Magnetism of ultrathin films: Theory and Experiment

1/23Freie Universität Berlin UC Irvine 26.-28. May 2010

Magnetism of ultrathin films:Magnetism of ultrathin films: Theory and ExperimentTheory and Experiment

Klaus Klaus BaberschkeBaberschke Institut fInstitut füür Experimentalphysikr Experimentalphysik

Freie UniversitFreie Universitäät Berlint Berlin


New and fundamental aspects are found in nanomagnetism with no counterpart in bulk materials

281. WE-Heraeus-Seminar “Spin-Orbit Interaction and Local Structure

in Magnetic Systems with Reduced Dimensions“ June 2002 in Wandlitz


Yi Li, K. B., PRL 68, 1208 (1992)

For thin films the Curie temperature can be manipulated

thickness (ML)0 5 10

0

200

400

600

Ferromagn.

Paramagn.finite sizeNi(001)/Cu(001)

M

M

T=300Kd=7.6

P. Poulopoulos and K. B. J. Phys.: Condens. Matter 11, 9495 (1999)

/1

)()()(

cd

TdTT

C

CC


2 4 6 8 10 12 14 16 18-0.3

-0.2

-0.1

0.0

0.1

vacu

um12 ML Ni

Cu(1

00)s

ubst

rate

Cu(100)/Ni12 / Vac

unrelaxed relaxed -2.5 % relaxed -5.5 %

Eb(m

eV)

layer

C. Uiberacker et al. Phys. Rev. Lett. 82, 1289 (1999)

“volume”, and “surface” MAE

vacuum

substrateKS2

KS12= -3.2%

1= +2.5%

K = K + 2i iV Ki

S

d

New artificial structures, like tetragonal (fct) Ni, Fe, Co are grown

Ni 2.49 ÅCu 2.55 Å


Interlayer Exchange Coupling and f (T)

J int

er

TCNi

TCCo

IEC

Ni

Co

Cu

full trilayer grows in fct structure

0 200 400

x 1.5

6000

Cu(001) d =1.81 ij Å

d =1.70 ij Å

Ni9

Cu Ni6 9

Ni Cu Ni8 6 9

Energy (eV)

LEED

I(V)

Inte

nsity

(arb

. uni

ts)

R. Nünthel, PhD Thesis FUB 2003

A trilayer is a prototype to study magnetic coupling in multilayers. What about element specific Curie-temperatures ?

Two trivial limits: (i) dCu = 0

direct coupling like a Ni-Co alloy (ii) dCu = large

no coupling, like a mixed Ni/Co powder

BUT dCu

2 ML

?


M (k

A/m

)

0 30 60 90 120 150 180 210 2400

100

200

300

1200

1600

T (K)

Cu (100)

2.8 ML Ni

3.0 ML Cu

2.0 ML Co

Cu (100)

2.8 ML Ni

3.0 ML Cu

TC,Ni

T*C,Ni

38 KC,NiT

T*Ni

M (a

rb. u

nits

)

TCNi = 275K

2.8 ML Cu4.8 ML NiCu(001)

150 200 250 300 350

2.8 ML Co2.8 ML Cu4.8 ML NiCu(001)

T (K)

0

0.25

0.50

0.75

1.75

2.00

37K

P. Poulopoulos, K. B., Lecture Notes in Physics 580, 283 (2001) A. Scherz et al. PRB 65, 24411 (2005)

The large shift of TCNi can NOT be explained

by the static exchange field of Co.


Crossover of MCo (T) and MNi (T)

Two order parameter of TCNi and TC

Co

A further reduction in symmetry happens at Tclow

A. Scherz et al. J. Synchrotron Rad. 8, 472 (2001)

760 800 840 880-60

-40

-20

0

20

x2

Norm

.XM

CDDi

ffere

nce

(arb

.uni

ts)

Photon Energy (eV)

Cu(001)

2.1ML Cu

4ML Ni

Cu(001)

2.1ML Cu

4 ML Ni

1.3ML Co

-edgesL3,2Co Ni -edgesL3,2

45K

0 40 80 120 160 200 2400

100

200

300

500

750

1000

Mag

netiz

ation

M(G

auss

)Temperature (K)

MNieasy

MCoeasy

H ,ext k

MNiAFM

[110]

[100]

Msat

M sat

2

[110

]

L. Bergqvist, O. Eriksson J. Phys. Conds. Matter 18 ,4853 (2006)


J =J [ ]inter inter,0 1-(T/T )C 3/2

P. Bruno, PRB 52, 411 (1995); V. Drchal et al. PRB 60 , 9588 (1999) N.S. Almeida et al. PRL 75, 733 (1995)

J =J inter inter,0 [ ]T/T0

sinh(T/T )0

T = hv / 2 k d0 F B

Interlayer exchange coupling and its T-dependence.


in-situ FMR in coupled films

J. Lindner, K. B. Topical Rev., J. Phys. Condens. Matter 15, R193-R232 (2003)

in-situ UHV-experiment

theory

FMR

IEC => f(T) in µeV/ particle

Advantage: FM and AFM


Ni7 Cu9 Co2 /Cu(001) T=55K - 332K

(Fe2 V5 )50 T=15K - 252K, TC =305K

0 2000 4000 6000 80000

10

20

T3/2

T3/2

T5/2J (µ

eV/a

tom

)in

ter

v =2.8 10 cm/sF8

v =2.8 10 cm/sF 7

T=294K

0 0.2 0.4 0.6 0.80

50

100

150

J (µ

eV/a

tom

)in

ter

(T/T )C3/2

(T/T )C3/2

(T/T )C5/2

v =5.3 10 cm/sF6


J(T)

1- A(d)Tn , with n 1.5

A(d)

const. (interface) A(d)

linear function (electronic bandstructure)

A(d)

osc. function (spin wave excitation)


See yesterdays talk by Talat Rahman


constantKV

0 0.05 0.10

10d(ML) 57

0.15 0.20-20

-15

-10

-5

0

5

10

15

20

25

Ni vacuum

Ni/Cu(001)

Ni + Cu capNi + O surfactant

t=0.752 M 2

1/d (1/ML)

K (

µeV

/ato

m)

2

10.8

7.6

7.3

6.84.9

-107

-59

-81

-70-17

Ni/vacuum

Ni/Cu

Ni/CO (van Dijken et al.)

(van Dijken et al.)

(surfactant)Ni/ONi/H2

Interface KS ( eV/atom) d C (ML)

J. Lindner et al. Surf. Sci. Lett. 523, L65 (2003)

Changes of KS shift the spin reorientation transition dC

Manipulation of surface MAE, KS by adsorbed molecules, metal cap and surfactant growth

K. B. Handbook of Magnetism and Advanced Magnetic Materials, Vol. 3 Ed. Kronmüller and Parkin, 2007 John Wiley & Sons, Ltd.

K = K + 2i iV Ki

S

d

KNi cubic


Results of ab initio calculations

clean Ni

O/Ni

0

10

20

MA

E (m

eV)

X

O-induced surface state seen in the vicinity of X-point is responsible for change in MAE

MAE along X axis

0

10

-10

20

30

40

0 0.02 0.04 0.06 0.08 0.1 0.12

MA

E (µ

eV /

atom

)

1/d (1/ML)

O/Ni /On

Cu /Ni5 n

clean Nin

R. Q. Wu & coworkers Phys. Rev. Lett. 92, 147202 (2004)

Nin slabs, n = 9, 11, 13: clean, Nin Cu5 superlattice, and c(2x2) O/Nin on each side


effdd Hmm

t

Gilbert damping

Landau-Lifshitz-Gilbert equation(1935)

t

ddmm

Bloch-Bloembergen Equation (1956)

2

,,eff

,

1eff

)(d

d

)(d

d

Tm

t

mT

Mm t

m

yxyx

yx

Szz

z

Hm

Hm

spin-spin relaxation (transverse)

spin-lattice relaxation

(longitudinal)

Mz =const.

|M|=const.M spirals on a sphere into z- axis

Spin Dynamics: Damping and Scattering


Gilbert damping versus magnon-magnon scattering.

In nanoscale magnetism path 2 has been discussed very very little.

Mostly an effective damping (path 1) is modeled/fitted.

Path 3: magnon-phonon scattering, see Bovensiepen PRL 2008


k||

(k )||

FMR

k|| c< k|| c>

H ( ) = Gil G2MS

0 2 S B

2

S

= (2K - 4 M ), =( /h)gK - uniaxial anisotropy constantM - saturation magnetization

H ( ) = arcsin2Mag 2 2 1/2+( /2) ] - 0 0/2 2 2 1/2+( /2) ] + 0 0/2

1 = _ M MMS

G2(M H ) eff ( )M t t+

Landau-Lifshitz-Gilbert-Equation

Gilbert-damping ~

2-magnon-scattering

FMR Linewidth - Damping

R. Arias, and D.L. Mills, D.L. Mills and S.M. Rezende in‘ ‘ , edt. by B. Hillebrands and K. Ounadjela, Springer Verlag

Phys. Rev. B , 7395 (1999);

Spin Dynamics in Confined Magnetic Structures

60

viscous damping, energy dissipation

Which (FMR)-publication has checked (disproved) quantitatively this analytical function?


• Gilbert damping contribution: • linear in frequency• two-magnon excitations (thin films):

non-linear frequency dependence

0

100

200

H

(Oe)

Hinhom

H0*

0 20 40 60 80/2

(GHz)

H

inhomogeneous broadening

HGilbert +Hinhom

H2-magnon

H

R. Arias et al., PRB 60, 7395 (1999)

2/)2/(2/)2/(arcsin)(

02

02

02

02

magnon2

H

eff0with M

K. Lenz et al., PRB 73, 144424 (2006)


G H0

(kOe) (108 s-1) (108 s-1) (10-3) (Oe)Fe4V2 ; H||[100] 0.270 50.0 0.26 1.26 0Fe4V4 ; H||[100] 0.139 26.1 0.45 2.59 0Fe4V2 ; H||[110] 0.150 27.9 0.22 1.06 0Fe4V4 ; H||[110] 0.045 8.4 0.77 4.44 0Fe4V4 ; H||[001] 0 0 0.76 4.38 5.8

• two-magnon scattering observed in Fe/V superlattices –

• J. Lindner et al., PRB 68, 060102 (2003)

0 50 100 150 2000

200

400

HP

P(O

e)

f (GHz)

0 4 80

40

80

15 Oe !

real relaxation – no inhomogeneous broadening

two-magnon damping dominates Gilbert damping

by two orders of magnitude:

1/T2 ~109 s-1 vs. 1/T1 ~107 s-1

G

isotropic dissipation and anisotropic spin wave scattering


Angular- and frequency-dependent FMR on

Fe3 Si binary Heusler structures epitaxially grown on MgO(001)

d = 40nmKh. Zakeri et al.

PRB 76,104416 (2007) PRB 80, 059901 (2009)

Angular dependence at 9 and 24 GHz

(26 –53) • 107 sec-1, anisotropicG

5 • 107 sec-1, isotropic

A phenomenological effective Gilbert damping parameter

gives very little insight into the microscopic relaxation and scattering .


Doug, we wish you all the best !


Magnetism of ultrathin Ferromagnets: Theory and Experiment

Klaus Baberschke

Institut für Experimentalphysik, Freie Universität Berlin,

Arnimallee 14, D-14195 Berlin, Germany

Ultrathin films of few atomic layers thickness only, are a new type of “designer materials”. They have no counterpart in bulk magnetism; they offer the opportunity to study new fundamental aspects of magnetism: The critical temperature Tc changes as function of the thickness from

Tcbulk to zero. Modification of the n.n. distance by few hundreds of Å may change the magnetic part of the free energy by orders of magnitude. In multilayer ferromagnetic- and antiferromagnetic-coupling can be manipulated via the spacer thickness. The unusual static properties as well as

dynamic characteristics (magnons) are investigated by theory and experiment. Recent specific example will be discussed1,2. This field of low dimensional magnetism demonstrates the very successful collaboration between theory and experiment, and gives some insight for the

fundamental understanding of magnetism.

1 D. L. Mills and S. M. Rezende in Spin dynamics in confined magnetic structures II Topics in Applied Physics vol. 87, p.27 Springer 2003

2 K. Baberschke in Handbook of magnetism and advanced magnetic materials vol. 3, p.1617 John Wiley & Sons 2007

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UCI 28.5.2010

Magnetism of ultrathin films: Theory and Experiment

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