Probing microscopic magnetic dots and their periodic arrays with ferromagnetic resonance G.N....

Probing microscopic magnetic dots and their periodic arrays with ferromagnetic resonance

G.N. Kakazei Institute of Materials Science of Madrid, CSIC

Institute of Magnetism National Academy of Sciences of Ukraine, Kiev

Tim MewesMINT/Department of Physics and Astronomy, University of Alabama, USA

Phil WigenDepartment of Physics, Ohio State University, Columbus, USA

Ferromagnetic Resonance

H0

µ

Hrf

natural response

driven response

Precession and relaxation of M in response to an applied field H.

Lorentzian absorption line typical of FMR showing microwave power absorption as a function of swept bias field.

ω = 2πf = γB

0

1HM

t

M

Ferromagnetic resonance spectrometer

X-band : 9-10 GHz

K-band : 24-25 GHz

Q-band 34-36 GHz

)(sinsincoscos2

)coscossinsin(sin22

1222

Hus

HHs

KKM

HME

Calculation of the angular dependence for thin film

0E

s

us M

KMHHH

24 where,cossin)sin( effeffH

22

22

22

2

2

sin

1

EEE

M s

1st : Zeeman; 2nd : demagnetization energy

3rd : out-of-plane anisotropy 4th : in-plane uniaxial anisotropy

If in-plane uniaxial anisotropy is absent or negligible y

x

zz’

Ms

H

θ1

θH

From this equation we can find equilibrium θ can be found for each particular H

cos)cos(

2cos)cos(

eff

eff

2

HH

HH

H

H

g=2.2

Ms (from SQUID)=1.3103 emu/cm3

Ku=-4.3 105 erg/cm3

easy plane type

Micro-fabrication process (lift-off)

Exposed Areas

Double Layer Resist Spin-coating

EB Patterning

Resist Development

EB Deposition (1 A/sec) (FeNi target)

Lift-off process FeNi circular dot

Obtained circular dot array (AFM and SEM)

Si substrate

Permalloy,1 m,

t = 50 nm

Magnetic Vortex State in circular ferromagnetic dot

Magnetization reversal due to formation of the magnetic vortex state in circular dot

-150 -100 -50 0 50 100 150

-1.0

-0.5

0

0.5

1.0 (e)

(c)

(d)

(b) (a)

Mag

net

izat

ion

, M/M

s

Field, mT

H

(a) (b) (c) (d) (e)

H

“Vortex” nucleation

annihilation

Ferromagnetic resonance vs. Brillouin light scattering (BLS)

FMR advantagesHigh speed (1 minute per spectra with standard Bruker EMX-300 ESR

spectrometer)High resolution (position of the mode can be determined with an

accuracy of few Oersteds)External field can be applied at the arbitrary angle to the sample normal

(in BLS only in the sample plane)It is possible to study relaxation processes by measuring resonance

linewidth

FMR disadvantagesLower sensitivity (for patterned 20 nm thick Permalloy minimal sample

size is 0.2 mm x 0.2 mm)Fixed frequencyNot all types of modes can be exited in FMR studies

Rectangular arrays of magnetostatically coupled Ni dots

0.25 m0.8 m

1 m

0.05 m 0.10 m

It is known that Magnetostatic interaction in rectangular dot arrays affects the nucleation and annihilation fields, as well as the initial susceptibility.

Ni_1 Ni_2 Ni_3 Ni_4

Diameter (μm) 1 1 1 1

Thickness (nm) 70 70 70 70

Interdot distance a (μm)

1 1 1 1

Interdot distance b (μm)

0.05 0.1 0.25 0.8

Ni_1 Ni_2 Ni_3 Ni_4

Ni dots and continuous film – out-of-planeFMR angular dependence

210 / 101.9

kOe, 1.87/3

4 films, continuousFor

Gs 480 ,

cmdin

MH

πN

MHMNH

s

dem

ssdem

film. nuous

-conti for the than less 10%~ kOe, 1.65

ratio.aspect dot a is / where

)5.0)/8(ln(2 cylinder For

)31(4)(4

σ

yyxx

xxxxzzdem

H

rtb

bbNN

NNNN

Ni dots – FMR in-plane angular dependence

0 90 180 270 360

1.8

1.9

2.0

Res

onan

ce f

ield

Hr, k

Oe

Angle , degree

Ni_1 (Hin-plane~120 Oe)Ni_3 (Hin-plane~60 Oe)

Ni_4 (Hin-plane~ 0 Oe)

2

5.1

2

2

, If

minmax

max

maxminmax

HH

HH

HHHHH

HH

planein

planein

0.05 m 0.25 m

0 90 180 270 360

1.8

1.9

2.0

Res

onan

ce f

ield

Hr, k

Oe

Angle , degree0 90 180 270 360

1.8

1.9

2.0

Res

onan

ce f

ield

Hr, k

Oe

Angle , degree

Modeling: an array of magnetostatically coupled dots

HumHm Kww 2cos2/

k

k

2cos8

, 22

21

2

k

kRJkRf

TTK

yxu

kx=2/(2R+dx)

ky =2/(2R+dy)

2R

dy

dxFor rectangular array of cylindrical dots we can obtain the following decomposition of the magnetostatic energy density (in units of M2 and normalized per unit dot volume):

0.0 0.2 0.4 0.6 0.80

25

50

75

100

125

In-p

lane

ani

sotr

opy

fiel

d 2K

U/M

, Oe

Interdot distance dx, m

where δ=d/R (dx=d) is the normalized inter-dot distance, =L/R, J1(x) is the Bessel fun-ction, φk and φH are the polar angles of the vectors k and H, respectively. The function Ku( , δ) < 0 have sense of uniaxial anisotropy induced by interdot coupling with an easy magnetization axis parallel to the shor-test period Tx of the rectangular dot array (φH =0).K.Yu. Guslienko et.al. Phys. Rev. B 65, 024414 (2002).

In-plane anisotropy in square array of Py dotsPy square lattice of closely packed circular dots, 1/1.1 µm

Four-fold anisotropy (FFA) fields for square arrays are significantly smaller than in-plane uniaxial anisotropy fields in rectangular arrays. However it is was not clear what is a source of FFA. In completely magnetized square arrays noanisotropy should appear at all.

0 45 90 135 180 225 270 315 360

1060

1080

1100

1120

1100

1120

1140

1160

(b)

Res

onan

ce f

ield

(O

e)

Azimuthal angle (degrees)

(a)

Dependencies of the mean FMR field Hr,av and 4th order anisotropy constant H4 on the interdot spacing a in the square

array of circular dots.

1.0 1.5 2.0 2.5

1.10

1.12

1.14

Hr,

av (

Oe)

Center-to-center distance a (m)

1.0 1.5 2.0 2.50

5

10

15

20

25

Four

-fol

d an

isot

ropy

fie

ld (

Oe)

Center-to-center distance (m)

Correlations between 4-fold anisotropy and FMR resonance linewidth in square arrays of circular magnetic dots

0 30 60 90 120 150 1801090

1100

1110

1120

1130

Res

onan

ce f

ield

(O

e)

Angle between [10] direction and applied field (degree)

Evidence of 8-fold anisotropy for closely packed square array of Py dots

0 45 90 135 180 22526

28

30

32

34

36

Experimental data Fit axcos(4+bxsin(8R

eson

ance

line

wid

th (

Oe)

Azimuthal angle (degree)




accuracy of few Oersteds)External field can be applied at the arbitrary angle to the sample

normal (in BLS only in the sample plane)It is possible to study relaxation processes by measuring resonance

linewidth



H = 2πMs ≈ 3 kOe

H = 0

BLS studies of Ni nanowires in nanoporous alumina

H ~ 2 kOe

Z. K. Wang, M. H. Kuok, S. C. Ng, D. J. Lockwood, M. G. Cottam, K. Nielsh, R. B. Wehrsphon, and U. Gosele, Phys. Rev. Lett. 89, 027201 (2002).

1 μm

30 nm

Spin wave resonance in normally magnetized Ni dots(experiment)

5000 6000 7000

Mic

row

ave

abso

rbtio

n de

riva

tion

(a.u

.)

Magnetic Field (Oe)

6000 8000

Mic

row

ave

abso

rbtio

n de

riva

tion

(a.u

.)

Magnetic Field (Oe)

Ni witness continuous film Array of Ni dots (Ni_1)

When the applied field was close to normal of the sample, additional sharp resonant peaks were observed below the main ferromagnetic resonance peak. No sight of such periodic SW spectra was found for the reference Ni continuous film, which supports the idea that in dots SW modes with discrete frequencies due to restricted sample geometry will dominate.

Spin wave resonance in circular Ni dots

For all the dot samples the differences ΔHr between neighbor modes, excluding the main one, were approximately the same ( ~ 250 Oe), indicating that the interdot interactions (different for each sample) do not affect magnetostatic spin wave modes in perpendicular geometry.

0.8 m

1 m

0.10 m

Two dimensional Bessel function modes of a disc

(1,0) (2,0) (3,0) (4,0)

Phase of the transverse (rf) moment

For perpendicularly saturated cylindrical dots these modes have circular symmetry and are spatially non-uniform due to the non-ellipsoidal dot shape. Condition for the existing of standing waves between specific turning points leads to the quantization of the observed resonance fields.

0.0 0.2 0.4 0.6 0.8 1.0-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

()()

SW

eig

enfu

ncti

ons,

mn(

r)

Radius vector, /R

()

Eff

ecti

ve d

emag

neti

zing

fac

tor

-N(r

)

Comparing theory and experiment

Comparison of measured and calculated FMR resonance peak

positions: (a) patterned Ni film, parameters used

in calculation are Ms = 484 G, γ/2π = 3.05 MHz/Oe, L=70 nm, R=500 nm, H = 1.84 kOe, A=8×10-7 erg/cm;

(b) patterned NiFe film, parameters used in calculation are Ms=830 G, γ/2π = 2.96 MHz/Oe, L = 50 nm, R=500 nm, H=0, A=1.43×10-6 erg/cm.

1 2 3 4 5 6 7 8

10

11

12

1 2 3 4 5 6 7 84

5

6

7

b) Permalloy patterned film

experimental data calculations

Res

onan

ce f

ield

(kO

e)

Resonance mode number

a) Ni patterned film

experimental data calculations

Angular dependence of SWR in Py circular dots

8 10

= 6o

Magnetic Field (Oe)

10 12

Magnetic Field (kOe)

= 0o

10 12

= 4o


Angular dependence of SWR in Py circular dots (contin.)

6 8

= 10o

Magnetic Field (kOe)3 4 5

= 20o


1200 1500 1800

= 90o


Out-of-plane angular dependence of the main peak

0 15 30 45 60 75 900

2

4

6

8

10

12

14

Mai

n pe

ak r

eson

ance

fie

ld (

kOe)

Angle (degree)

Experimental data calculations for Kittel uniform mode calculations for J

01 mode R∂m/∂n+dmR=0 (1)

pinned d=, mR=0

unpinned d=0, ∂m/∂nR=0

d is pinning parameter [1,2]. We can assume from experimental results that for perpendicularly magnetized dot (θ = 0o) pinned boundary conditions are realized, but for θ > 7o uniform Kittel mode perfectly describes the experiment. For Kittel mode pure UNPINNED boundary conditions are valid. So, in the range 0o < θ < 7o d varies from to 0 and, consequently, the basic mode varies from J0(K), where K is the first Bessel function root = 2.4, to J0(0)=Kittel mode. Between these points K can be determined as a root of (1) with corresponding d.[1] K.Yu. Guslienko, S.O. Demokritov, B. Hillebrands, A.N.Slavin, PRB 66, 132402 (2002)[2] R. Zivieri, R.L. Stamps PRB 73, 144422 (2006)

Transition from J0 to J1 near θ =0?

In-plane SWR in square array of Py dots

1200 1500 1800

[10]

[11]M

W a

bsor

btio

n de

riva

tion

(a.u

.)

Magnetic Field (Oe)

Py square lattice of closely packed circular dots, 1/1.1 µm

It is important to note that in-plane additional spin-wave modes for [10] and [11]are shifted in a different way with respect to the main one, indicating that interdot interactions DO AFFECT magnetostatic spin wave modes in in-plane geometry.

0 45 90 135 180

1100

1200

1300

1400

1500

1600 4th peak

3rd peak

2nd peak

Re

son

an

ce fi

eld

in-plane angle

1st peak




accuracy of few Oersteds)External field can be applied at the arbitrary angle to the sample normal

(in BLS only in the sample plane)It is possible to study relaxation processes by measuring resonance

linewidth



Resonance linewidth

0 30 60 900

100

200

300

400

Res

onan

ce li

new

idth

H

pp (

Oe)

Angle (degree)

continuous film patterned film

For patterned film at perpendicular the linewidth is considerably smaller. This is because the density of spin-waves that the resonance can scatter into is much reduced, kmin = 2π/d.At parallel the internal fields will be much more inhomogeneous leading to a stronger coupling to higher order spin-waves and a shorter relaxation time. As a function of angle from the perpendicular the inhomogeneities gradually increases and the linewidth increases.

MRFM Spectrometer

Sputter Coated NiFe Tip

Bias Field Solenoid (± 300 G)

Bias Field H(permanent magnet)

H

DetectionCantilever(with H)

RF Microstrip ()

Sample on substrateModulation Field, Hmod

Fiber opticinterferometer

xy

z

Force

J. A. Sidles, Appl. Phys. Letts. 59, 2854 (1991)D. Rugar, C. S. Yannoni and J. A. Sidles, Nature, 360, 563 (1992)

Resonance Slice

Resonance Slice = Hres

Ftip = m(r,t)dH/dz

M Htip(r)

Happ < Hres

h(t)

Hint > Hres

Bint < Bres

FMRFM spectra of circular dot array

Spatially resolved FMRFM

Conclusions

FMR has shown its very high effectiveness in determination of different types of anisotropy in rectangular and square arrays of circular submicron dots

It is shown that, even under strong enough FMR field H, the dipolar coupling in the square array of circular magnetic microdots is able to produce some continuous deformation of uniformly magnetized state, depending on the in-plane field orientation.

We observed the multi-resonance FMR spectra of laterally confined spin wave modes in nickel and Permalloy circular dot arrays. These spectra are quantitatively described by a simple dipole-exchange theory of spin wave dispersion in a perpendicularly magnetized film.

The global FMR properties of circular submicron dots determined using magnetic resonance force microscopy are in a very good agreement with results obtained using X-band conventional FMR and with theoretical description.

AcknowledgementV.O. Golub, E.V. TartakovskayaInstitute of Magnetism, Kiev, UkraineP.C. HammelDepartment of Physics, Ohio State University, USAA.N. SlavinDepertment of Physics, Oakland University, USAYu.G. Pogorelov, M. CostaDepartment of Physics, University of Porto, PortugalK.Yu. Guslienko, V. NovosadMaterials Science Division, Argonne National Laboratory, Y. OtaniFrontier Research System, RIKEN, JapanS. BatraSeagate Research, Pittsburgh, USA

Probing microscopic magnetic dots and their periodic arrays with ferromagnetic resonance G.N....

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