SPIN DYNAMICS IN NANOSCALE MAGNETISM BEYOND THE …users.physik.fu-berlin.de/~bab/teaching/4Bochum/Sfb491_WEB.pdf · 5. Freie Universität Berlin SFB 491, Bochum 13.3.2008. M (kA

1Freie Universität Berlin SFB 491, Bochum 13.3.2008Freie Universität Berlin

Klaus BaberschkeKlaus Baberschke

Institut fInstitut füür Experimentalphysikr Experimentalphysik Freie UniversitFreie Universitäät Berlint Berlin

Arnimallee 14 DArnimallee 14 D--14195 Berlin14195 Berlin--Dahlem GermanyDahlem Germany

1. Element specific magnetizations and TC ’s in trilayers.

2. Interlayer exchange coupling and its T-dependence.

3. Gilbert damping versus magnon-magnon scattering.

SPIN DYNAMICS IN NANOSCALE MAGNETISM SPIN DYNAMICS IN NANOSCALE MAGNETISM BEYOND THE STATIC MEAN FIELD MODELBEYOND THE STATIC MEAN FIELD MODEL

J inte

r

TCNi

TCCo

IEC

Ni

Co

Cu

ICNM 2007, Istanbul: ICNM 2007, Istanbul: physicaphysica status status solidisolidi bb 245245, 174 ff (2008), 174 ff (2008) Handbook of Magnetism Adv. Handbook of Magnetism Adv. MagnMagn. Mater.. Mater. (Wiley & Sons 2007) (Wiley & Sons 2007)

D. L. Mills, p. 247ff and K. Baberschke p.1618ffD. L. Mills, p. 247ff and K. Baberschke p.1618ff

2Freie Universität Berlin SFB 491, Bochum 13.3.2008

BESSY-crew: H. Wende, C. Sorg, A. Scherz, J. Luo, X. Xu

Lab. experiments: K. Lenz, J. Lindner, E. Kosubek, S. Kalarickal, X. Xu

Acknowledgement

Support: BMBF (BESSY), DFG (lab.)

Theory: H. Ebert, LMU; J.J. Rehr, UW; O. Eriksson UU; P. Weinberger, TU Vienna;

R. Wu, D.L. Mills, UCI; P. Jensen + K.H. Bennemann, FUB; W. Nolting, HUB

www.physik.fuwww.physik.fu--berlin.de/~babberlin.de/~bab


Physica B 384, 147 (2006)

S Si j +

t Spin-Spin correlation function

S i S S S S S S S j i i j i j i S S i j+ + + + ++ z z

RPA…

A whole variety of experiments on nanoscale magnets are available nowadays. Unfortunately many of the data are analyzed using theoretical static mean field (MF) model, e. g. by assuming only magnetostatic interactions of multilayers, static exchange interaction, or static interlayer exchange coupling (IEC), etc. We will show that such a mean field ansatz is insufficient for nanoscale magnetism, 3 cases will be discussed to demonstrate the importance of higher order spin-spin correlations in low dimensional magnets.


1. Element specific magnetizations and TC ’s in trilayers.

U. Bovensiepen et al., PRL 81, 2368 (1998)

760 780 800 820 840 860 880 900

-40

-20

0

336K

336K

290K

290K

x 2

Ni L3,2

Co L3,2

XMCD

(arb

.uun

its)

Photon energy (eV)

Cu (001)

2.0ML Co

2.8ML Cu

4.3ML Ni

MCo

MNi

290 300 310 320 3300.0

0.1

0.4

0.8

TCCo = 340 K

T*C

Ni = 308 K

T (K)

M (a

rb. u

nits

)

0

200

400 Ni L3,2Co L3,2

x 1.72

norm

. abs

orpt

ion

(a.u

)

760 800 840 880-100

-80

-60

-40

-20

0

20

T = 140K

2.2 ML Co3.4 ML Cu3.6 ML NiCu(001)

Cu(001)

XMCD

(arb

.uun

its)

h (eV)


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

P. Poulopoulos, K. B., Lecture Notes in Physics 580, 283 (2001)

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

A. Scherz et al. PRB 65, 24411 (2005)

The large shift of TCNi can NOT be explained

by the static exchange field of Co.


J.H. Wu et al. J. Phys.: Condens. Matter 12 (2000) 2847

-0.02

0.00

0.02

EFM2ENMEFM1ETOT

0 1 2 3 4 5 6 7d NM

60

30

0

30

60 T1/ max

FM coupled

AFM coupled

1/m

ax (

arbi

trary

uni

t)

-0.010

-0.005

0.000

0.005

T=0oK

T=250oK

(c)

(a)

(b)

T (o K)

E=E

AFM

EFM

(eV

/ML)

-

+

+

Single band Hubbard model: Simple Hartree-Fock (Stoner) ansatz is insufficient Higher order correlations are needed to explain TC -shift

Enhanced spin fluctuations in 2D (theory)T

/ T

CN

i

3 K

1 K

1 2

Co/Cu/Nitrilayer

d (ML)Ni

J =3 Kinter

MF

0 3 4 5 60.0

0.3

0.6

0.9 Tyablikov (or RPA)decoupling

, mean field ansatz (Stoner model) is insufficientto describe spin dynamics at interfaces of nanostructuresS S i j

+z

S Si j +

t Spin-Spin correlation function

S i S S S S S S S j i i j i j i S S i j+ + + + ++ z z

RPA…

P. Jensen et al. PRB 60, R14994 (1999)


FM1 (Ni)

FM2 (Co)

NM (Cu)

IEC ~ 1dNM

2

dNM

dFM1

Jinter

2D spin

fluctu

ations

TC, Ni

Evidence for giant spin fluctuations (A. Scherz, C. Sorg et al. PRB 72, 54447 (2005))


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 ,1 (2006)


In situ UHV-ESR/FMR set up 1, 4, 9 GHz

pressure: 10-11mbar temperature: 20K - 500K

quartzfinger

thermocouple

lHe cryostat

sample

electromagnet

UHV

cavity

M. Zomak et al., Surf. Sci. 178, 618 (1986)

ESR of 0.01L NO2 /10L Kr/Ag(110); T=20K 1/100 ML

1012 particles

M. Farle, K.B. PRL 58, 511 (1987)

318 K

1.6 ML Gd/W(110)295 K

2. IEC in coupled films measured withUHV-FMR


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)

Th.v. Waldkirch, K.A. Müller, W. Berlinger, PRB (1973)

Fe3+-VO / SrTiO3


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


a) J. Lindner, K. B., J. Phys. Condens. Matter 15, S465 (2003) b) A. Ney et al., Phys. Rev. B 59, R3938 (1999) c) J. Lindner et al., Phys. Rev. B 63, 094413 (2001) d) P. Bruno, Phys. Rev. B 52, 441 (1995)

Theory d)

2 3 4 5 6 7 8 9-20

-15

-10

-5

0

5

10

15

20

25

J inte

r (eV

/ato

m)

d (ML)Cu

FMR / / / /

/ / /

XMCD / / /

Cu Cu Cu(001)

Cu Cu(001)Cu Cu(001)

FMR

Ni Ni

NiNiCo

Co

a)b)c)


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

J. Lindner et al. PRL 88, 167206 (2002)

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

Interlayer exchange coupling and its T-dependence.


S. Schwieger, W. Nolting, PRB 69, 224413 (2004)

T dependence of IEC

S. Schwieger et al., PRL 98, 57205 (2007)


PRB 75, 224429 (2007)

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)


3. Gilbert damping versus magnon-magnon scattering.

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

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


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


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)

H inhom

H 0*

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(R) (2003)

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

0 50 100 150 2000

200

400H

PP(O

e)

f (GHz)

0 4 80

40

80

15 Oe !

• recent publications with similar results:– Pd/Fe on GaAs(001) – network of misfit

dislocations G. Woltersdorf et al. PRB 69, 184417 (2004)

– NiMnSb films on InGaAs/InP B. Heinrich et al. JAP 95, 7462 (2004)

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


Angular- and frequency-dependent FMRon

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

d = 40nmKh. Zakeri et al.

PRB 76,104416 (2007)

Angular dependence at 9 and 24 GHz

(26 –53) • 107 sec-1, anisotropic

G

5 • 107 sec-1, isotropic


Conclusion

Higher order spin-spin correlations are important to explain the magnetism of nanostructures.

In most cases a mean field model is insufficient.

A phenomenological effective Gilbert damping parameter gives very little insight into the microscopic relaxation mechanism. It seems to be more instructive to separate scattering mechanisms within the magnetic subsystem from the dissipative damping into the thermal bath;

Todays advanced experiments and analysis result in:

G

isotropic dissipation and

anisotropic spin wave scattering

Documents

SPIN DYNAMICS IN NANOSCALE MAGNETISM BEYOND THE …users.physik.fu-berlin.de/~bab/teaching/4Bochum/Sfb491_WEB.pdf · 5. Freie Universität Berlin SFB 491, Bochum 13.3.2008. M (kA