range of 214 counts was inserted.

The maximum readout noise Nreadout can be approximated analogously:

Nreadout ≈15 e−

s⋅pixel

26000 e−

214 counts

≈ 10counts

pixel ⋅ s(4.6)

Shot noise, however, is determined by the number of incident photons and thus by the

number of counts in the end. During operation the number of counts detected by the

CCD is usually around 10000 resulting in a shot noise of

Nphoton ≈√

10000counts

pixel ⋅ s= 100

counts

pixel ⋅ s. (4.7)

This short noise evaluation points out, that signal detection is limited by shot noise

due to the large light intensities [5]. Neglecting dark noise and readout noise, Eq. (4.4)

simplifies to

S

N=√Np ⋅ ∝

√texp ⋅Apixel ⋅ (4.8)

where Apixel is the active pixel area and texp the exposure time [81]. Thus, an increase

in exposure time or pixel size via binning improves the signal-to-noise ratio. The accumu-

lation and averaging of several images per field point is another method of improving the

signal-to-noise characteristics. Of course, the dynamic range of the camera or unwanted

drift effects set limits to long exposure times. Other sources of noise in the imaging


M

s

p

ya

polarizer analyzer

sample

fk-fk

incidentlight

reflectedlight

(a)

- 4 0 - 2 0 0 2 0 4 08 0

8 2

8 4

MOKE

signa

l (arb.

units)

µ0 H ( m T )

S m o

(b)

Figure 4.6: (a) Schematic illustration of polarized light amplitude vectors before and after reflection

from the sample, which is composed of domains with opposite magnetization direction.

Definition of the Kerr angle 'k and the analyzer angle a. (b) Definition of the absolute

magneto-optical signal Smo.

system are fluctuations in the intensity of the light source or in the optical path. Those

noise contributions are not discussed here, since they can be hardly quantified and have

proven not to have substantial influence onto the imaging quality.

4.5.2 Magneto-Optical Contrast

The figure of merit in Kerr microscopy is the magneto-optical contrast. In the preceding

section parameters like exposure time and binning and their effect on the S/N ratio have

already been explained. Albeit the magneto-optical contrast depends also crucially on the

settings of polarizer and analyzer as defined in Fig. 4.6(a). Ideally the polarizer transmits

only s-polarized light. Then the intensity I(±M) of the black and white domains with

respect to the total intensity I0 reflected by the sample is given by the law of Malus

[82, 83]

I(±M) = I0 ⋅ sin2( a ± 'k) + Ir. (4.9)

Ir denotes the non-zero residual transmitted intensity through the analyzer in extinc-

tion, which arises from depolarization effects and finite illumination apertures. a is the

angle of which the analyzer is opened from extinction and 'k stands for the Kerr rotation.

The relative magneto-optical signal smo can be expressed as the difference between the

two intensities I(±M):

smo = I(+M) − I(−M) = I0 sin 2 a sin 2'k (4.10)

In [45, 84] it is is shown how to extract the analyzer angle of optimum signal by

4.5 Characterization 37

minimizing the normalized signal Ik =smo

Iwith respect to a. The resulting analyzer angle

of optimum signal is found to be at 'a =√Ir/I0. However, the best visibility of domains

is rarely given by the criterion of optimum signal as defined above. First, if the analyzer

angle a is too small, the light intensity reaching the camera is not sufficient and domains

will be barely visible. Second, the relative magneto-optical signal increases in first order

with 2a (cf. Eq. (4.9)) which corresponds to an increase of the visible contrast. Third, the

increase in signal is accompanied by an increase in photon noise. All in all, good domain

visibility rather requires a large signal-to-noise ratio. The absolute magneto-optical signal

as seen in Fig. 4.6(b) is given by Smo = A ⋅Np ⋅smo, where A is a constant of proportionality

depending on the quantum efficiency and the amplification and conversion process of the

detected photons [5, 84]. Shot noise is then given by Nphoton =

√12ANp (I(+M) + I(−M)).

Applying Eq. (4.4) in the limit of high light intensities we obtain the following expression

for the Smo/N ratio [5]:

Smo

N=√ANp ⋅

I(+M) − I(−M)√

12 (I(+M) + I(−M))

(4.11)

Inserting Eq. (4.9) and minimizing with respect to a gives [5]

tan opta =

4

¿ÁÁÀ'2

k + Ir/I0

1 + Ir/I0

, (4.12)

where opta denotes the analyzer angle of maximum contrast visibility. Assuming an

extinction ratio of Imin/I0 ≈ 10−6 according to the specifications of the Glan Thompson

polarizers and a Kerr rotation e.g. for Fe50Co50 of 'k ≈ 0.03° [45] the angle of optimal

contrast is given by opta ≈ 1.9°. Although this result can only be a rough estimation, it

points out that the analyzer has to be opened beyond extinction. In reality the extinction

ratio of the polarizers is probably larger because of depolarization effects or imperfections

in the illumination path. Also noise contributions arising from fluctuations in the light

source or in the optical path have not been taken into consideration. In the experiment

the analyzer is usually opened as far as necessary to obtain good imaging results without

being in camera saturation.

An additional element that enhances the magneto-optical contrast is the inserted quar-

ter wave plate. It removes the ellipticity of the reflected light and thus enhances the signal

amplitude. Comparing hysteresis loops obtained on an identical sample with and without

quarter wave plate the magneto-optical contrast doubles (cf. Fig. 4.7) without changing

noise characteristics.

4.5.3 Sensitivity

Having explained the fundamentals of noise and magneto-optical contrast, the sensitivity

of the established Kerr setup regarding the minimal resolvable Kerr rotation is analyzed


- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0- 6

- 3

0

3

6

S m o w i t h o u tλ/ 4 p l a t e

MOKE

signa

l (arb.

units)

µ0 H ( m T )

S m o u s i n gλ/ 4 p l a t e

Figure 4.7: Comparison of the magneto-optical signal obtained by hysteresis measurements with (red

curve) and without (black curve) quarter wave plate.

and compared to the original MOKE setup described in [45]. The procedure is as follows:

First, the signal-to-noise ratio of a single pixel of the CCD camera is extracted. Using this

result, the minimum resolvable Kerr rotation of the Kerr imaging system is approximated.

In magneto-optical Kerr effect measurements the relevant signal is Smo as depicted in

Fig. 4.6(b). Noise, however, sets an ultimate limit on the camera’s sensitivity. The fol-

lowing analysis regarding the camera sensitivity was done using a polycrystalline Ni-film

with a thickness of 100 nm (sample M090224A). A M(H) hysteresis loop was recorded

with an exposure time texp = 1 s, an analyzer angle of a = 2° and four accumulations per

field point. This means, that four single images per field point were taken and averaged.

The resulting M(H) curve of one example pixel can be seen in Fig. 4.8(a).

To determine the signal Smo and the noise N , mean and standard deviation of 45

measurement points on the lower and upper branch of the hysteresis loop were calculated

for this particular pixel. The same evaluation was also done for the sum signal of several

pixels. The calculated signal-to-noise ratios are plotted in Fig. 4.8(b) as a function of the

number of pixels Npixel that were summed. As expected, Smo/N increases with√Npixel.

A function fit (f = Afit

√Npixel) with the fit parameter Afit leads to an average signal-to-

noise ratio per pixel of Afit = S/N ≈ 2. By integrating over many pixels, the total S/N

ratio can be improved notably. For instance, if the signal of all camera pixels (658× 496)

is summed up, the resulting integral signal-to-noise ratio yields S/N ≈ 1140, assuming

a constant signal-to-noise ratio per pixel of 2. Often only small sample regions are of

interest regarding an M(H) characterization. Then, the usual procedure is to define a

region of interest (ROI). Hence, the hysteresis curve M(H) is obtained by integrating

over all pixels which belong to the ROI.

4.6 Imaging of Thin Ferromagnetic Films 39

- 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0

1 2 0

1 2 4

1 2 8MO

KE sig

nal (a

rb. un

its)

µ0 H ( m T )(a)

0 3 0 6 0 9 0 1 2 00

5

1 0

1 5

2 0

2 5

S mo/N

Νp i x e l

m e a s u r e m e n t d a t a f i t d a t a

(b)

Figure 4.8: (a) Signal of a single pixel in a M(H) measurement. (b) Smo/N ratio in dependence of the

number of integrated pixels Npixel. The black curve represents the measured data, the red

curve is a fit curve f = Afit

√Np with fit parameter Afit.

To estimate the minimum Kerr rotation which is resolvable by the novel Kerr setup,

the Kerr rotation of the used Ni-film has to be calculated first. For a wavelength of

= 627 nm, the refractive index of Ni is given by n = 1.98 + i3.74 [85] and the magneto-

optical constant yields Q = 0.0005 − i0.0002 [86]. Applying Eq. (2.32), the real part of

the Kerr rotation is given by ∣'k,Ni∣ ≈ 0.02°. Then, the minimum resolvable Kerr rotation

Δ'k is given by the ratio of 2 ⋅ 'k,Ni and S/N [84]. Inserting S/N = 1140 from above for

an integrally recorded hysteresis loop, the minimum resolution finally yields Δ'k ≈ 0.15′′.

Comparing this sensitivity with the one of the original MOKE setup (Δ'k ≈ 1.8′′ [45]),

the resolution of the novel Kerr imaging setup in terms of the Kerr rotation is superior

by an order of magnitude.

4.6 Imaging of Thin Ferromagnetic Films

In this section imaging experiments on thin ferromagnetic films are presented in order

to visualize the capabilities of the low resolution imaging system. A cobalt (Co) and a

chromium dioxide (CrO2) thin film are chosen as examples. In both cases reference images

at large negative saturation fields were taken and the technique of difference imaging was

applied to obtain optimal magnetic contrast.

Cobalt thin film

A polycrystalline Co thin film (sample M090512A) with a thickness of 50 nm was prepared

on a Silicon (100) oriented substrate by electron beam evaporation at a base pressure of

approximately 1.9×10−7 mbar. The coercive field was determined to be 0Hc = 1.81 mT.


(a) (b)

(c) (d)

(e) (f)

1 mm

Figure 4.9: Domain pattern of a polycrystalline Co thin film at (a) 0H = 1.73 mT, (b) 0H = 1.78 mT,

(c) 0H = 1.81 mT, (d) 0H = 1.83 mT, (e) 0H = 1.86 mT, (f) 0H = 1.91 mT.

4.6 Imaging of Thin Ferromagnetic Films 41

1mm e.a.(a) (b) (c) (d)

Figure 4.10: Domain evolution in an epitaxial CrO2 thin film with a thickness of 200 nm. Domains

nucleate in form of stripes.

The imaging was done with an exposure time of texp = 1 s and one image accumulation

per field point. In Fig. 4.9 the domain pattern is depicted.

In Fig. 4.9(a) and Fig. 4.9(f) the image color is homogeneously dark gray or white,

respectively. Thus the Co thin film is in a single domain state at the corresponding

magnetic fields. In contrast, Fig. 4.9(c)-(e) reveal domain patterns which are called

zigzag walls [5]. This kind of domain wall typically exist in polycrystalline ferromagnetic

films of corresponding thickness. Higher resolution imaging would probably allow to see

the internal structure of the domain wall, which is a cross-tie wall [5].

CrO2

Chromium dioxide is a half-metallic ferromagnet and is a very promising candidate for

spintronic applications because its spin polarization is 100% [87]. The magneto-optic

investigations were done on an epitaxial (110)-oriented CrO2 thin film grown on a titani-

umdioxide substrate (TiO2) with a film thickness of 200 nm. The film was prepared by

chemical vapor deposition of the group of A. Gupta, University of Alabama, Tuscaloosa,

USA. In Fig. 4.10 the evolution of magnetic domains can be seen, with the easy axis

being oriented parallel to the external magnetic field.

Domain wall nucleation and motion dominates the easy axis magnetization reversal,

as already observed in [88]. Stripe-like domains characterize the pattern of the mag-

netic substructure. The formation of stripe domains has also been observed in other

ferromagnetic films [5].


Imag

e inte

nsity

(arb.

units)

M a g n e t i z a t i o n a n g l e

c a l i b r a t i o n

(a) (b)

Figure 4.11: (a) Calibration of image intensities to the corresponding magnetization directions for quan-

titative Kerr microscopy. (b) Domain pattern of a Co thin film quantitatively evaluated.

4.7 Quantitative Kerr Microscopy

So far, the obtained Kerr microscopy images were only analyzed from a qualitative point

of view. Apart from that, it is also possible to do a quantitative determination of mag-

netization directions [89, 90]. The proposed method is based on a combination of the

longitudinal and the transverse Kerr effect and works for thin films where the magne-

tization lies in the film plane. In essence, an identical domain pattern is recorded in

longitudinal and transverse configuration. In addition, calibration experiments for neg-

ative and positive magnetization saturation for both measurement configurations have

to be performed. The information of both effects is then digitally combined. Longitu-

dinal Kerr effect measurements with s-polarized incident light are only sensitive to the

longitudinal component of the magnetization. For a quantification of the longitudinal

component at first two images in negative and positive saturation have to be recorded

and their image intensities serve as calibration measurements (cf. Fig. 4.11(a)). Since

the longitudinal magnetization component is the projection of the total magnetization

onto the longitudinal direction, every color value can be assigned to a longitudinal mag-

netization component by fitting a cosine function to the calibration points. The same

procedure would be necessary for the transverse magnetization component. But in the

current setup no calibration measurement for the transverse Kerr effect can be done, since

the used electromagnet only allows magnetic fields along one direction. Therefore, it is

not possible to determine the transverse magnetization direction quantitatively.

In Fig. 4.11(b) an example for a quantitatively evaluated image obtained by the new

Kerr microscope setup is depicted. Small image regions that have a uniform color are

analyzed and the average image intensity is calculated. Then a magnetization direction

can be assigned. As seen by the color code in Fig. 4.11(b), the transverse direction cannot

4.8 Summary 43

be assigned uniquely. For illustration purposes, one of the two possible magnetization

orientations is chosen as represented by the red arrows.

4.8 Summary

Summing up, spatially resolved magneto-optical Kerr imaging has been established at the

WMI in the framework of this thesis. The new setup allows Kerr imaging with a spatial

resolution on the order of 10 µm and with an integral sensitivity in terms of the Kerr

rotation of about 0.15′′. Therefore, large scale domain patterns of typical ferromagnetic

thin film samples prepared at the WMI can be studied.

Chapter 5

Magneto-Optics on

Ferromagnetic/Ferroelectric Hybrids

The magnetoelastic, magnetoelectric and piezoelectric effect introduced in Chapter 2 can

be used to achieve an electric field control of ferromagnetism. Many different approaches

involving different kinds of ferroelectric and ferromagnetic materials have been proposed

to this end [12, 13, 14, 16, 17]. Among the most promising candidates are novel hybrid

structures consisting of ferroelectric substrates and ferromagnetic thin films [18, 21, 91].

The concept and functionality of these hybrids has already been discussed extensively

elsewhere [19, 20, 34, 92]. However, the magnetic microstructure of the ferromagnetic

constituent has not been subject to any investigation so far. Consequently, the magneto-

optical Kerr setup allowing to resolve local magnetic substructure established in this

thesis (cf. Chapter 4) has been used to study these hybrid structures intensively.

In this chapter ferromagnetic films affixed to ferroelectric substrates are investigated

by means of Kerr microscopy. Hybrids consisting of Ni or Fe50Co50 films deposited onto

piezoelectric actuators are discussed and compared to bilayers of BaTiO3 substrates and

ferromagnetic thin films. In both cases, the voltage dependence of the magnetic hysteresis

and the corresponding domain evolution of the ferromagnetic films shall be studied in

detail. Moreover, experiments demonstrating the magnetization switching induced by

strain are presented.

5.1 Ferromagnetic Thin Films on Piezoelectric Actuators

Polycrystalline Ni thin films on piezoelectric actuators have been studied by means of

ferromagnetic resonance spectroscopy and SQUID magnetometry in [34, 92]. In these

papers it was shown that a rotation of the magnetic easy axis by 90° upon changing the

polarity of the piezo-voltage is possible. Moreover, it was reported that the application

of electric fields allows to switch the magnetization and also to adjust the magnetization

direction reversibly within a range of approximately 70° in nickel thin films.

Following up on these results this section deals with the magneto-optic investigation of

the same kind of hybrid structures. At first, the preparation of the samples is presented

45

46 Chapter 5 Magneto-Optics on Ferromagnetic/Ferroelectric Hybrids

dominantelongationaxis

piezoelectricactuator

FM

Vp

x

y

z glass isolation

electrodes

PZT

(a)

2 mm(b)

Figure 5.1: (a) Schematic view of the prepared samples and illustration of the on stack isolating design of

the actuator. The ferromagnet is deposited onto the face of the actuator [92]. (b) Photograph

of a Ni film cemented onto piezoelectric actuator.

before dealing with measurement results.

5.1.1 Sample Preparation

Commercially available Piezomechanik PSt 150/2×3/5 actuators [65] serve as piezoelectric

substrates. They are built in an on stack isolating design as illustrated in Fig. 5.1(a):

100 µm thick PZT active layers are embedded by metal electrodes with a thickness of

10 µm forming a multilayer structure with dimensions x × y × z = 2 × 3 × 5 mm3. Due to

the interdigitated contact scheme, the direction of the electric field as well as the electric

polarization within adjacent PZT monolayers alternates. The actuator has a nominal

expansion of Δyy = 0.13% along the dominant axis of elongation (d33 effect) in the semi-

bipolar range of −30 V ≤ Vp ≤ +150 V. As shipped, the actuator’s face is covered with a

50 µm thick polymer coating. This coating has to be removed via polishing prior to the

deposition of the ferromagnetic films onto the actuator. Two different techniques have

been used to deposit the ferromagnet onto the actuator.

Evaporation of Ni Thin Films onto Piezoelectric Actuators

Prior to the evaporation process, the coating-free face of the actuator has to be cov-

ered with an isolating PMMA (polymethylmethacrylate) layer. Therefore, PMMA 950K

is spin-coated onto the actuator’s face. After that, the sample is baked at 110° C for

approximately 30 minutes. This process is repeated twice in order to obtain a result-

ing PMMA thickness of approximately 140 nm. Then a polycrystalline Ni thin film is

deposited onto the PMMA covered actuator by electron beam evaporation at a base pres-

sure of around 1×10−7 mbar and with deposition rates of 1−2 A/s. A list of the prepared

samples and further details about material, film thickness and deposition technique can

5.1 Ferromagnetic Thin Films on Piezoelectric Actuators 47

Sample Material Deposition technique Thickness of FM film (nm)

M090213P Ni Direct evaporation 100M090713A Ni Direct evaporation 100M090715A Ni Direct evaporation 120M090220Aa Ni Cementation 50M090220Ac Ni Cementation 50B080623Ad Fe50Co50 Cementation 20

Table 5.1: Overview of prepared samples.

be found in Tab. 5.1.

Cementation of Ni and Fe50Co50 Thin Films onto Actuators

In an alternative preparation procedure ferromagnetic films are first evaporated onto MgO

(100) (magnesium oxide) substrates under the same conditions as described above. After

the evaporation the MgO substrates underneath the ferromagnetic film are polished down

to a thickness of approximately 50 µm and then cemented onto the face of the actuator

using Vishay M-Bond 600 epoxy [30] (cf. Fig. 5.1(b)).

Comparison of the Fabrication Techniques

The evaporation technique yields the advantage that the thickness of the PMMA buffer

layer can be adjusted in such a way that the strain transmission from the substrate onto

the ferromagnet is almost perfect. Moreover, the surface of the PMMA buffer layer is very

flat and smooth which is essential for high quality of the ferromagnetic thin film regarding

its magnetic and optical properties. In contrast, in samples prepared by the cementing

technique, the actual strain onto the MgO is about 70% smaller than the nominal stress

exerted by the actuator [34]. The reduction of strain transmission can be attributed to

the use of epoxy and strain relaxation in the MgO substrate. A further drawback is the

fact that constant thickness and uniformity of the applied epoxy throughout the sample

cannot be guaraneed. Thus the strain transmission might vary across one and the same

sample and it most likely also differs from sample to sample. However, the cementing

technique offers significant advantages compared to the evaporation technique as it allows

to structure well defined Hall-bars into the ferromagnet.

5.1.2 Strain Control of the Magnetic Anisotropy

In this section the phenomenology of strain-induced anisotropy in polycrystalline ferro-

magnetic films on piezoelectric actuators will be reviewed, which has been discussed in

detail in [92]. The free energy density approach introduced in Chapter 2 is applied in


Vp > 0 V

y

x

M

(a)

Vp < 0 V

y

x

M

(b)

Figure 5.2: Deformation of the actuator and attached ferromagnetic film upon applying a voltage

Vp ≠ 0 V. The dotted contours depict the relaxed actuator at Vp = 0 V and the red ar-

row indicates the orientation of the induced easy axis within a Ni thin film. (a) Tensile

strain along y induces a magnetic easy axis along x. (b) Compressive strain along y induces

a magnetic easy axis along y [92].

order to deduce the orientation of the magnetic easy and hard axis upon deformation of

the actuator.

Applying voltages Vp > 0 to the actuator results in an expansion along its dominant

elongation axis y (cf. Fig 5.2(a)). This is accompanied by a contraction along the two

orthogonal axes. Thus tensile strain along y is exerted onto the attached ferromagnetic

film, whereas the strain along x is compressive. In contrast, for Vp < 0 the situation is

inverted as depicted in Fig. 5.2(b). In the following the strains along x, y and z are

expressed as "1, "2 and "3 in Voigt matrix notation [38]. Shear strains can be neglected

since they average out in polycrystalline films. According to elastic theory the strains

along x- and y-axis, "1 and "2, are linked by the Poisson ratio

= −"1

"2

(5.1)

with = 0.45 [65]. The out-of-plain strain "3 is given by [19]

"3 = −c12

c11

("1 + "2) (5.2)

where c11 and c12 are the elastic moduli of the chosen ferromagnetic material (cf.

Chapter 3). The strain "2 along the y-axis can be calculated assuming a linear expansion

of the actuator:

"2 =Δz

z

Vp

180 V(5.3)

According to Eq. (5.1)-(5.3), all strains in the ferromagnetic film can be calculated for


any given piezo-voltage Vp assuming perfect strain transmission through the buffer layer.

In order to determine the equilibrium orientation of the magnetization as a function of

Vp the free energy ansatz introduced in Eq. (2.14) is chosen:

Ftot = Fstat + Fdemag + Fmagel (5.4)

In absence of external magnetic fields, the Zeeman term vanishes leaving the demag-

netization term and the magnetoelastic contribution. For thin films it can be assumed

that the shape anisotropy dominates over the magnetoelastic energy causing the magne-

tization to remain only within the film plane. However, no further anisotropy is induced

by the demagnetization term. Consequently the free energy density simplifies to

Ftot = Fmagel =Kmagel,x sin2 Θ +Kmagel,y cos2 Θ, (5.5)

where the polar coordinates introduced in Fig. 2.2 have been applied considering

Φ = 90°. Inserting the strains calculated above into the expression for Kmagel,x and Kmagel,y

(cf. Eq. (2.16)) and minimizing Eq. (5.5) with respect to Θ yields the orientation of the

magnetically easy and hard axes. The following results have been obtained for Ni [92]

and Fe50Co50, respectively:

• Ni: Applying tensile strain along y (Vp > 0) the easy axis is oriented along x (cf.

Fig. 5.2(a)). For compressive strain along y (Vp < 0) it is aligned parallel to the

y-direction (cf. Fig. 5.2(b)).

• Fe50Co50: Tensile strain along y (Vp > 0) induces an easy axis that is oriented along

y. For compressive strain along y (Vp < 0) the easy axis points along the x-axis.

In sum, the response of the magnetic anisotropy onto the applied strain is opposite in

the two materials. This behavior originates from the opposite sign of the magnetostrictive

coefficients Ni = −32.9⋅10−6 and FeCo = 72.5⋅10−6 (cf. Chapter 3). In the following section

it will be checked whether the theoretical prediction of the easy axis orientation can be

corroborated with magnetic hysteresis measurements at constant strain.

5.1.3 Voltage Dependence of the Magnetic Hysteresis

The influence of strain onto the magnetic hysteresis is analyzed in this section

following [92, 93, 94]. At first, measurements of ferromagnetic films cemented onto ac-

tuators are presented. Then ferromagnets evaporated directly onto actuators are inves-

tigated. All measurements were done with the imaging setup including LED and CCD

camera described in Chapter 4. If not stated otherwise, the hysteresis curves were ob-

tained by integrating over all pixels of the CCD camera (cf. Chapter 4).


-10 -5 0 5 10

-1

0

1

M/M

s

µ0H (mT)

Vp=+150 V Vp=0 V Vp=-30 V

Vp

H||x

Ni

(a)

-40 -20 0 20 40

-1

0

1

M/M

s

µ0H (mT)

Vp=+150 V Vp=0 V Vp=-30 V

Vp

H||y

Fe50Co50

(b)

Figure 5.3: Hysteresis curves at different applied voltages Vp for (a) Ni at H∥x (sample M090220Ac) and

(b) Fe50Co50 at H∥y (sample B080623Ad).

Ferromagnetic Films Cemented onto Piezoelectric Actuator

In Fig. 5.3(a) three M(H) curves of Ni (sample M090220Ac) at different strain states

can be seen. The external magnetic field was prepared at 0H = −60 mT, then swept

to 0H = 60 mT and cycled back to 0H = −60 mT again. It was oriented along the

x-axis (cf. Fig. 5.1(a)). The piezo-voltage remained constant during one sweep. The

three hysteresis measurements were recorded at Vp = −30 V, Vp = 0 V and Vp = +150 V,

respectively.

The hysteresis curves obtained for the Fe50Co50 sample (B080623Ad) are depicted in

Fig. 5.3(b). The magnetostrictive constants of Ni and Fe50Co50 have different signs (cf.

Chapter 3). Therefore, the dependence of the orientation of the easy axis on the applied

strain is inverted in Fe50Co50 compared to Ni as explained above. To allow for a direct

comparison with the hysteresis curves shown for Ni, the results for the Fe50Co50 sample

being rotated by 90° are shown. Thus H pointed along the y-axis. The measurement

procedure was analogous to the Ni sample above.

According to the theory of magnetoelasticity presented above, the magnetic easy axis

should be aligned parallel to the external magnetic field for voltages Vp > 0 in both mate-

rial systems considering their orientation as described above. However, this expectation

cannot be corroborated without ambiguity by the measurement results. Generally, a

rectangular hysteresis loop indicates a magnetic easy axis, whereas a harder axis is char-

acterized by a smooth and S-shaped loop [32]. But the measured hysteresis curves are

equally smooth and S-shaped for both Vp = +150 V and Vp = −30 V. Thus a clear de-

termination of the orientation of hard and easy axes upon applied voltage is not possible

considering the measurement results for Ni and Fe50Co50.


However, the coercive field in both samples is shifted to larger magnetic field values for

Vp = 150 V and to slightly smaller fields for Vp = −30 V compared to the relaxed state for

Vp = 0 V. The absolute difference is approximately 2 mT for Ni as well as for Fe50Co50.

Thus a larger relative shift of the coercive field for different strain states can be observed

in the Ni sample.

Two arguments can be given to support this observation. First, the coercivity can be

calculated for a single domain particle using a Stoner-Wohlfarth approach [32, 95]. In

this simple approximation the coercive field is given by Hc = 3/Ms, where denotes

the applied stress and Ms the saturation magnetization. The magnitudes of the magne-

tostrictive constants can be estimated as ∣FeCo∣ ≈ 2 ⋅ ∣Ni∣ and the values for saturation

magnetization yield MFeCos ≈ 4 ⋅MNi

s (cf. Chapter 3). Assuming that the applied stress

onto Ni and FeCo is the same, the relative shift in the coercive force is expected to be

approximately twice as large for Ni compared to Fe50Co50. Second, Fe50Co50 has a larger

coercive field than Ni and is therefore the harder magnet. As a consequence Fe50Co50

has a larger resistivity against demagnetization caused by external fields or applied strain

than Ni [26].

The results shown above were reproducible and have been observed for all the samples

prepared by the cementing technique. Therefore, the presentation of results obtained

with other samples is omitted.

Ferromagnetic Films Evaporated onto Piezoelectric Actuators

All the samples prepared by direct evaporation showed qualitatively the same results

and therefore the following study is restricted to the results obtained with the sample

M090713A. The corresponding M(H) curve at different strain states can be seen in

Fig. 5.4, with the external magnetic field being aligned along the x-axis. In this sample,

the Vp = +30 V-hysteresis curve is clearly rectangular, whereas for Vp = −30 V the loop

is smooth and S-shaped. According to [32], these results indicate that a magnetic easy

axis is induced parallel to the magnetic field for Vp = +30 V whereas the x-direction

is magnetically harder for Vp = −30 V. This observation is in full agreement with the

theoretical predictions made in Section 5.1.2.

The absolute shift in the coercive field from the Vp = −30 V curve to the Vp = +30 V

curve is about 5 mT and also the magnetic remanence has clearly increased in the same

voltage range.

Comparison

In samples prepared by the cementing technique, the determination of the easy axis

orientation on the basis of the magnetic hysteresis loops at different applied voltages Vp

is difficult. In contrast, the evaporated samples permit a clear distinction between the

magnetic easy and hard loop. Moreover, the shift in the coercive field is more pronounced

in samples prepared by direct evaporation than in samples prepared by cementation.


-20 -10 0 10 20

-1.0

-0.5

0.0

0.5

1.0

M/M

s

µ0H (mT)

Vp=+30 V Vp=0 V Vp=-30 V

Vp

Ni

H||x

Figure 5.4: Hysteresis curve of Ni evaporated onto actuator at different applied voltages (sample

M090713A).

Thus, the magneto-elastic coupling must be a lot more efficient and homogeneous in the

evaporated samples, meaning that the strain exerted on the ferromagnetic film is larger.

In order to confirm these findings the evolution of the magnetic microstructure of both

types of samples is investigated in the following section.

5.1.4 Domain Evolution at Constant Strain

So far, the analysis was restricted to the voltage dependence of the magnetic hysteresis

loops, which have been obtained by integration over all camera pixels. Thus information

about local magnetic substructure was neglected. However, Kerr imaging allows to di-

rectly observe processes in the local magnetic microstructure of thin films. In order to get

a more detailed understanding about the strain dependence of ferromagnetic hysteresis,

the domain evolution of the ferromagnetic thin films will be investigated for different

voltages applied at the actuator.

Ferromagnetic Films Cemented onto Piezoelectric Actuator

This paragraph deals with the domain evolution at different strain states of ferromagnets

cemented onto actuators. In particular, results obtained with sample B080623Ad will be

shown. The corresponding M(H) curve was presented in Fig. 5.3(b).

At first, the magnetic field was prepared again at 0H = −60 mT before it was swept

to 0H = 60 mT. At each field point a Kerr image was recorded and the difference

imaging technique was applied to enhance the magnetic contrast (cf. Chapter 4). The

domain evolution of Fe50Co50 for Vp = +150 V and Vp = −30 V is depicted in Fig. 5.5


1 mm

µ0H = 13.9 mT µ0H = 16.4 mT µ0H = 17.9 mT

ROI

H||y

V p = +

150

VV p =

-30

V

(a) (b) (c)

(d) (e) (f)

Figure 5.5: Comparison of the domain evolution in Fe50Co50 at Vp = +150 V and Vp = −30 V at (a)/(d)

0H = 13.9 mT, (b)/(e) 0H = 16.4 mT, (c)/(f) 0H = 17.9 mT. Definition of a region of

interest (ROI) in (a) for quantitative evaluation (see text).

by means of six images at different magnetic field values. H was oriented along the y-

direction, which corresponds to the easy axis for positive Vp. The images in the upper

row (cf. Fig. 5.5(a),(b),(c)) were taken with an applied piezo-voltage of Vp = +150 V,

the ones in the bottom row at Vp = −30 V (cf. Fig. 5.5(d),(e),(f)). At an external

field of 0H = 13.9 mT domains have already nucleated and propagated at the left and

right edges of the sample simultaneously for both voltages (cf. Fig. 5.5(a) and (d)).

Going to larger magnetic fields, the domain pattern starts to differ for the different strain

states. At 0H = 16.4 mT the magnetic microstructure for Vp = +150 V (cf. Fig. 5.5(b))

exhibits basically the same characteristics as in Fig. 5.5(a). However, for Vp = −30 V,

the magnetization in center regions of the sample has switched (cf. Fig. 5.5(e)). At

even larger fields (0H = 17.9 mT) the magnetization has switched almost completely

for Vp = −30 V and the sample is uniformly magnetized except for some small regions at

the edges (cf. Fig. 5.5(f)). In contrast, for Vp = +150 V, the domain wall motion is not

finished yet, since there is a region in the sample center with black domains. Thus, the

magnetization still points along the original direction (cf. Fig. 5.5(c)).


- 4 0 - 2 0 0 2 0 4 0- 1

0

1

H | | y

V p = - 3 0 V

w h o l es a m p l e

s a m p l ec e n t e r( R O I )M/

M s

µ0 H ( m T )(a)

- 4 0 - 2 0 0 2 0 4 0- 1

0

1

H | | y

V p = + 1 5 0 V

w h o l es a m p l e

s a m p l ec e n t e r( R O I )M/

M s

µ0 H ( m T )(b)

Figure 5.6: Comparison of the M(H) hysteresis loops evaluated for the sample center (red curve) and

the total sample (green curve) at (a) Vp = −30 V and (b) Vp = +150 V.

Obviously, strain influences the domain evolution as expected from the M(H) curves

in Fig. 5.3. However, a noticeable feature is the fact that at 0H = 13.9 mT the domain

patterns for Vp = +150 V and Vp = −30 V do not differ significantly, because in both

cases the edge regions show white domains. Going to larger magnetic fields, the domain

structure remains more or less unchanged over a magnetic field range of approximately

4 mT for Vp = +150 V. In contrast, for Vp = −30 V the magnetization switches within

the sample center in the same field range. This behavior indicates that the left and right

edge regions of the sample switch at a certain magnetic field regardless the applied strain.

It is only in the sample center where the magnetization switching differs for positive and

negative Vp. As a consequence, the strain transmission at the left and right edge regions

must be different from the strain transmission in the sample center.

To confirm this assumption, the sample center was evaluated separately in the M(H)

hysteresis measurement at Vp = +150 V and Vp = −30 V (cf. Fig. 5.3(b)) by defining a

region of interest (ROI) as depicted in Fig. 5.5(a). The resulting hysteresis curve can be

seen in Fig 5.6. For comparison, the hysteresis curve of the whole sample is also depicted.

The M(H) loop evaluated in the sample center clearly differs from the hysteresis curve of

the total sample for Vp = −30 V (cf. Fig 5.6(a)) as well as for Vp = +150 V (cf. Fig 5.6(b)).

This measurement result proves the assumption that strain is not distributed uniformly

in the ferromagnetic film. As mentioned in Section 5.1.1, reasons might be inhomogenous

strain transmission arising from imperfect pre-polishing of the actuator or non-uniform

epoxy distribution.


referenceimage

H||x (a) (b)

(c)

-40 -20 0 20 40

-1

0

1M

/Ms

µ0H (mT)

Vp=-30 V

Figure 5.7: Domain evolution in Ni at Vp = −30 V. The images are obtained at an external magnetic

field of (a) 0H = −9.7 mT, (b) 0H = 3.4 mT, (c) 0H = 16.9 mT. The magnetization

reversal is characterized by a coherent magnetization rotation.

Ferromagnetic Films Evaporated onto Piezoelectric Actuators

Figure 5.7 and Fig. 5.8 depict the domain evolution in Ni evaporated onto an actuator

(sample M090713A) at piezo-voltage of Vp = −30 V and Vp = +30 V, respectively. In both

cases H was aligned parallel to x and the measurement procedure was equal to the one

described above. Unfortunately this particular sample exhibits a rough surface which

arises from an imperfect polishing of the piezoelectric actuator prior to the evaporation

of the metal, although the most fine-grained abrasive paper was used. Nevertheless it is

shown here, since this sample yields good domain visibility during magnetization reversal.

Generally, the same results have been obtained with other evaporated samples.

Let us first consider the situation for the hard axis magnetization loop, i.e. for

Vp = −30 V (cf. Fig 5.7). The image color changes gradually from black to white across

the whole sample with increasing magnetic field as seen in Figs. 5.7(a),(b),(c). Hence,

the sample is uniformly magnetized throughout the process of magnetization rotation


-40 -20 0 20 40

-1

0

1

M/M

s

µ0H (mT)

Vp=+30 V

H||xH||xH||x (a)

(b)

(c)

(d)

referenceimage

Figure 5.8: Domain evolution in Ni at Vp = +30 V. The images were obtained at an external magnetic

field of (a) 0H = 6.6 mT, (b) 0H = 6.8 mT, (c) 0H = 6.9 mT, (d) 0H = 7.2 mT. The

magnetization reversal is dominated by domain nucleation.


and the magnetization reversal resembles a coherent magnetization rotation as predicted

for an ideal single domain state by Stoner-Wohlfarth theory [32, 95].

The situation is different for positive voltages applied to the actuator, e.g. Vp = +30 V

(cf. Fig 5.8). At 0H = 6.6 mT, domains start to nucleate in form of stripes distributed

uniformly within the sample (cf. Fig. 5.8(a)). Then, at larger magnetic fields, the white

domains propagate into the region between the “stripes” as depicted in Fig. 5.8(b),(c).

Finally the magnetization reversal is completed as depicted in Fig. 5.8(d). These Kerr

images prove, that domain nucleation and domain wall motion play an important role

in the process of magnetization reversal along the easy axis [5] in samples prepared by

direct evaporation.

(a) (b)

Vp

P

+-

FM

(c)

Figure 5.9: (a) Domain nucleation in Ni on actuator at Vp = 0 V. (b) Domain nucleation in Ni on

actuator at Vp = 0 V after the polarization of PZT was inverted. (c) Schematic illustration

of positive (red) and negative (blue) electrodes embedded in the piezoelectric actuator. In

(a), nucleation is primarily on top of the positive electrodes. In (b) nucleation on top

of negative electrodes dominates. Note that measurements were done at different sample

alignments.

The nucleation pattern observed in Fig. 5.8 for an applied piezo-voltage of Vp = +30 V

was examined more closely, since the regularity of the distance between the stripes was

remarkable. For all positive as well as for small negative applied voltages Vp (depending

on the remnant strain of the actuator) the striped characteristic was found. In Fig. 5.9(a),

the domain pattern for Vp = 0 V and H∥x is depicted. Domains start to nucleate on top of

every second metal electrode embedded in the piezoelectric actuator. This is evident from

Fig. 5.9(a) in which the electrodes are schematically represented by red and blue lines.

Moreover, in the positive polarization state of the PZT based actuator, those electrodes

are the positive ones (red color, cf. Fig. 5.9(c)), regardless of the history of the strain

state (cf. Fig. 5.9(c)). After domains have nucleated on top of the positive electrodes, a

nucleation center on top of the negative electrodes (blue color) can be found, although

this behavior is not as distinct. Thus, the region on top of the actuator-electrodes must

be the preferred center of nucleation. Imaging results at Vp = 0 V and H∥x after a


polarization reversal of the actuator can be seen in Fig. 5.9(b). Note that the images

were obtained after a readjustment and thus the location of red and blue electrodes in the

two neighboring images differs. This time the domain nucleation on top of the negative

electrodes dominates.

Several effects could in principle account for this nucleation pattern. First, intrinsic

regular surface roughness of the actuator could induce domain nucleation centers. How-

ever, optical microscopy and scanning electron microscopy measurements of untreated

piezoelectric actuator stacks did not reveal any surface roughness or intrinsic imperfec-

tions which are related to the surface region of the electrodes. Therefore, inherent sur-

face effects attributing to the actuator can be excluded. Second, electric stray fields

generated by the electrodes can be ruled out since the stripes appear at Vp = 0 V.

FMPMMA

piezoelectricactuator (side view)

relaxed

deformed(Vp>0)

PZT

electrodes

y

z

x

Figure 5.10: Schematic illustration of the actua-

tor, PMMA and FM film deforma-

tion.

Finally, the most promising explanation is

that the strain induces surface imperfections

in the PMMA buffer layer as schematically

illustrated in Fig. 5.10. An elongation of the

piezoelectric actuator along y for Vp > 0 is

accompanied by a contraction along x and

z governed by the Poisson ratio = 0.45

[65] of the PZT ceramics. The electrodes

embedded in the PZT ceramic are made of

platinum (Pt) [96]. Assuming perfect strain

coupling at the PZT-electrode interfaces, the

electrodes are comparably deformed along

the x- and z-direction. However, the corre-

sponding dilation of the electrodes along y is

determined by the Poisson ratio of platinum

= 0.38 [97], which is slightly smaller than

the one of PZT. As a consequence, the rel-

ative elongation of the electrodes along y is slightly larger (cf. Eq. (5.1)). Thus, the

strain exerted onto the affixed PMMA buffer layer is not totally homogeneous resulting

in small deformations in the PMMA as schematically depicted in Fig. 5.10. These strain-

induced surface imperfections might trigger the preferential domain nucleation on top

of the actuator-electrodes. However, the asymmetry in the domain nucleation pattern

regarding the poling of the electrodes cannot be explained.

5.1.5 Strain Induced Birefringence

The effect of strain onto the magnetic hysteresis and onto the domain evolution has been

discussed so far. Hence, this and the following sections focus onto the voltage control

of the magnetization orientation at constant magnetic field. The obvious measurement

sequence to prove the possibility of magnetization control would be to record Kerr im-


ages as a function of the applied piezo-voltage at constant magnetic bias field [92]. If

the magnetization switched by means of the voltage change, the strain control of the

magnetization would be successful.

A

B

µ0HVp,A

-60 mT

Vp

Vp,B

Figure 5.11: Sequence for refer-

ence measurement.

However, at first a reference measurement was done to

rule out strain induced contrast changes in the Kerr im-

ages. The measurement sequence is schematically depicted

in Fig. 5.11. The magnetic field was set to 0H = −60 mT in

order to assure a magnetic saturated state since H >> Hc.

Then the piezo-voltage was cycled starting from Vp,A to Vp,B

at constant magnetic field. Due to the large external mag-

netic field, the voltage sweep should have no influence onto

the state of magnetization because in this regime the Zee-

man term dominates over the magnetoelastic contribution

to the free energy (cf. Chapter 2). For Kerr microscopy, a

reference image was recorded in the beginning at Vp,A and

then the difference imaging technique (cf. Chapter 4) was

applied.

The result of the reference experiment can be seen in Fig. 5.12. In (a) a Fe50Co50 film

cemented onto the actuator is depicted. The image was obtained at Vp,B = −30 V after a

voltage sweep from Vp,A = +120 V. A rectangular area in the sample center is certainly

darker than the rest of the sample. Only beneath this region of the Fe50Co50 sample the

strain was applied, whereas beneath the left and the right edges no strain was exerted

(see Chapter 6 for further details on local strain generation). Obviously, the variation

of strain caused changes in the contrast pattern of the Kerr images. This effect cannot

be attributed to a magnetization rotation, because the ferromagnetic film is uniformly

magnetized along the external magnetic field. Furthermore, one can observe ripples and

speckle in the image which can be attributed to surface unevennesses generated by the

application of the local strain.

Ferromagnetic films evaporated onto actuators show a similar behavior (cf. Fig 5.12(b)).

This time, strain was applied to the whole ferromagnetic film and the voltage at the ac-

tuator was cycled from Vp,A = +60 V → Vp,B = −30 V. A pattern of regular horizontal

stripes can be clearly seen. These stripes can again be identified as the electrodes embed-

ded in the actuator beneath the ferromagnetic film (cf. 5.1.3). Once more, every second

electrode dominates the pattern.

Contrast changes in the Kerr images were recorded upon sweeping Vp, although the fer-

romagnetic film was saturated. Thus, the detected contrast patterns cannot be attributed

to magnetoelastic effects. It is the applied strain that induces the image patterns as ob-

served in Fig. 5.12. Two aspects may explain this phenomenon. First, the applied stress

might induce surface effects which alter the intensity of the reflected light. A variation

of light intensity changes of course the contrast in the difference imaging technique and


1mm H||y

µ0H=-60 mT

(a)

1mm H||x

µ0H=-60 mT

(b)

Figure 5.12: Visualization of strain induced birefringence in (a) Fe50Co50 cemented onto actuator

(sample B080623A) and (b) Ni evaporated onto actuator (sample M090213P). Measure-

ments were done at constant magnetic field 0H = −60 mT. Vp was cycled from (a)

Vp,A = −30 V → Vp,B = +120 V and from (b) Vp,A = +60 V → Vp,B = −30 V, respectively.

The images correspond to “Vp,B − Vp,A” in both cases.

thus might explain the observed contrast patterns. Second, stress induces variations

of the refractive indices of the MgO or PMMA buffer layer [98, 99, 100]. Assuming a

penetration depth of light comparable to the film thickness, the measured effect could

arise from strain induced birefringence in the MgO or the PMMA. Since the reference

images are recorded at different strain states than the images in Fig. 5.12, strain induced

birefringence might be responsible for the anomalous contrast patterns. In order to rule

out strain induced birefringence effects, equivalent measurements with a sample having

an intermediate buffer layer between the MgO/PMMA and the ferromagnetic film, for

instance gold, would be necessary. If the gold buffer layer had a sufficient thickness, no

birefringence in the MgO or PMMA would occur due to the limited penetration depth of

light (cf. Chapter 4). However, this experiment was not accomplished during this thesis.

All in all, it is evident that the applied stress induces changes in the contrast of the

recorded images. Regardless of the true origin of this effect, it will be denoted as stress

induced birefringence in the following. Thus, the measurement sequence proposed in

the beginning of this section cannot be used, since the magnetic Kerr rotation would be

superimposed by a stress induced signal. It would be impossible to draw conclusions about

the magnetic properties of the sample. Therefore, another method has been devised, as

described in the next Section 5.1.6.


- 4 0 - 2 0 0 2 0 4 0

- 1

0

1 V p = + 3 0 VV p = - 3 0 V

DBA

M/M s

µ0 H ( m T )

C

(a)

A B

CD

Sequence Sequence

~

C

B,B~A,A

µ0H

Vp

VpC

VpB

µ0H

Vp

VpC

VpB

(b)

Figure 5.13: Schematic illustration of the proposed measurement sequences in order to extract the mag-

netic effects contributing to birefringence. (a) Hysteresis loop with indicated measurement

points. (b) Illustration of sequence ◻ and sequence .

5.1.6 Extraction of the Magnetic Contribution to Birefringence

In order to extract the Kerr rotation originating from the magnetic nature of the sample,

another measurement sequence has been proposed. It is denoted as sequence ◻ and is

illustrated in Figs. 5.13(a),(b).

• A: Preparation of the sample at 0H = −60 mT and on a magnetically easy loop

(e.g. V Ap > 0 V for H∥x in Ni) .

• B: Sweep H to measurement field at constant voltage V Ap = V B

p . Usually the mea-

surement field yields H ≲Hc.

• C: Sweep Vp to desired value V Cp at constant magnetic field.

• D: Sweep magnetic field back to start value 0H = −60 mT at constant piezo-voltage

V Cp = V D

p .

• Image subtraction: Subtract image obtained at point B from the image obtained at

point A (B−A) and the image obtained at point D from image at point C (C−D).

Applying this measurement sequence, the image subtraction is always among images of

equal strain state. Therefore, the resulting contrast in the difference images contains only

information of magnetic origin. This method allows the investigation of strain induced

magnetization reversal by means of Kerr microscopy.

In order to check for reversible magnetization switching sequence was proposed as

sketched in Fig. 5.13(b). After the sweep of Vp to the desired value V Cp , it is cycled back

to the original value on the easy axis loop (denoted as V Bp ). In the end the difference

images B −A and B − A are generated and compared.


5.1.7 Strain Induced Magnetization Switching

Having introduced sequence ◻ and sequence the magnetization switching in ferromag-

netic films upon changing the voltage at the actuator is analyzed. At first cemented

samples are studied before turning to the evaporated samples.

Magnetization Switching in Ferromagnetic Films Cemented onto Actuators

(a) (b)

(c) (d)

1 mm H||y

Vp=0 V

Vp=-30 V Vp=+150 V

Vp=+150 V

Figure 5.14: Magnetization switching in Fe50Co50 (sample B080622Ad) cemented onto actuator by

changing the applied voltage Vp at 0H = 18 mT. The difference images (a) B − A at

V Bp = +150 V, (b) C−D at V C

p = 0 V, (c) C−D at V Cp = −30 V and (d) B−A at V B

p = +150 V

are displayed. The corresponding parts of sequence ◻ and are orange-colored.

In principle all prepared samples have shown the same characteristics and therefore

only the results of the Fe50Co50 sample B080623Ad are presented. Preparation of the

sample was at 0H = −60 mT and V Ap = +150 V and the external magnetic field was

aligned along the y-axis, which corresponds to the easy axis. The measurement field was


chosen to be 0H = 18 mT, because it is slightly below the coercive field (cf. Fig. 5.3(b)).

Figure 5.14(a) displays the difference image B−A of the Fe50Co50 sample at V Bp = +150 V.

At the left and right sample edges the switching of M has already taken place, whereas

in the sample center M still points into its original direction. Thus the magnetization

switching in those areas has to be attributed to the magnetic field sweep from point A

to point B. As discussed above (cf. Section 5.1.4), the strain transmission at the edge

regions of the sample can be neglected anyways. In Fig. 5.14(b) the difference image

C−D at V Cp = 0 V can be seen. The magnetization has been switched also in the sample

center except for a region on the upper edge. A complete magnetization switching has

been achieved after a voltage sweep to V Cp = −30 V as depicted in Fig. 5.14(c). The

Fe50Co50 film is uniformly magnetized since only white domains are visible. Therefore,

the magnetization in the sample center was switched by means of the applied voltage

only.

Moreover, sequence was applied to check the reversibility of the magnetization switch-

ing. Therefore, the voltage was cycled V Bp = +150 V → V C

p = −30 V → V Bp = +150 V still at

the same magnetic field. The difference image B−A is depicted in Fig. 5.14(d). Evidently,

the original magnetization configuration seen in Fig. 5.14(a) cannot be reproduced with

a second voltage cycle. This behavior indicates, that the magnetization switching is not

reversible. However, a more quantitative analysis presented in Chapter 6 will reveal, that

reversible magnetization switching is indeed partly possible.

Magnetization Switching in Ferromagnetic Films Evaporated onto Actuators

In Fig. 5.15 the voltage control of M in evaporated ferromagnetic films (sample M090713P)

is depicted. The magnetic field was applied along the x-direction and the images were

obtained at a measurement field of 0H = 8 mT, which is slightly below the corresponding

coercive field for Vp = +30 V (cf. Fig. 5.4). The image B −A (cf. Fig. 5.15(a)) contains

only black domains indicating that no domain nucleation has taken place yet. Sweeping

the voltage from V Bp = +30 V to V C

p = 0 V changes the magnetic state. The resulting

magnetic microstructure is visible in Fig. 5.15(b), which is the corresponding difference

image C − D. Domain nucleation has started on top of the positive piezo-electrodes. A

consecutive measurement sequence with a voltage cycle to V Cp = −8 V yields the image

C − D depicted in Fig. 5.15(c). The stripe pattern is more distinct and domains have

started to propagate into the region in between the stripes. Going to V Cp = −30 V as

depicted in Fig. 5.15(d) the magnetization has switched completely and the sample is

uniformly magnetized again. Thus magnetization switching within the whole thin film

by means of a variation in the piezo-voltage has been achieved.

The reversibility of this process was also checked by applying sequence . However, in

analogy to the cemented samples a reversible control could not be detected and therefore

the presentation of the corresponding Kerr image is omitted.


1 mm H||x

Vp=+30 VB

(a)

Vp=0 VC

(b)

Vp=-8 VC

(c)

Vp=-30 VC

(d)

Figure 5.15: Magnetization switching in Ni (sample M090213P) evaporated onto actuator by changing

the applied voltage Vp at 0H = 8 mT . (a) Difference image B-A at V Bp = +30 V; (b)

Difference image C-D at V Cp = 0 V; (c) Difference image C-D at V C

p = −8 V; (d) Difference

image C-D at V Cp = −30 V.

Discussion

To sum up, voltage-induced magnetization switching has been reported for ferromagnetic

films cemented onto actuators as well as for evaporated films in agreement with results

from [92]. Furthermore, it became evident, that the process of magnetization switching

is accompanied by domain nucleation in samples prepared by the evaporation technique.

However, reversible control of the magnetization orientation could not be confirmed by a

qualitative analysis of the Kerr images. A more quantitative study presented in Chapter 6

will demonstrate, that reversible M control is indeed possible depending on the external

magnetic field.

5.2 Ferromagnetic Thin Films on BaTiO3 Substrates

In the previous section, hybrid structures based on ferromagnetic thin films and piezo-

electric actuators have been studied. In these hybrids, MgO or PMMA buffer layers

separate the ferroelectric and the ferromagnetic material. The coupling between the two

phases is governed by the magneto-elastic effect (cf. Chapter 2). This section deals with

another multiferroic heterostructure consisting of a BaTiO3 substrate and a ferromag-

netic thin film. Thus, a direct phase boundary between both constituents is present. The

coupling between the ferromagnet and the ferroelectric is attributed to the converse mag-

netoelectric effect - the effect of an electric field onto the magnetization (cf. Chapter 2).

However, in heterostructures, the converse magnetoelectric effect is primarily caused by

strain coupling at the interface [15, 101, 102, 103, 104]. In essence, there are mainly two

contributions to the internal stress at the interface [34]: First, the conventional piezo-

electric effect which describes the macroscopic deformation of the ferroelectric phase as

5.2 Ferromagnetic Thin Films on BaTiO3 Substrates 65

a function of the electric field. Second, considerable local strains arise from changes in

the ferroelectric domain structure. As explained in Chapter 3, a- and c- domains coexist

in a BaTiO3 single crystal at room temperature. Since the lattice constants a and c are

not equal, changes in the ferroelectric domain structure cause strains in the clamped fer-

romagnetic film [105]. A comparison of both contributions [34] revealed that the strain

induced by domain reorientation in BaTiO3 dominates over the strain induced by the

linear piezoelectric effect. In addition to the sources of strain, the magnetoelastic effect

in the ferromagnetic constituent is fundamental for the strain coupling at the interface

of the ferromagnet/BaTiO3 heterostructure.

The following treatment and analysis of the ferromagnet/BaTiO3 composite struc-

ture are in analogue to the ferromagnet/actuator samples above. The magnetoelectric

coupling in those bilayers is investigated using the magneto-optical Kerr effect. At first,

characteristic features of the sample are pointed out before the effect of an applied electric

field onto the magnetic hysteresis and the corresponding domain evolution is discussed.

Finally, magnetization control by means of electric fields is studied.

5.2.1 Sample Characteristics

Au

Ni

E

VBTO

BaTiO3

(a)

- 4 0 0 - 2 0 0 0 2 0 0 4 0 0- 6 0

- 3 0

0

3 0

6 0

I (nA)

E ( V / m m )(b)

Figure 5.16: (a)Schematic illustration of the Ni/BaTiO3 sample setup allowing the application of out-

of-plane electric fields [34]. (b) I(E) curve of Ni on BaTiO3 with out-of-plane oriented

electric field.

The samples were fabricated by Stephan Geprags and consisted of an approximately

500 µm thick BaTiO3 single crystal substrate on top of which a polycrystalline ferromag-

netic film with a thickness of 50 nm was deposited by electron beam evaporation. Ni

and Fe50Co50 were chosen as ferromagnetic constituents again. However, the following

analysis is restricted to the results of one Ni/BaTiO3 sample (NB5), since all investigated

samples showed similar characteristics. The lateral dimensions of this particular sample


are 5×5 mm2. The substrate side of the sample is covered by a sputtered gold layer which

was finally attached to a copper piece using silver glue (cf. Fig. 5.16(a)). In order to

control the polarization of the BaTiO3 substrate, an electric field along the out-of-plane

direction (001) was applied. The gold layer and the polycrystalline Ni film served as

electrodes. In this configuration, the application of a large electric field E > Ec ideally

results in a uniform ferroelectric state only consisting of c-domains (cf Chapter 3).

In Fig. 5.16(b) the resulting I(E) curve for an out-of-plane oriented electric field is

depicted. At E ≈ +50 V/mm and at E ≈ +210 V/mm the curve exhibits peaks whereas

at E ≈ −80 V/mm and at E ≈ −160 V/mm minima are present. These extrema can

be referred to as the displacement currents indicating the polarization reversal at the

coercive field of the ferroelectric BaTiO3. Evidently two positive as well as two negative

extrema are observed. This unusual behavior is attributed to the imperfect substrate

quality. Grains and small cracks in the single crystal BaTiO3 substrate can be seen by

the naked eye. Therefore, the electric field distribution within the BaTiO3 might be

inhomogeneous which can explain the observed data. The asymmetry of the observed

coercive fields can be attributed to the use of different electrode materials [45]. For the

magneto-optical investigation the sample was mounted such that a 2 × 2 mm2 large and

crack-free section of the surface was imaged onto the CCD camera.

5.2.2 M(H) Measurements at Constant Strain

Following the procedure of Section 5.1.3 the M(H) hysteresis curves for different applied

electric fields were recorded. A corresponding analysis of Ni on BaTiO3 can be found in

[45]. As above, the magnetic field was swept and the voltage at the BaTiO3 substrate

VBTO remained constant. The Kerr signal of a 2 × 2 mm2 section of the sample was

monitored by integrating over all camera pixels.

In Fig. 5.17 the resulting M(H) loops for three different applied electric fields,

E = −60,0,+400 V/mm, can be seen. Evidently, the coercive field is shifted by approxi-

mately 1.5 mT from the E = −60 V/mm curve to the E = +400 V/mm curve [34, 45]. Also

the remanence increases with growing electric field. These results resemble strongly the

behavior of the Ni/piezoactuator samples. However, the distinction between the magnet-

ically easy and hard axis upon application of strain is not as unique as in the evaporated

ferromagnet/actuator hybrids (cf. Fig. 5.4). As mentioned, the strain is caused by a

combination of linear piezoelectric effect and changes in the domain structure of the fer-

roelectric BaTiO3 substrate. As a consequence, strain coupling at the interface of the

Ni/BaTiO3 composite results in changes of the magnetic anisotropy in the Ni film.

In accordance to Section 5.1.4, the magnetic substructure during the magnetization

reversal was investigated. In Fig. 5.18, domain images at E = +400 V/mm are de-

picted. A few scratches on the sample surface which arise from sample cleaning are

evident. Fig. 5.18(a) depicts the domain pattern at 0H = 8.3 mT. The magnetization

switching has already started at the upper left sample edge. Going to larger magnetic


- 1 0 0 1 0- 1

0

1

E = 0 V / m m

E = - 6 0 V / m mM/

M s

µ0 H ( m T )

E = + 4 0 0 V / m m

Figure 5.17: Hysteresis curve of Ni on BaTiO3 for E = −60,0,+400 V/mm. Remanence and coercivity

increase with growing electric field.

fields, 0H = 8.6 mT, causes the domain walls to propagate into the sample center (cf.

Fig. 5.18(b)). The characteristic feature of the domain boundaries is their zig-zag struc-

ture as already mentioned in Chapter 4 [5]. Also Fig. 5.18(c) displays a similar domain

wall structure at 0H = 9.0 mT.

In contrast, the images displayed in Fig. 5.19 exhibit a very rough surface pattern in

form of vertical stripes. The origin of this behavior is the multi-domain state of the

BaTiO3 substrate at E = −60 V/mm . Referring to Fig. 3.2, the tilting of the a-domains

with respect to the c-domains results in surface unevenness. One would expect, that

the difference imaging technique averages out these surface effects. However, as already

mentioned in Chapter 4, small fluctuations in the light intensity or the components are

1 mm H

(a) (b) (c)

Figure 5.18: Domain evolution in Ni on BaTiO3 at E = +400 V/mm. The images are obtained at an

external magnetic field of (a) 0H = 8.3 mT, (b) 0H = 8.6 mT, (c) 0H = 9.0 mT.


(a) (b)

Figure 5.19: Kerr images of Ni on BaTiO3 at E = −60 V/mm. The images are obtained at an external

magnetic field of (a) 0H = −7.0 mT and (b) 0H = −7.9 mT. The origin of the surface

unevenness can be attributed to the multi-domain structure of the BaTiO3 substrate.

always present and thus cause imperfections in the difference imaging technique. As a

consequence, domain visibility is strongly suppressed in this case. Fig. 5.19(a) depicts

the image at 0H = −7.0 mT in comparison to the image at 0H = −7.9 mT depicted

in Fig. 5.19(b). Although a change in the overall contrast is present, a distinct domain

pattern cannot be determined.

5.2.3 Magnetization Switching at Constant Magnetic Field

Up to now, the electric field dependence of the M(H) curve has been studied. The more

interesting question is however, if the magnetization can be controlled by means of the ap-

plied out-of-plane electric field only. In Section 5.1.7 the successful voltage control of the

magnetization in a ferromagnet/actuator hybrid structure was demonstrated. Following

this approach the bilayer sample consisting of Ni/BaTiO3 was studied for its capability

in magnetization control via electric fields. Therefore, sequence ◻ and (cf. Fig. 5.13)

were applied again to make sure that only magnetic contrast is visible.

The sample was prepared at 0H = −100 mT and EA = +400 V/mm. Then the mag-

netic field was swept to the measurement field at point B, which was slightly below the

coercive field (cf. Fig. 5.17). At constant magnetic field the electric field was cycled

to EC = −60 V/mm. In the end, the difference images B − A and C − D as defined in

Section 5.1.6 are compared.

In Fig. 5.20 the corresponding results for a magnetic field of 0H = 7.3 mT at point B

and C can be seen. The difference image B−A (cf. Fig. 5.20(a)) is uniformly black. This

is to be expected as Vp = const and H <Hc. The difference image C−D after the voltage

sweep to EC = −60 V/mm is depicted in Fig. 5.20(b). As above, the surface roughness

induced by the domains of the BaTiO3 substrate dominates the image. But apart from

that, also domain nucleation centers have been generated by the electric field sweep. In


EB =+400 V/mm

(a)

EC =-60 V/mm

(b)

EB =+400 V/mm

(c)

Figure 5.20: Magnetization switching in Ni on BaTiO3 by changing the out-of-plane electric field at

0H = 7.3 mT. (a) Difference image B−A at EB = +400 V/mm. (b) Difference image C−D

at EC = −60 V/mm. (c) Difference image B −B at EB = +400 V/mm.

Fig. 5.20(c), the difference image B − B acquired in a consecutive sequence is shown.

The image does not display any surface inhomogeneity because the substrate is in the

single domain state at EB = +400 V/mm. But the most striking feature is the fact that

the second electric field sweep from EC = −60 V/mm at C back to EB = +400 V/mm

at B has enhanced the magnetization switching, as the difference image B −B is mainly

composed of white domains. Consequently the magnetization switching at this magnetic

field is not reversible at all, since the initial domain state cannot be re-established. In

contrast, further domain wall propagation is induced by the second electric field cycle.

EB =+400 V/mm

(a)

EC =-60 V/mm

(b)

EB =+400 V/mm

(c)

Figure 5.21: Magnetization switching in Ni on BaTiO3 by changing the out-of-plane electric field at

0H = 8.0 mT. The difference images (a) B − A at EB = +400 V/mm, (b) C − D at

EC = −60 V/mm and (c) B −B at EB = +400 V/mm are depicted. The magnetization has

been switched upon the electric field cycle exclusively.

Accordingly Fig. 5.21 displays the results for a measurement field of 0H = 8.0 mT at

point B and C. In analogue, the difference image B − A (cf. Fig. 5.21(a)) is uniformly


black and thus no magnetization reorientation has taken place yet. After an electric field

sweep from EB = +400 V/mm to EC = −60 V/mm, the resulting magnetic state contains

almost only white domains as can be seen in Fig. 5.21(b), which depicts the difference

image C−D. Therefore, a complete magnetization switching induced by the electric field

sweep has been achieved. In a consecutive measurement, sequence was applied to check

the reversibility of the magnetization switching. In agreement to the measurement above,

no reversible M control is detected in the difference image B − B (cf. Fig. 5.21(c)). In

contrast, the resulting magnetic state consists only of white domains, whereas the initial

state has black domains. Thus the magnetization was switched completely by means of

the electric field sweep in the investigated sample sector, however, no reversible M control

can be achieved.

In a nutshell, the above experiments prove, that magnetization control by means of an

electric field is also possible in multiferroic heterostructures consisting of Ni and BaTiO3.

The converse magnetoelectric effect enables to switch the magnetic state at magnetic

fields close to the coercive field of the ferromagnetic constituent. No reversible M control

has been found, in contrast, the second voltage cycle applied in sequence enhances the

magnetization switching.

5.3 Summary

All in all, electric field control of the magnetization has been imaged by means of spa-

tially resolved Kerr effect. Multifunctional hybrid structures consisting of ferromag-

net/piezoactuator have been prepared and investigated. It has been reported, that the

magnetization of the ferromagnetic thin film can be switched upon the application of a

piezo-voltage and the observed data is in agreement with the findings of [92]. In addition,

electric field controlled ferromagnetism was also established in multiferroic heterostruc-

tures consisting of ferromagnetic thin films and piezoelectric BaTiO3 substrates.

Chapter 6

Local Magnetization Control

In the previous chapter the potential of electric field controlled ferromagnetism in mul-

tiferroic hybrid structures was demonstrated. By means of Kerr microscopy the mag-

netization switching induced by applied electric fields was visualized. However, the re-

sults shown were all obtained in mm-scale “large” samples. To be relevant for eventual

technological application, scaling to smaller dimensions is mandatory. Therefore, it is

necessary to demonstrate a local control of the magnetization. Several concepts based

on magnetostriction have been proposed in order to aim for local magnetization con-

trol [106, 107, 108]. Usually they combine electrostrictive grids with magnetostrictive

materials to propose a voltage controlled non-volatile magnetic random access memory.

However, an effective coupling of ferromagnetic and piezoelectric properties in hybrid

structures at small scales is the key point to achieve local magnetization control. There-

fore, two architectures for ferromagnetic/piezoelectric heterostructures are proposed and

investigated in this chapter. Magneto-optic methods are again applied in order to charac-

terize them. In the first part of this chapter locally controllable hybrid structures based

upon the piezoelectric actuators introduced in Chapter 5 are discussed. Their potential

for local magnetization switching is presented. Moreover, results of magnetotransport

measurements will be shown and correlated to the magneto-optical data. After that, a

novel design allowing local magnetization control is established. This architecture re-

lies on micron-sized electrodes that are patterned onto different piezoelectric substrates.

Local polarization and magnetization control in the novel hybrid structure is studied.

6.1 Ferromagnets on Piezoelectric Actuators

In Chapter 5 multifunctional hybrid structures consisting of a piezoelectric actuator and

a ferromagnetic thin film were introduced and their potential for magnetization control

via electric fields was demonstrated. These hybrids can be modified in order to allow for

local magnetization control. The concept and functionality of this approach is presented

in the following.

71

72 Chapter 6 Local Magnetization Control

FM

x

y

z

electrodes

electrodes

(a)

(b)

(c)

1 mm 5 mm

Figure 6.1: (a) Schematic illustration of a locally contacted actuator with affixed ferromagnetic film. (b)

Photograph of a ferromagnet on actuator with local contacts. (c) Assembly of the actuator

onto a L-shaped brass part mounted onto a chip carrier in order to allow for free expansion

and contraction of the actuator.


The hybrid structures enabling local magnetization control are based on the piezoelectric

actuators which have been introduced in Chapter 5 (cf. Fig. 5.1). As mentioned, the

actuator consists of 100 µm thick PZT piezo-active layers which are separated by 10 µm

thick metal electrodes. Those electrodes are connected by a conducting band on the

two sides of the actuator. Every second electrode is isolated by sintered glass to assure

alternating electric fields. In order to enable local control of the PZT active layers the

actuator has to be modified as can be seen schematically in Fig. 6.1(a). At first, the con-

ducting band electrode on the two actuator sides has to be removed by careful polishing.

The glass isolation, however, is maintained. Then the electrodes are contacted one by

one by bond wires as depicted in Fig. 6.1(b). This allows an independent control of each

PZT layer embedded by electrodes. The actuator with affixed ferromagnet is mounted

on a L-shaped brass part (cf. Fig. 6.1(c)) in order to assure free expansion and contrac-

tion. Finally the brass part is adjusted onto a chip carrier and thus the electrodes can

be connected one by one with the pins of the carrier to provide an independent voltage

supply of several actuator electrodes. Since the actuator consists of 20 electrode pairs,

usually only about five electrode pairs are contacted selectively since the number of bond

pads is limited. The remaining electrodes of each side face are connected to a common

contact pad. Thus the remaining part of the actuator can also be voltage-controlled and

6.1 Ferromagnets on Piezoelectric Actuators 73

Vp

P

A

(a)

- 8 0 0 - 4 0 0 0 4 0 0 8 0 0- 1 5 0

0

1 5 0

P

I (nA)

E p ( V / m m )

P

(b)

Figure 6.2: (a) Schematic illustration of the polarization control within one monolayer of PZT. (b)

Measurement of the I-Ep curve of a single PZT layer. The distinct peaks can be referred

to as the displacement current indicating a polarization reversal in the corresponding PZT

monolayer.

thus exert homogeneous stress.

The samples M090213P, B080623Ad and M090220Ac (cf. Tab. 5.1) were modified

accordingly to allow for local control of the piezoelectric actuator. On the basis of these

three samples the following measurement results were obtained.

6.1.2 Local Polarization Control

Having contacted PZT layers of the actuator locally, it has to be checked whether it is

possible to really control their polarization selectively without affecting adjacent PZT

monolayers. This characteristic is fundamental to also exert locally confined strain. Usu-

ally the actuator is operated in the semi-bipolar voltage range −30 V ≤ Vp ≤ +150 V.

In this voltage regime the inherent polarization P of the PZT monolayers is alternating

due to its particular contact scheme (cf. Fig. 6.2(a)). Contacting two adjacent elec-

trodes of the multilayer PZT actuator as schematically depicted in Fig. 6.2(a) enables

to control the polarization of the embedded PZT layer. The resulting I(Ep) curve can

be seen in Fig. 6.2(b). The voltage was cycled from Vp = 80 V → −80 V → +80 V

(−800 Vmm ≤ Ep ≤ +800 V

mm) and the current was recorded. Two distinct peaks at around

Ep = +420 Vmm and Ep = −420 V

mm , respectively, can be seen. Those can be referred to

as the displacement currents, which indicate a polarization reversal. Thus it is possible

to control the polarization of a single PZT layer. To check whether the polarization di-

rection of neighboring layers is affected by a reversal of P in the embedded layer, their

polarization was checked before and after the reversal again using the I(Ep) technique

just described. It turned out that the polarization direction of adjacent PZT layers is not


x

y

Vp=+28 Vµ0H=-60 mT

1 mm(a)

Vp=-30 Vµ0H=-60 mT

(b)

Vp=+28 Vµ0H=-60 mT

(c)

Figure 6.3: Voltage cycle Vp = +30 V → −30 V → +30 V at selectively contacted actuator for 0H =

−60 mT (sample M090213P). A reference image was recorded at Vp = +30 V. Kerr images

at (a) Vp = +28 V, (b) Vp = −30 V (the red and blue lines indicate the positive and negative

electrodes) and (c) Vp = +28 V are depicted.

affected by a polarization reversal in a particular PZT monolayer. Thus the polarization

of each PZT layer can be controlled individually.

6.1.3 Local Strain Control

Apart from the polarization, the more important aspect is local strain control. In order

to examine local strain generation, strain induced birefringence was exploited. This

phenomenon was observed in Chapter 5 and it implicates contrast changes in the Kerr

images induced by surface or birefringence effects.

At first a sample with an evaporated Ni film was investigated (sample M090213P)

for local strain generation. Therefore, a voltage Vp was applied to two electrodes em-

bedding one PZT monolayer, whereas the remaining actuator electrodes were supplied

with a constant voltage Vp,r = +30 V. The two electrodes, to which Vp was applied, are

depicted as red and blue lines in Fig 6.3(b). Furthermore, a large magnetic field was

applied, 0H = −60 mT, to assure magnetic saturation of the ferromagnetic film affixed

to the locally contacted actuator. Then the voltage at the two electrodes was cycled

from Vp = +30 V to Vp = −30 V and back. A reference image was recorded in the begin-

ning at Vp = +30 V and the difference imaging technique (cf. Chapter 4) was applied. In

Fig. 6.3(a) the image obtained at Vp = +28 V (with reference image subtracted) is de-

picted. Since the strain state had not changed appreciably with respect to the reference

image, no contrast pattern is present. Contrarily, at Vp = −30 V (cf. Fig. 6.3(b)) a clear

contrast pattern in form of a stripe can be seen. Evidently, the stripe appears mainly


y

x

Vp=-20 Vµ0H=-60 mT

1 mm

(a)

Vp=+150 Vµ0H=-60 mT

(b)

Vp=-20 Vµ0H=-60 mT

(c)

Figure 6.4: Ferromagnetic film cemented on actuator undergoes a voltage cycle Vp = −30 V → 150 V →

−30 V at three locally contacted electrode pairs at 0H = −60 mT (sample B080623Ad).

The reference image was recorded at Vp = −25 V. (a) Vp = −20 V, (b) Vp = +150 V, the

blue lines indicate the electrodes connected to the common ground, the red lines represent

the sweeping electrodes and the electrodes represented by the white lines were on a constant

potential Vp,r = −30 V. (c) Vp = −20 V.

between the locally contacted actuator-electrodes to which Vp was applied. Therefore,

the contrast of the Kerr image has changed in the region on top of the embedded PZT

layer. This contrast pattern disappeared again after the back sweep to Vp = +28 V (cf.

Fig. 6.3(c)) indicating that the actuator is in the initial strain state again.

The same experiment has also been done with a ferromagnetic film cemented onto a

piezoelectric actuator (Fe50Co50, sample B080623Ad). This time, the contact scheme was

slightly different. Six adjacent PZT monolayers were exposed to Vp, the remaining ones

were supplied with a constant voltage Vp,r. The corresponding electrodes are represented

by the lines indicated in Fig. 6.4(b). The red electrodes were connected to the high output

of the source-meter and therefore they will be referred to as positive electrodes. The blue

ones will be denoted as negative electrodes. The white electrodes were supplied with a

constant voltage Vp,r = −30 V during the measurement. The voltage at the red electrodes

was cycled from Vp = −30 V → +150 V → −30 V . Once more, the external magnetic field

was sufficiently large (0H = −60 mT) in order to achieve a uniform magnetized state

throughout the measurement. The reference image was recorded at the beginning of the

cycle at Vp = −25 V and the difference imaging technique was applied. Fig. 6.4(a) was

obtained at Vp = −20 V and does not reveal any contrast pattern, since the strain state

was not altered significantly with respect to the reference state. In contrast, a distinct

contrast pattern is present in Fig. 6.4(b), depicting the difference image obtained at

Vp = +150 V. Evidently, there is a strain induced contrast pattern in the sample center,

which corresponds to the individually controlled PZT layers. Hence, locally confined

birefringence is induced by the applied strain. The contrast pattern vanishes again when


H||y Vp=+150 VB

(a)

Vp=-30 VC

(b)

Vp=+150 VB

(c)

Figure 6.5: Local magnetization control in Fe50Co50 cemented onto actuator (sample B080623Ad). The

red and blue lines indicate the actuator-electrodes which were locally contacted. The mea-

surement was done applying sequence ◻ and at 0H = 18 mT. (a) Difference image B−A

at V Bp = +150 V, (b) C −D at V C

p = −30 V, (c) B − A at V Bp = +150 V.

going back to the initial strain state (cf. Fig. 6.4(c)). Thus local and reversible strain

variation is also possible in ferromagnets cemented onto piezoelectric actuators.

6.1.4 Local Magnetization Switching

In Chapter 5 the voltage controlled switching of M in a ferromagnetic film was demon-

strated. Having achieved local strain control by contacting the PZT layers individually,

local magnetization switching within small regions of the ferromagnet should be possible.

In the following experiments on the hybrid structures allowing local strain control are

presented. The measurement procedure and notation is identical to the one applied in

Chapter 5, where sequence ◻ and (cf. Fig. 5.13) were introduced in order to extract

the Kerr rotation.

Ferromagnet cemented onto actuator

Both prepared samples, B080623Ad and M090220Ac, yield similar results, and therefore

the following analysis is restricted to the results obtained on the Fe50Co50 based sample

(B080623Ad), which can be seen in Fig. 6.5. The magnetic field was oriented along the

y-axis, which corresponds to the easy axis for Vp > 0. The field and actuator preparation

was at 0H = −60 mT and at V Ap = +150 V, respectively. The actuator electrodes that

underwent the voltage cycle are depicted again as red lines in Fig. 6.5, whereas the blue

electrodes were connected to ground. The remaining part of the actuator was supplied

with a constant voltage of Vp,r = +150 V during the measurement sequence.

Then sequences ◻ and were applied in order to investigate the magnetization switch-

ing. In Fig. 6.5(a), the difference image B−A at V Bp = +150 V is depicted. The originally


black domains have already started to be switched into white domains due to the mag-

netic field sweep to 0H = 18 mT , especially at the sample edges. After the magnetic

field sweep the voltage was cycled at the denoted electrodes. The obtained difference

image C−D at V Cp = −30 V can be seen in Fig. 6.5(b). Further domain wall propagation

has taken place upon the voltage sweep. Evidently, the locally confined strain induced

a local magnetization switching. However, the application of local strain did not result

in complete magnetization switching, since there are still edge regions with the original

magnetic state. Also the magnetization switching was not only confined to the region

where the PZT layers are cycled but it also occurred also in adjacent parts of the ferro-

magnet. The reversibility of this switching process was measured applying sequence .

The corresponding difference image B− A can be seen in Fig. 6.5(c). As in Chapter 5, no

reversible magnetization switching is observed.

Ferromagnet evaporated onto actuator

H||x

Vp=+60 VB

(a)

Vp=-30 VC

(b)

Vp=+60 VB

(c)

Figure 6.6: Local magnetization control in Ni evaporated onto actuator (sample M090213P). The red

and blue lines indicate the locally contacted actuator-electrodes which embed four PZT

layers in total. Note that the nearest-next electrodes (yellow) were not contacted to prevent

direct contact of regions with opposing strain. The remaining electrodes were supplied with

Vp,r = +60 V. The measurement was done applying sequence ◻ and at 0H = 8 mT. (a)

B −A at V Bp = +60 V, (b) C −D at V C

p = −30 V, (c) B − A at V Bp = +60 V.

Nickel films evaporated onto actuators have also been studied for local magnetization

switching (sample M090213P). The number of PZT monolayers, that underwent a voltage

cycle, varied between two and six and the corresponding electrodes are again depicted as

insets in Fig. 6.6 and Fig. 6.7. Note that in this particular measurement the two nearest-

next electrodes (depicted as yellow lines) were not contacted, in order to prevent a direct


contact of regions with opposing strain and thus possible sample damage. The remaining

electrodes were again supplied with a constant voltage Vp,r = +60 V, but they are omitted

for clarity. The magnetic field was aligned along x, which is the easy direction for Vp > 0 V.

Sequence ◻ and were applied again and the sample was prepared at 0H = −60 mT

and V Ap = +60 V before the magnetic field was swept to point B. The subsequent voltage

cycle yielded V Bp = +60 V → V C

p = −30 V.

Figure 6.6 displays the results of a measurement with four selectively contacted PZT

layers for 0H = 8 mT. The difference image B − A depicted in Fig. 6.6(a) reveals

that H < Hc, since no domain nucleation has occurred yet apart from a small region

near the image bottom. A voltage cycle at the particular electrodes to V Cp = −30 V

results in domain nucleation as visible in Fig. 6.6(b). Evidently, the domain nucleation

is limited to the region of the cycled electrodes, which are indicated by the red and blue

lines. Therefore, the local strain generation has successfully inverted the magnetization

direction without affecting the magnetic state of the remaining ferromagnetic film. As

already observed in Chapter 5, the dominating nucleation center is on top of the metal

electrodes. To check reversibility, sequence was also applied and the difference image

B−A was obtained (cf. Fig. 6.6(c)). The initial magnetic state could not be re-established

after a second voltage cycle.

To corroborate these findings, the same experiment was performed when two or re-

spectively six PZT layers were selectively contacted. The measurement configuration

and procedure was identical to the one above. For two contacted PZT layers, the imag-

ing results in terms of difference images B−A and C−D are depicted in Figs. 6.7(a),(b).

They were obtained at a magnetic field of 0H = 8.5 mT. Apart from a small region near

the image bottom no domains have nucleated in B − A. In contrast, in C − D domains

have nucleated on top of the selectively contacted red electrode due to the corresponding

voltage sweep. Also the region on top of the neighboring non-contacted electrodes (yel-

low) is partly affected and domain nucleation is visible, probably due to strain coupling

in the ferromagnetic film or the PMMA buffer layer. In the remaining ferromagnetic film

no further domain nucleation is observed. A similar behavior is found in Figs. 6.7(c),(d),

which display the difference images B − A and C − D for six controlled PZT layers at

0H = 7.0 mT. Local magnetization switching is observed upon the voltage sweep at the

selectively contacted electrodes.

Discussion

In summary, local magnetization switching was successfully achieved in both types of

hybrid structures. The magnetization switching in evaporated samples is more distinct

than in the samples prepared by cementing technique and also the local confinement of

the magnetization switching is superior. However, as already observed in Chapter 5,

the nucleation of domains happens preferably on top of the electrodes embedded in the

actuator underneath the ferromagnetic film.


(a)

H||x

(c)

(b)

(d)

Vp=-30 VC

Vp=+60 VB

Figure 6.7: Local M control in Ni for different contact schemes. (a),(b) Difference images B − A and

C−D for voltages V Bp = +60 V → V C

p = −30 V at 0H = 8.5 mT with two selectively contacted

PZT layers. (c),(d) Difference images B−A and C−D for voltages V Bp = +60 V → V C

p = −30 V

at 0H = 7.0 mT with six selectively contacted PZT layers.

6.1.5 Magnetotransport Measurements

In the previous section the possibility of local magnetization control in hybrid systems

was demonstrated by means of Kerr microscopy. In order to corroborate these findings,

magnetotransport (MTR) measurements were applied to this ferromagnetic/piezoelectric

hybrid system. In the following a short introduction into the theory of the anisotropic

magneto resistance will be given before dealing with MTR measurements on integrally

and locally strained Ni thin films.

Anisotropic Magneto Resistance

The anisotropic magneto resistance (AMR) is a phenomenon which implies that the

resistance of a ferromagnet depends on the orientation of the magnetization with respect


Vp

IV

H

y

xVp

I V

H

(a) (b) (c)I||H I H

2 mm

Figure 6.8: (a) Photograph of the ferromagnetic/piezoelectric hybrid system with contacts to allow four-

point MTR measurements. Schematic illustration of the measurement configuration and

contact contact scheme of the (b) I∥H and (c) I ⊥H orientation.

to the electric current. In thin ferromagnetic films, the magnetization generally lies within

the film plane (cf. Chapter2). The resistivity for a current flowing perpendicular to the

magnetization is given by ⊥ which differs from ∥ denoting the resistivity of a current

parallel to the magnetization [109]. In 3d transition elements and alloys this anisotropy

originates from the non spherical-symmetrical charge distribution of the outer atom shell

[109]. Consequently, spin-orbit coupling between the conducting electrons and the shell

electrons is asymmetric with respect to the orientation of the electrical current. All in

all, the result is an anisotropic scattering of the conduction electrons, which depends

on the orientation of current with respect to the magnetization direction. Whenever the

material is composed of several magnetic domains, this is taken into account by averaging

over all magnetization orientations. However, spin scattering occurring at domain walls

[110] will not be accounted for.

Assuming a current density j that encloses an angle of with the magnetization M,

the longitudinal and transversal resistivity (long and trans) in polycrystalline samples

can be expressed as follows [111]:

long = ⊥ + (∥ − ⊥) cos2( ) (6.1)

trans = (∥ − ⊥) sin cos (6.2)

In general, the resistivities fulfill the relation ∥ > ⊥, which holds also true for Ni

with ∥ − ⊥ = 0.16 µΩcm [109]. All in all, MTR measurements possess the potential

to make quantitative statements about the magnetization orientation. Therefore, this

technique was applied to the prepared hybrids in order to confirm the data obtained by

the magneto-optical analysis.

In Fig. 6.8 the contact scheme allowing for MTR measurements on a Ni/actuator hy-


brid structure is depicted. The Ni film was contacted on top with four contacts (cf.

Fig. 6.8(a)), whereas the actuator was prepared as described above. This contact scheme

enables a four-point resistance measurement. In Fig. 6.8(b), the current is oriented par-

allel to the external magnetic field. As the current is driven between two contacts, the

voltage is measured at the two remaining ones. In contrast, the current is oriented per-

pendicular to H in Fig. 6.8(c). During the MTR measurements a constant bias current

of Ibias = 10 mA was set and the voltage Vlong was recorded. The geometry of the present

four-point AMR configuration is not well enough defined to allow for a quantitative mea-

surement of . Therefore, the resistance Rlong =VlongIbias

is used to characterize the measure-

ments. It is assumed that the geometry of the current flow remains constant regardless

the applied strain = const ⋅R and thus Eq. (6.1) remains valid and can be expressed in

terms of Rlong, R∥ and R⊥. MTR measurements on a micro-patterned Hall-bar would be

the ultimate solution to imply a defined geometry, but this was not achieved during this

thesis. The transversal resistance Rtrans was not recorded. Moreover, the dominant axis

of elongation of the piezoelectric actuator (y-axis) was always oriented perpendicular to

H as depicted in Figs. 6.8(b),(c). Thus the easy axis pointed along x for Vp > 0 V.

Magnetotransport and Integral Strain

Having briefly explained the AMR theory and the sample preparation, measurement

results will be shown in the following. At first integral strain is applied to the Ni film

as described in Chapter 5. In Fig. 6.9(a) results with current aligned parallel to the

external field can be seen, whereas Fig. 6.9(b) displays the result of I ⊥H. In both cases,

the voltage Vlong was recorded in dependence of the applied magnetic field for different

applied voltages Vp. The obtained results were in accordance with [112].

At first, the behavior in magnetic saturation (0H ≈ ±60 mT) for both current orien-

tations is analyzed, which directly reflects the characteristic of the AMR. The measured

resistance for I∥H is about Rlong ≈ 403 mΩ, whereas for I ⊥ H the resistance yields

Rlong ≈ 355 mΩ. This difference can be easily understood by AMR theory. In magnetic

saturation, the magnetization is aligned along the external magnetic field. Thus, for I∥H,

M is aligned parallel to I, but for I ⊥H, M is perpendicular to I. Therefore, the observed

resistance difference can be understood, since R∥ > R⊥.

In both current configurations the resistance curves for different applied voltages Vp

do not overlap for H >> Hc. The origin of this behavior cannot be the AMR effect

since the magnetization is saturated and points along the external field. Drift or offset

effects can also be excluded, since this phenomenon was observed in several measurements

and analogous in [112]. The magnitude of this shift in resistance also depends on the

orientation of the current. For I∥H, the change in the resistance at 0H = ±60 mT is

given by ΔR/R = (RVp=+60 V −RVp=−30 V)/RVp=+60 V ≈ −0.2%. In analogy, for I ⊥ H one

obtains ΔR/R ≈ 0.5%. The observed behavior can be attributed to the piezoresitive effect,

i.e. the so-called piezoresistance [113, 114, 115]. It describes the change of the electrical


- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 03 8 8

3 9 2

3 9 6

4 0 0

4 0 4

R long (m

Ω)

µ0 H ( m T )

I | | H V p = - 3 0 V

V p = 0 V

V p = + 6 0 V

(a)

- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0

3 5 6

3 6 0

3 6 4

3 6 8

V p = 0 VV p = + 6 0 V

V p = - 3 0 V

R long (m

Ω)

µ0 H ( m T )

I H

(b)

Figure 6.9: Magnetotransport measurement on a Ni thin film at different applied voltages Vp with (a)

I∥H and (b) I ⊥H.

resistance upon the application of mechanical stress. In contrast to the piezoelectric effect,

the applied stress only causes a change in the resistance, but no electrical potential is

generated. The resistance change due to the piezoresistive effect can be expressed as

ΔR

R=K ⋅

ΔL

L(6.3)

where K is a gauge factor and ΔLL the nominal expansion or contraction [113, 114]. The

gauge factor K implies the change of the cross-sectional area as well as eventual resistivity

changes caused by the deformation ΔLL . For evaporated Ni films, a gauge factor of K = 2.7

at room temperature was reported [116]. Moreover, the nominal stroke of the piezoelectric

actuator along the dominant axis of elongation (y-axis) is (ΔLL

)y= 1.3 × 10−3 [65]. Using

the Poisson relation with the given Poisson ratio = 0.45 (cf. Chapter 5), the nominal

deformation along x is given by (ΔLL

)x= − ⋅ 1.3 × 10−3 ≈ −0.6 × 10−3 . Inserting this data

into Eq. (6.3), the nominal resistance change for the I∥H configuration can be calculated

as ΔR/R ≈ −0.2% which is in agreement with the measurement data. In the transverse

configuration, the theoretical piezoresistance is given by ΔR/R = 0.4%, which is slightly

smaller than the observed value of ΔR/R ≈ 0.5%. For the purpose of exact quantification

of the piezoresistance, measurements at larger magnetic fields than 0H = ±60 mT are

indispensable. This quantification was not done in this thesis due to the limited field

range of the home-built electromagnet. Nevertheless, the presented data reveals clearly,

that the observed effect can be attributed to piezoresistance.

The resistance curves exhibit minima (maxima) for I∥H (I ⊥H) at the coercive fields

of the Ni thin film. For I∥H, the components of M perpendicular to the current grow and

thus Rlong decreases until the coercive field is reached. Then Rlong goes up again since


the components of M perpendicular to the current decrease. The same argumentation

holds true for the I ⊥ H configuration. Thus the extrema in the resistance curves are a

consequence of the AMR.

Another striking feature is the variation of the resistance curves for different ap-

plied piezo-voltages Vp. In both measurement geometries equivalent patterns can be

seen. The minimum, or maximum respectively, is more pronounced at Vp = −30 V

than at Vp = +60 V. Putting this into numbers, the anisotropic magneto resistance

(AMR = (Rmax −Rmin)/Rmin) × 100%) for I∥H yields AMRVp=−30 V ≈ 3.6% and

AMRVp=+60 V ≈ 0.8%, respectively. Similar magnitudes are obtained for I ⊥ H with

AMRVp=−30 V ≈ 3.6% and AMRVp=+60 V ≈ 0.3%.

Assuming a simple single domain Stoner-Wohlfarth model, this feature can be ratio-

nalized as follows. Applying Vp = +60 V to the actuator induces a magnetic easy axis

along x as discussed in Chapter 5. According to Stoner-Wohlfarth [95], the magnetization

reversal along the easy axis is characterized by a flip of the magnetization by 180° at the

coercive field [32]. As a consequence, there should be no change in the resistance ideally,

since no magnetization component perpendicular to the field is present. However, this

argument holds only true for perfect alignment of current parallel (perpendicular) to the

magnetic field, which is never given in reality. Thus the extrema in the resistance curve

for Vp = +60 V are a consequence of misalignment of I and H. Concerning the hard axis

magnetization reversal (Vp = −30 V) the Stoner-Wohlfarth theory predicts a coherent

magnetization rotation. Thus the transverse magnetization component increases steadily

until the maximum is reached at the coercive field before it decreases again. According

to AMR theory Rlong has a minimum (maximum) for I∥H (I ⊥ H) at the coercive field

which is more pronounced than for Vp = +60 V.

The Stoner-Wohlfarth approach enables to explain the observed strain dependent char-

acteristics in the resistance curves. However, in Chapter 5 Kerr imaging proved that the

easy axis magnetization loop is dominated by domain nucleation, whereas coherent mag-

netization rotation was found for the hard axis magnetization reversal. Thus the above

explanation using Stoner-Wohlfarth theory holds basically only true for the Vp = −30 V

curve. The magnetization reversal for Vp = +60 V as observed in Chapter 5 is abrupt and

accompanied by the formation of stripe domains. However, averaging over all domains

the magnetization component perpendicular to H remains also small compared to the

hard axis magnetization reversal and therefore a smaller extremum is expected. Hence,

considering the above explanations the resistance curves are in good agreement with the

Kerr images obtained in Chapter 5.

Magnetotransport and Local Strain

In the preceding section, the piezoelectric actuator was integrally strained and magne-

totransport was recorded simultaneously. In this paragraph, the concept of local strain

generation described above (cf. Fig. 6.1) is implemented together with four-point MTR


measurements (cf. Figs. 6.8(b),(c)). The aim of this experiment is to correlate the

Kerr imaging results obtained in Section 6.1.4 for hybrids prepared by the evaporation

technique with magnetotransport. Therefore, eight PZT monolayers were selectively con-

tacted, whereas the remaining part of the piezoelectric actuator was held on a constant

potential. The resulting configuration is schematically depicted in Fig. 6.10. The area

comprised by the red box represents the eight selectively contacted PZT layers and thus

the region of local strain variation. The current geometries I∥H and I ⊥ H are also dis-

played with respect to the region of local strain. A corresponding domain image indicating

the locally controlled PZT layers can be seen in Fig. 6.7(d).

Vp

HI||

I

Figure 6.10: Local mag-

netization

control and

MTR.

The resistance curves of Ni for different applied local

strains and for both current orientations are depicted in

Fig. 6.11. Comparing these curves with the MTR results ob-

tained with a collectively strained actuator (cf. Fig. 6.9),

it can be noted that the characteristic features are again

present. However, the dependence of the anisotropic magneto

resistance on the applied voltage is not as distinct as above.

Calculating AMR = (Rmax −Rmin)/Rmin) × 100% for I∥H yields

AMRVp=−30 V ≈ 1.6% and AMRVp=+60 V ≈ 1.3% respectively. For

I ⊥ H the AMR can be calculated as AMRVp=−30 V ≈ 1.1% and

AMRVp=+60 V ≈ 0.7%. This behavior is of course an indication for

the generation of local strain whose influence onto magnetotrans-

port is inferior compared to the application of integral strain. For

I∥H, the resistances for Vp = −30 V and Vp = +60 V in magnetic saturation disperse no-

ticeable in comparison to the I ⊥ H configuration. The origin of this behavior are most

likely unwanted drift effects in addition to the already mentioned piezoresistance.

In Section 6.1.4 the domain nucleation and evolution in Ni on actuator under local

applied stress was discussed. Therefore, sequences ◻ and were applied as introduced

in Chapter 5. In order to compare and correlate MTR measurements with the observed

magnetic microstructure, sequence ◻ and were applied again and Vlong was recorded

simultaneously to the Kerr images at the measurement points B, C and B (cf. Fig. 5.13)

of the respective sequence. In order to minimize the statistical error, the voltmeter

was read out ten times per measurement point. The sample was prepared at A with

0H = −100 mT and V Ap = +60 V. The measurement field at B and C was iteratively

increased from 0H = −20 mT to 0H = 20 mT in each consecutive measurement sequence.

The corresponding voltage was cycled from V Bp = +60 V to V C

p = −30 V.

In Figs. 6.12(a),(b) the MTR measurement results for I∥H and I ⊥ H are depicted.

The resistances Rlong at B, C, and B (denoted as RB, RC and RB) are displayed for both

configurations. For I∥H, RB decreases with increasing magnetic field until the coercive

field is reached before it increases again. This behavior is in analogy to the resistance

curve for Vp = +60 V shown in Fig. 6.11(a). Below the coercive field the voltage cycle


- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 03 9 4

3 9 6

3 9 8

4 0 0R lon

g (mΩ

)

µ0 H ( m T )

I | | H V p = - 3 0 VV p = 0 V

V p = + 6 0 V

(a)

- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0

3 6 8

3 7 0

3 7 2

R long (m

Ω)

µ0 H ( m T )

I H V p = - 3 0 V

V p = 0 V

V p = + 6 0 V

(b)

Figure 6.11: Magnetotransport measurement on a Ni/piezoactuator hybrid structure with (a) I∥H and

(b) I ⊥H. The actuator is strained locally by a variation of the applied voltage Vp.

from B to C certainly increases the M component perpendicular to H as observed in

the Kerr images depicted in Figs. 6.7(c)(d). As a consequence the decrease of RC with

increasing magnetic field is more distinct than for RB. Above the coercive field, both

voltage curves overlap again. Accordingly the behavior of RC and RB for I ⊥ H can be

explained.

RB does not differ from RB at first glance, regardless the current orientation. However,

the Kerr image shown in Fig. 6.6(c) suggested, that local magnetization switching induced

by a voltage cycle is not reversible. Therefore, it was expected that RB equals RC, which

is in contradiction to the observed data.

In order to investigate this behavior more closely, the difference of Rlong at C and

B (ΔRlong = RC-RB) and at B and B (ΔRlong = RB-RB) was derived from the MTR

measurement data and is represented by the closed symbols in Figs. 6.12(c),(d). Moreover,

the obtained Kerr images at points B, C and B were evaluated quantitatively as also done

in Section 4.7. Therefore, a region of interest (ROI), which comprises the region of strain,

was defined first (cf. Fig. 6.12(e)). Then the intensity of all pixels belonging to the ROI

was summed in order to get the integral MOKE signal. This evaluation yields an effective

M averaged over all local domains, which then can be described with a Stoner-Wohlfarth

model. Of course this approach does not reflect the real magnetic microstructure, but

nevertheless this model has proven to describe the transport data accurately as outlined

above. Using the relation cos = M/Ms [45, 117] the angle between magnetization and

external field can be determined. Obviously, this angle equals the angle between M

and I for I∥H. For all obtained images at B, C and B this evaluation was done and the

result can be seen in Fig. 6.12(f), where cos2( ) is plotted against the magnetic field.

Let us first consider the cos2( ) graphs for B and B depicted in Fig. 6.12(f). For

0H < 3.5 mT and 0H > 11.5 mT the curves are basically identical. This behavior indi-


(b)

(d)

(f)

(a)

(c)

M

ROI

(e)

-20 -10 0 10 20396

398

400

402

Rlo

ng (m

Ω)

µ0H (mT)

I||H

RC

RB

RB

-20 -10 0 10 20

367

368

369

370

RB

RB

RC

Rlo

ng (m

Ω)

µ0H (mT)

I H

-20 -10 0 10 200.0

0.2

0.4

0.6

0.8

1.0

γ

H,I

M

BC

B

cos2 γ

µ0H (mT)

A B

CD

A,A B,B

C

-20 -10 0 10 20

-4

-2

0

2

4

I||H

RB-RB

RC-RB

∆R

long

(mΩ

)

µ0H (mT)

calculationMTR measurement

-20 -10 0 10 20

-2

-1

0

1

2

calculationMTR measurement

I H

∆R

long

(mΩ

)

µ0H (mT)

RC-RB

RB-RB

Figure 6.12: Results of MTR measurements in locally strained Ni applying sequence ◻ and for (a) I∥H

and (b) I ⊥ H. Plot of ΔRlong for (c) I∥H and (d) I ⊥ H. The closed symbols represent

the MTR measurement data, the open symbols represent the data calculated from the

Kerr images (see text). (e) Difference image obtained by Kerr microscopy. The ROI for

quantitative evaluation of Kerr images is depicted. The magnetization vector represents

the averaging over the whole magnetic substructure within the ROI. (f) Plot of cos2( )

versus 0H for B, C and B.


cates, that the magnetization rotation induced by Vp is reversible in this field regime. For

3.5 mT < 0H < 11.5 mT the curves differ, which means that the magnetization cannot

be rotated reversibly in this field range. This characteristic is in agreement with the qual-

itative analysis of the Kerr images shown in Section 6.1.4 which yielded no reversibility

regarding magnetization control by strain at magnetic fields close to the coercive field.

Thus reversible magnetization rotation is not possible within field range of 0Hc ± 4 mT.

Comparing the cos2( ) graphs for B and C (cf. Fig. 6.12(f)), the voltage sweep from B

to C induces a magnetization rotation away from the original state for 0H < 15 mT in the

depicted range, since both curves do not overlap in this field regime. For 0H > 15 mT,

the Zeeman energy dominates and thus the magnetization is aligned along the external

field regardless the applied strain.

With the knowledge of cos2( ), ΔRlong = RC-RB and ΔRlong = RB-RB can be calculated

according to Eq. (6.1) as:

RC −RB = (R∥ −R⊥) ⋅ (cos2 C − cos2 B) (6.4)

RB −RB = (R∥ −R⊥) ⋅ (cos2 B − cos2 B) (6.5)

The difference R∥−R⊥ can be approximated from the MTR data shown in Fig. 6.11. For

I∥H, R∥ is obtained directly as R∥ = Rlong(±60 mT) ≈ 401 mΩ (considering Vp = 0 V). For

the matter of simplicity, R⊥ is taken as the minima in the resistance curve at the coercive

field which yields R⊥ = Rlong(±10 mT) ≈ 395 mΩ. As a consequence, R∥ −R⊥ ≈ 6 mΩ. In

accordance, for I ⊥H the difference R∥ −R⊥ yields R∥ −R⊥ ≈ 3 mΩ.

ΔRlong = RC-RB and ΔRlong = RB-RB calculated from the MOKE data is displayed

with open symbols in Figs. 6.12(c),(d).

Comparing the calculated curves for ΔRlong (open symbols) with the measured curves

(closed symbols) for both current orientations, the general shape of both, calculated and

measured curve, is similar for RC-RB as well as for RB-RB. However, there are also several

discrepancies.

Regarding RC-RB, the piezoresistive effect has not been taken into account in the

calculated data, since the Kerr effect measurements are not sensitive onto piezoresistance.

This explains the difference of calculated and measured curve in magnetic saturation,

which is especially distinct in the I ⊥ H configuration. Apart from that, the shape of

both curves is basically equivalent except that the two extrema at the coercive field are

much more pronounced in the curve calculated from the MOKE data.

Accordingly, concerningRB-RB the discrepancy in the extrema around the coercive field

is even larger. Comparing the shape of both, measured and calculated curves, similarities

are present. However, from a quantitative point of view their features are very different.

Concluding, it is possible to reconstruct the general shape of the ΔRlong curve from

the MOKE measurement data especially for RC-RB, however there are still major dis-


crepancies, which are attributed to the simplifications that have been made regarding

the calculation of the ΔRlong data. First, the approximation of R∥ −R⊥ from the MTR

measurement curve in Fig. 6.11 is surely a considerable simplification. For the matter of

correctness, a proper simulation of the MTR data of Fig. 6.11 would certainly yield more

correct results for R∥ −R⊥. Second, the definition of the ROI in Fig. 6.12(e) is random

and must not be the right choice. The actual current paths are certainly more compli-

cated but this is not reflected by the choice of the ROI. Third, the Stoner-Wohlfarth

approach to average over the magnetic substructure in the ROI and thus neglecting any

domain structure of the ferromagnet might be to simple at this point. It has been shown

that domains play also a significant role in magnetotransport [110]. Finally, the varia-

tion of strain in locally confined regions might influence the current flow such that the

assumption of constant current geometry is erroneous.

Nevertheless, the above analysis has proven, that local magnetization control in

Ni/actuator hybrids can be corroborated by MTR measurements. A further important

result of this paragraph is that the possibility of reversible/irreversible control of M de-

pends upon the magnetic field. These findings are in agreement with the Kerr images of

Section 6.1.4.

6.2 Patterned Ni Electrodes on Piezoelectric Substrates

In this section a novel approach for local magnetization control is presented. So far,

magnetization switching in non-patterned ferromagnetic films was demonstrated. Piezo-

electric actuators served as substrates. In the following the direct control of a patterned

ferromagnet will be analyzed. In particular, the piezoelectric actuator used so far is

replaced by other piezoelectric substrates. The aim of this section is to show that in

principle anisotropy and magnetization control is possible in small scale samples if an

effective coupling between ferroelectric and ferromagnetic properties is achieved.


In the preceding experiments Ni has proved to be a promising candidate for hybrid

structures allowing voltage controlled ferromagnetism. Although its magnetostrictive

constant is smaller than the one of Fe50Co50 (cf. Chapter 3), the strain induced effects

on the magnetic properties were more distinct in Ni than in Fe50Co50 as discussed in

Section 5.1.3. Therefore, Ni was chosen to serve as the ferromagnetic constituent for the

novel hybrid structure design. However, different kinds of piezoelectric substrates, namely

PZT, LiNbO3 and BaTiO3, have been investigated on their effectiveness in magnetoelastic

coupling.

6.2 Patterned Ni Electrodes on Piezoelectric Substrates 89

V+

V-

200 µm

V+

V-

z

xy

(a) (b)

(c)

(d)

1 cm

Figure 6.13: (a) Schematic view of an untreated PZT-5H plate. (b) Illustration of patterned Ni electrodes

deposited onto a PZT plate. (c) Photograph of contacted Ni electrodes on a PZT disk. (d)

Microscope image of Ni electrodes on PZT. Surface imperfections are clearly visible.

Ni on PZT

PZT exhibits a very high inverse piezoelectric effect (cf. Chapter 3) and is thus an

ideal candidate for application in piezoelectric/ferromagnetic hybrids. Therefore, PZT-5H

plates fabricated by Morgan Electroceramics [66] were used as substrate. They come with

a diameter of 10 mm and a thickness of 0.35 mm. The top and bottom face is covered

by a metal electrode which allows to apply an electric field along z in the conventional

mode of operation as depicted in Fig. 6.13(a). Thereby the dominant axis of elongation

and also the intrinsic polarization is aligned along the z-axis. For the purpose of this

thesis, the original top and bottom electrodes had to be removed prior to the deposition

of ferromagnetic electrodes onto one face of the substrate. Therefore, the faces of the

PZT disks were polished with an abrasive paper with smallest available graining (5 µm)

first. Additionally the substrate was polished with a 1 µm diamond suspension. However,

even after an extensive polishing process the surface of the PZT plate was still very rough

and porous as can be seen in Fig. 6.13(d). Even polishing in the TUM crystal laboratory

did not bring any major improvements.

Nevertheless, Ni electrodes were deposited onto the x-y-face of the plate as seen

schematically in Fig. 6.13(b). Fabrication of this electrode configuration allows to create

electric fields within the x-y-plane and thus it can be assumed that also lateral polariza-


Sample Substrate Electrode geometries l∣w∣s

M090522A PZT 1000∣50∣50, 1000∣100∣100, 1000∣200∣100M090716A PZT 1000∣50∣50, 1000∣100∣100, 1000∣200∣100BTOM1 BaTiO3 1000∣50∣50LNOM1 LiNbO3 1000∣50∣50, 1000∣100∣100, 1000∣200∣100

Table 6.1: Overview of prepared samples for local magnetization control.

tion components are generated. Consequently lateral stress can be exerted by making use

of the d33 effect. The geometry of the electrode configuration is very important, since it

determines the device performance and stress distribution [118]. On the one hand a large

spacing between the electrodes improves the homogeneity of the electric field and thus

the strain between the electrodes. On the other hand large spacings require large applied

voltages to efficiently produce strain. Three different electrode geometries with length l,

width w and spacing s have been designed and fabricated; l∣w∣s in µm: I) 1000∣50∣50, II)

1000∣100∣100, III) 1000∣200∣100.

Firstly, optical lithography is used to generate the desired mask pattern onto one x-

y-face of the plate. After the lithography, polycrystalline Ni is deposited onto the PZT

plate via electron beam evaporation at a base pressure of approximately 1 × 10−7 mbar

and with a deposition rate of 1-2 A/s up to a final thickness of 100 nm. The photoresist is

removed by doing a lift-off in acetone under exposure to short ultrasound pulses. At last

the thus obtained electrodes are bonded onto contact pads as depicted in Fig. 6.13(c).

Details about the prepared samples can be found in Tab. 6.1.

Ni on BaTiO3 and LiNbO3

Besides PZT, also BaTiO3 and LiNbO3 were used as piezoelectric substrates. The prop-

erties of these two materials have been reviewed in Chapter 3. Compared to the PZT

plate, these substrates did not need a special treatment prior to the deposition of Ni apart

from cleaning. The lithography and evaporation process was equivalent to the method

presented above. Exemplary, the result for BaTiO3 can be seen in Fig. 6.14. The sample

was mounted onto a chip carrier and the electrodes were bonded (cf. Fig. 6.14(a)). In

contrast to PZT, the surfaces of the used BaTiO3 and LiNbO3 substrates are smooth and

thus the quality of the patterned Ni electrodes is superior (cf. Fig. 6.14(b)).

6.2.2 Polarization and Strain Control

In order to achieve local magnetization control via magnetoelastic coupling, the ability

of local polarization and strain generation in the substrates has to be verified. In the

present electrode structure it is assumed that the electric field penetrates laterally onto the

adjacent surface layers of the piezoelectric substrate and is distributed inhomogeneously.


200 µm

(a) (b)

Figure 6.14: (a) Photograph of Ni electrodes patterned on a BaTiO3 substrate. The sample is mounted

onto a chip carrier. (b) Microscopy image of Ni electrodes on BaTiO3.

It has been shown for similar electrode designs, that three main regions regarding the

electric field distribution have to be considered [118, 119]: First, the electric field is

homogeneous and parallel to the surface between the patterned electrodes and close to

the surface. Second, at the electrode edges the field concentration is largest. Finally,

below the electrodes there is a region of depletion, since the electrodes are equipotential

areas. Having these considerations in mind the prepared samples were investigated upon

local polarization control.

In Fig. 6.15(a) an exemplary contact scheme of the electrodes is depicted. During the

measurement voltages were applied to the electrodes and the current was measured using

the standard two point technique. The result of an INi measurement of Ni on PZT in

a 1000∣50∣50 geometry can be seen in Fig. 6.15(b). Apart from the virgin curve, dis-

tinct peaks can be seen at VNi,pol ≈ ±100 V which correspond to displacement currents.

These peaks were reproducibly observed in consecutive cycles. Neglecting any inhomo-

geneous electric field distribution at the electrode edges and assuming a uniform electric

field within the PZT plate in between the patterned electrodes, the corresponding electric

field values can be estimated as Epol = VNi,pol/d. d = 4×50 µm denotes the spacing between

the contacted electrodes excluding the width of the three inner electrodes. Thus lateral

polarization reversal of the PZT plate can be achieved with an electric field of approxi-

mately Epol ≈ ±500 V/mm, which is in good agreement with the value Epol ≈ ±420 V/mm

measured for the PZT in the PSt 150/2 × 3/5 piezoelectric actuators in Section 6.1.2.

Equivalent measurements were done with different contact schemes and in different

electrode geometries for PZT. It was found that the spacing of PZT between the contacted

electrodes has a great influence on the measurement of the displacement current, as

expected. In general, the following observation was made. If the spacing d between the

contacted electrodes was greater than 200 µm, no displacement currents were found. This


VNi

P

A

(a)

- 2 0 0 - 1 0 0 0 1 0 0 2 0 0

- 1 0

0

1 0

I (nA)

V N i ( V )

P

P

(b)

Figure 6.15: (a) Schematic illustration of poling and field generation in Ni electrodes patterned on piezo-

electric substrates. (b) I(VNi) curve obtained with patterned Ni electrodes on PZT in the

1000∣50∣50 geometry contacted as depicted in (a). The distinct peaks at VNi,pol = ±100 V

correspond to the displacement currents indicating that lateral polarization control is pos-

sible (sample M090716A).

is likely a consequence of the limited voltage supply by the source meter.

Doing the same measurements on Ni electrodes patterned on LiNbO3 and BaTiO3, no

displacement currents were found for any of the investigated electrode geometry. In case

of LiNbO3 no displacement current is expected, since LiNbO3 is a pyroelectric material

(cf. Chapter 3). For BaTiO3, an in plane coercive field of Hc ≈ 50 V/mm was reported

in [73]. Although the geometry of the electric field distribution in the present electrode

pattern is undefined, there should be regions between the electrodes with a uniform

electric field [118, 119] and thus one would expect polarization reversal and displacement

current. Thus the observed behavior for BaTiO3 cannot be explained.

Besides the state of polarization the control of strain is of fundamental interest. The

electric field distribution discussed above results in the generation of inhomogeneous

strains. The strain is expected to be uniform between the electrodes. Maximum strains

should be generated at the electrode edges.

To study the strain variation, a similar approach as in Chapter 5 was chosen. Strains

were detected by means of Kerr imaging due to strain induced birefringence in the PMMA

or MgO buffer layer underneath the ferromagnet. Here, no buffer layer is present. How-

ever, the refractive indices of all used piezoelectric substrates change as a function of the

applied electric field as a consequence of the linear electro-optic effect (Pockels effect)

[120, 121, 122, 123, 124]. Thus strain variation in the substrate should be manifested

by contrast changes in the Kerr images as a function of the electric field. Therefore, a

large magnetic field (0H = −50 mT) was applied to the PZT based sample (M090716A)

to exclude any magnetic contribution to the detected birefringence. The Ni electrodes


-150 -100 -50 0 50

-3.0

-1.5

0.0

1.5

referenceimage

image (I)I (

nA)

VNi (V)

image (II) 1000|200|100

µ0H=-50 mT

VNi

H

(a)

(I)

(b)

(II)200 µm

(c)

Figure 6.16: (a) Measured I(VNi)-curve of Ni electrodes on PZT for 0H = −50 mT in the 1000∣200∣100

geometry and contact scheme as depicted in the figure inset. The reference image was

recorded at VNi = −160 V, image (I) at VNi = +30 V and image (II) at VNi = −160 V. (b)

Difference image (I), the red and blue lines indicate the contacted electrodes, the white

lines the non-contacted floating electrodes. The observed contrast shows that the strain

state has changed. (c) Difference image (II) at VNi = −160 V exhibits no contrast pattern.

The original strain state is again reached.

in the 1000∣200∣100 geometry were contacted as schematically illustrated in the inset of

Fig. 6.16(a). Then a I(VNi) cycle starting from VNi = −160 V was monitored. Simul-

taneously, Kerr images were recorded applying the difference imaging technique. The

resulting I(VNi)-curve is depicted in Fig. 6.16(a) indicating the voltages to the corre-

sponding difference images depicted in Fig. 6.16(b),(c). The red and blue lines in the

images represent the contacted electrodes, the white lines the floating electrodes respec-

tively. Sweeping the applied voltage from VNi = −160 V → +30 V the state of exerted

strain should change. This effect is manifested in Fig. 6.16(b), because a clear contrast

pattern in between the contacted electrodes is visible, whereas in the image part on the

right side the contrast has not varied significantly. Thus the applied voltage has gener-

ated strain locally in the PZT substrate. After the return sweep, the contrast pattern

vanishes completely again (cf. Fig. 6.16(c)), since present and original strain state are

equivalent. This observation proves that this electrode pattern onto the PZT substrate

is capable of local strain generation. The same characteristics were observed in BaTiO3

based samples. However, the LiNbO3 substrate did not reveal any local strain genera-

tion. This behavior is attributed to the low d33 coefficient of LiNbO3 compared to PZT

or BaTiO3 (cf. Chapter 3). Unfortunately, the Kerr technique does not straightforwardly

allow to quantify the strain and thus no strain comparison regarding different electrode

geometries or different piezoelectric substrates has been done.


-10 0 10

-1

0

1

VNi=

+180

V

VNi= -30 V

M/M

s

µ0H (mT)

Hc for V↑

VNi

H1000|50|50

(a)

-10 0 10

-1

0

1

VNi= -160 V

M/M

s

µ0H (mT)

VNi= +30 V

VNi

1000|200|100H

Hc for V↑

(b)

Figure 6.17: M(H) hysteresis curve of Ni on PZT under applied voltages VNi at the patterned elec-

trodes for different geometries and contact schemes. (a) l∣w∣s: 1000∣50∣50, contacted elec-

trodes frame three non-contacted electrodes. (b) l∣w∣s: 1000∣200∣100, VNi applied between

neighboring electrodes (sample M090716A). The strain induced shift of the coercive field

is indicated in both figures.

6.2.3 Strain Induced Shift of the Coercive Field

Having confirmed the ability of local strain generation in PZT and BaTiO3 substrates

mediated by patterned electrodes, the influence of strain onto the magnetic properties

of the patterned Ni electrodes is analyzed in the following. The applied experimental

technique is again magneto-optic spectroscopy. In Chapter 4 the nominal resolution of

the Kerr microscope was calculated as 8 µm. Consequently it should be possible to resolve

the designed electrode patterns with a minimum width and spacing of 50 µm.

At first, Ni on PZT in the 1000∣50∣50 geometry was investigated. Two electrodes were

contacted embedding three floating electrodes in between as schematically depicted in

the inset of Fig. 6.17(a). The measurement procedure was equal to the one described

in Chapter 5. At constant voltage VNi the M(H) was recorded. The magnetic field was

oriented perpendicular to the stripe electrodes (cf. Fig. 6.17(a)). In order to evaluate

the Kerr rotation properly, a region of interest was defined which comprised the two

contacted electrodes as well as the electrodes in between.

The resulting hysteresis curves for VNi = +180 V and VNi = −30 V are shown in

Fig. 6.17(a). Evidently there is a small shift of approximately 1 mT in the coercive

field, which was confirmed in several measurements. Thus, this shift has to be attributed

to the applied strain.

The same result was obtained for a 1000∣200∣100 structure on PZT depicted in

Fig. 6.17(b). This time neighboring electrodes were contacted and the voltage range

(VNi = −160 V and VNi = +30 V) was on the negative branch of the piezoelectric hystere-

sis. The magnetic field orientation was again perpendicular to the stripe electrodes as

6.3 Summary 95

depicted in the figure inset. Once more, there is a shift in the coercive field in the M(H)

curves for different applied voltages, which has approximately the same magnitude as

above but is different in sign.

This sign difference regarding the shift of the coercive field observed in Fig. 6.17(a)

and Fig. 6.17(b) can be rationalized by considering the ferroelectric hysteresis of the PZT

substrate as discussed in Chapter 2 and schematically depicted in Fig. 2.4. The M(H)

measurement of the 1000∣50∣50 patterned electrodes (cf. Fig. 6.17(a)) was prepared on

the positive hysteresis branch, whereas in the 1000∣200∣100 geometry (cf. Fig. 6.17(b)) the

PZT substrate was prepared on the negative hysteresis branch. Thus the sign difference

of the shift of the coercive field is consistent with the expected strain characteristic of the

piezoelectric substrate.

To conclude, the obtained results prove, that on application of voltages the coercive

field shifts. Thus, magnetoelastic coupling is indeed possible to some degree in the novel

Ni/PZT hybrid structures. However, in BaTiO3 and LiNbO3 based hybrids no coercivity

shift in dependence of the applied voltage VNi could be detected and therefore the data is

not shown here. This might be reasoned by their lower d33 coefficient compared to PZT

(cf. Chapter 3). Kerr imaging was also applied, but the structure size of the electrodes is

so small, that even if the highest possible magnification is used no statement about the

magnetic substructure can be made and thus the presentation of Kerr images is omitted.

Nevertheless, the novel design of patterned electrodes onto PZT disks has proven to

work in principle. In order to improve the efficiency of the magnetoeleastic coupling,

more sophisticated methods for sample preparation would be necessary, like for example

an interdigital electrode design. Moreover, the choice of the piezoelectric substrate also

plays a decisive role. PZT has proven to be the most promising candidate.

6.3 Summary

In this chapter the feasibility of local magnetization control by means of electric fields

in multiferroic hybrid structures was demonstrated. Hybrids based on piezoelectric ac-

tuators were modified and allowed local magnetization switching as observed with the

Kerr technique. This result was corroborated by magnetotransport measurements. Fi-

nally, a novel hybrid architecture consisting of patterned nickel electrodes on piezoelectric

substrates was proposed and first experiments proved its potential for local strain and

magnetization control.

Chapter 7

Conclusion and Outlook

The aim of this thesis was to investigate multiferroic hybrid structures focusing on mag-

netization control by means of electric fields on macroscopic as well as on microscopic

scales. This topic was motivated by the great fundamental and technological interest in

electric field controlled ferromagnetism at room temperature, which would substantially

facilitate scaling of spintronic devices to small dimensions. Magneto-optical Kerr imaging

was applied to study and illustrate the processes within the magnetic substructure of the

prepared multifunctional hybrid structures.

Establishment of Spatially Resolved Kerr Imaging

An existing magneto-optical Kerr setup was redesigned and extended to allow for spatially

resolved magneto-optical Kerr measurements. Additional components like an adequate

CCD camera, a LED-based light source and a quarter wave plate have been integrated

and the imaging procedures optimized in order to observe magnetic domains. With the

novel Kerr setup lateral resolutions on the order of 10 µm can be achieved considering

magnifications on the order of one. Therefore, it can be denoted a low resolution Kerr

microscope. As shown in Chapter 4, a characterization of the setup concerning imaging

contrast, noise and sensitivity has been implemented. For optimal contrast conditions

the difference imaging technique was applied and the settings of the polarization optics

has been discussed. The system’s sensitivity is limited by photon noise. A determination

of the minimum resolvable Kerr rotation in integral M(H) measurements yielded the

value of Δ'k ≈ 0.15′′ and thus beats the sensitivity of the original MOKE setup [45].

Moreover, the capabilities of the established setup in imaging of thin ferromagnetic films

were demonstrated and also the possibility of quantitative evaluation of domain patterns

was discussed.

Electric Field Control of Ferromagnetism

In Chapter 5 hybrid structures consisting of a ferromagnetic thin film and of either a

piezoelectric actuator or a BaTiO3 single crystal have been studied intensively by means

97

98 Chapter 7 Conclusion and Outlook

of the established magneto-optical Kerr setup. The influence of strain onto the magnetic

hysteresis was analyzed and it was found that the ferromagnetic properties of all sam-

ples exhibit strain dependence. The origin of this strain coupling is the magnetoelastic

effect and its strength depends crucially on the strain coupling of the piezoelectric and

ferromagnetic material.

Therefore, two different preparation techniques of the actuator/ferromagnet hybrids

have been compared by means of voltage dependent M(H) measurements, domain evo-

lution and magnetization switching. It was found that strain coupling in samples pre-

pared by direct evaporation of ferromagnet onto piezoelectric actuator is superior than

in samples prepared by the cementing technique. Apart from that, the capability of

electric field controlled magnetization switching in these large scale samples was investi-

gated. However, the application of strain also induces contrast changes in the Kerr images

resulting from strain induced birefringence or surface effects in the buffer layer of the ac-

tuator/ferromagnet hybrid structure. To exclude strain mediated contrast changes, two

measurement sequences (sequence ◻ and sequence ) have been proposed and successfully

applied to the actuator based samples as well as to the BaTiO3 based heterostructures.

In sum, all prepared samples allowed magnetization switching by means of electric field

sweeps which has been detected and visualized with the Kerr technique.

Local Magnetization Control

The feasibility of local magnetization control has been discussed in Chapter 6. Actuator

based hybrid structures were manipulated to allow for local strain control. This modifi-

cation proved to enable local magnetization control by applying local strains generated

by the piezoelectric effect. As a consequence, local switching of the magnetization by

means of electric fields has been observed. Moreover, magnetotransport measurements

were applied simultaneously to MOKE measurements and they confirmed magnetization

rotation induced by local strain. However, the scalability of the electric field controlled

ferromagnet is limited by the geometry of the piezoelectric actuator.

In order to achieve substrate-independent scaling to smaller dimension a novel archi-

tecture consisting of patterned ferromagnetic electrodes on piezoelectric substrate was

proposed and first samples were fabricated. PZT, BaTiO3 and LiNbO3 have been used

as piezoelectric substrates and nickel as the ferromagnetic constituent. First experiments

proved, that local strain generation is possible in the novel design and also successful mag-

netoelastic coupling has been observed by means of magnetic hysteresis measurements.

Outlook

Beyond the outlined achievements, further interesting implementations, applications and

fundamental studies exist. In the following a brief outlook on possible future projects is

99

given:

Although the established magneto-optical setup allows domain imaging and character-

ization of large scale samples prepared at the WMI, there are further issues that could be

implemented to improve the system. First, the light source and collimation optics cur-

rently integrated in the setup should only be a temporary solution, since homogeneous,

collimated illumination of sufficient intensity is one of the key-points to successful domain

visibility. Second, as mentioned in Chapter 4 the resolution is limited by diffraction, be-

cause simple wide angle objective lenses are used for imaging. In order to achieve higher

resolution together with considerable image brightness the use of microscope objectives

and eyepieces is indispensable. A new design of the setup involving smaller working dis-

tances, microscope optics and a well collimated incoherent light source would certainly

increase the resolution by at least an order of magnitude and thus allow high resolution

Kerr microscopy.

From the experimental point of view this thesis brought up some further ideas to aim

at the realization of electric field controlled ferromagnetism on all scales. Regarding the

actuator/ferromagnet hybrid structures, I can think of two major experiments that could

not be achieved in the framework of this thesis. First, a closer examination of the strain

induced contrast pattern presented in Chapter 5 would be appropriate. This anomalous

contrast pattern arises from birefringence effects in the buffer layer or from surface effects.

Inserting an intermediate buffer layer of sufficient thickness, like a gold thin film, would be

sufficient to rule out birefringence effects and thus clarify this open question. Concerning

local magnetization control experiments on actuators with integrated magneto-transport

measurements, well defined Hall-bar structures could finally resolve all doubts about local

magnetization control, since quantitative transport measurements or angular dependent

magnetoresistance measurements [125] would be possible.

The new architecture consisting of patterned ferromagnetic electrodes on piezoelectric

substrates proposed in Chapter 6 proved to be a substantial alternative for local magne-

tization control. PZT turned out to be the most promising candidate for the piezoelectric

constituent. However, surface quality of the used PZT plates was unsatisfactory. There-

fore, experiments using lead magnesium niobate-lead titanate (PMN-PT) single crystals

as piezoelectric substrates are planned. PMN-PT has piezoelectric coefficients which are

comparable to the ones of PZT, but the surface quality is superior. Thus the quality

of the magnetic thin films would be improved and an amplified coupling between the

piezoelectric and the ferromagnetic phase is expected.

In conclusion, the concept of multiferroic hybrid structures aiming at an electric field

control of ferromagnetism is still under vigorous research and it offers many open ques-

tions and unsolved applications. However, the great potential of these multifunctional

hybrid structures for fundamental research and possible technological applications has

100 Chapter 7 Conclusion and Outlook

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Acknowledgment

At this point I want to thank all the people who contributed to this thesis and supported

me during my time as diploma student at the Walther-Meissner-Institut:

Prof. Dr. Rudolf Gross, for giving me the opportunity to accomplish this thesis at the

WMI and for his supervision of this work. When looking back on this year as diploma

student, I will always remember it as very pleasant and instructive time!

Dr. Sebastian Gonnenwein, the mentor of this thesis, for his grand support and ad-

vice. His richness of ideas together with his infinite enthusiasm were important stimuli

regarding this thesis but also regarding my development as a physicist. I am grateful

for the many hours he spent in the lab together with me to discuss the experiment or

measurement results.

I am especially thankful to Andreas Brandlmaier, who was an excellent guide during

my time at the WMI. He introduced me to all experimental issues and it’s due to his

everlasting patience and motivation that I acquired all the experimental skills necessary

for this work. I also profited from the numerous discussions with him in which his aptitude

for criticism and foresight opened my eyes for novel approaches regarding experiments or

result interpretation.

Stephan Geprags, in first place for the preparation of the BaTiO3 based heterostructures

and his support regarding their measurement and result interpretation. On top of that, I

gratefully appreciate his humorous and friendly personality but also his professional skills

which he was always eager to share with me.

Dr. Matthias Opel, for his encouragement and motivation during the preparation of this

thesis.

All other members of the Magnetiker group, who were without exception always willing

to help concerning experimental problems or any other issue.

Thomas Brenninger, who was always helpful if problems with the EVAP occurred and

owing to his effort I always found excellent conditions for the thin film preparation.

Robert Muller, for the additional components he built for the new MOKE setup.

109

Special thanks to my office mates and “fellow sufferers”, in person Daniel, Michi, Timo,

Chris, Hajo, Themis and Martin, for sharing such a good time in and out of the office. I

wish you all the best for your future.

Last but not least, I want to say thank you to my family and to Martina, who were

always there for me and gave me the best imaginable support. Vielen Dank!

110

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