“Lectures on magnetism” at the FudanUniversity, Shanghai 10. –...

1K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Klaus BaberschkeKlaus Baberschke

Institut für ExperimentalphysikInstitut für ExperimentalphysikFreie Universität BerlinFreie Universität Berlin

Arnimallee 14 DArnimallee 14 D--14195 Berlin14195 Berlin--Dahlem Dahlem GermanyGermany

““Lectures on magnetismLectures on magnetism””

at the at the FudanFudan University, ShanghaiUniversity, Shanghai

10. 10. –– 26. October 200526. October 2005

2K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

These lectures will cover the recent development of magnetic nanostructures, which are of tremendous interest, be it for technological applications or for the fundamental understanding of magnetism. Magnetism in the past has mostly been discussed as a macroscopic function of the free energy. Today’s magnetic cluster and films of nanometer scale combined with UHV technique offer a new point of view to discuss magnetism in a microscopic atomistic picture.

Introduction

1. Introduction a) Orbital and spin magnetic momentsb) Which experimental technique measures what?

2. Magnetic Anisotropy Energy (MAE)a) Ferromagnetic resonance (UHV-FMR)b) ab initio calculations

3. ac – Susceptibility ?’, ?’’ in UHVa) TC, critical phenomena b) Oscillatory Curie temperaturesc) Higher harmonics ?(n? )

4. Trilayers a prototype of multilayers a) Optical and acoustic modes in the spin wave spectrumb) Interlayer exchange coupling (IEC)

5. X-ray magnetic circular dichroism (XMCD)a) Element specific XMCD, induced magnetism b) Sum rules and advanced theoryc) Importance of strong spin–spin correlations in 2D-magnets

6. Spin Dynamics a) Magnon-magnon scattering and Gilbert dampingb) Spin pumping

3K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Synchrotron (BESSY, ESRF):H. Wende, C. Sorg, N. Ponpandian, (M. Bernien, A. Scherz, F. Wilhelm), Luo Jun (AvH fellow)

Lab. Experiments (FMR, SQUID, χ ac, STM):K. Lenz, (T.Tolinski, J. Lindner, E. Kosubek, C. Rüdt, R. Nünthel, P. Poulopoulos, A. Ney)

Acknowledgement

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

⇒ http://www.physik.fu-berlin.de/~bab

4K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

1a Orbital and spin magnetic moments

−≡−−≡ −− 2}22{)2( 2/1

2ψ

The orbital moment is quenched in cubic symmetry

⟨2- LZ 2-⟩ = 0,

but not for tetragonal symmetry

L± • S

LZ • SZ

+λL • S +_

d1

5K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Orbital magnetism in second order perturbation theory

H '= µBH•L + λL•S

anisotropic µL ↔ MAE

ξLSMAE ∝ ∆µL4µB

Bruno (‘89)

6K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Direct Observation of Orbital Magnetism in Cubic Solids

W.D. Brewer, A. Scherz, C. Sorg, H. Wende, K. Baberschke, P. Bencok, S. Frota-Pessôa

Phys. Rev. Letters 93, 077205 (2004)

Standard exercise in solid state physics:cubic symmetry ⇒ ⟨Lz ⟩ =0

Is the orbital moment of 3d impurities in noble metal hosts completely quenched?

• XMCD investigations of Cr, Mn, Fe, Co in Au

• ab initio calculations of orbital moment

7K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Motivation

atoms metals

large µL(Hund’s rules)

µL mostly quenched(Fe, Co, Ni:

µL/µS~5-10%)

3d impuritiesin noble metalhosts:

⇓1970’s: indirect evidence forsurviving orbital moments(HF measurements)

here: first direct evidence (electronic structure) byX-ray absorption spectroscopy(XMCD)

⇓

8K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

•Brewer et al., ESRF Highlights 2004, p 96

impurityconcentrationin Au host:1.0 at. %

ESRF ID8:7 T, 7-18 K

9K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

dramatic increaseof orbital momentfor Co impurity(~4 times largerthan Co bulk)

(K)

10K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

subtle effect of hybridization and band-filling

S. Frota-Pessôa, PRB 69 (2004) 104401

Fe in Au:strong hybridization:µL quenched

Fe in Ag:weak hybridizationµL survives

11K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

• first direct experimental evidence for orbital moments in cubic symmetry

• text book arguments: weak Spin-Orbit coupling, distinct separation of t2g and eg, no intermixing

• comparison to ab initio calculations: delicate balance hybridizationbetween local impurity and host and the filling of the 3d states of the impurity

⇒ future works on Kondo systems, e.g. with STM, may include surviving orbital moment

⇒ description beyond pure spin magnetism (e.g. Kondo-like Hamiltonian JS·σ)

Conclusion

12K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

1b Which experimental technique measures what?

Orbital- and spin- magnetic moments at surfacesand interfaces of ferromagnetic nanostructures

1. µL + µS in UHV - SQUID

2. µL , µS in UHV - XMCD

3. µL / µS in UHV - EPR / FMR

13K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Design of the

UHV-SQUID

magnetometer

14K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Sensitivity

15K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

The effect of temperature

The magnetization of Co/Cu(001) vs the inverse

film thickness at different temperatures.

The bulk values for 4K (full line) and 300K

(dashed line) are indicated.

16K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

d2mm

mm intersurfvoltot

−++= (linear with 1/d)

Co moment distribution

Theory:Hjortstam et al., PRB 53, 9204 (1996)

Pentcheva et al., PRB 61, 2211 (2000)

A. Ney et al. Europhys. Lett. 54, 820 (2001)

17K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

X-ray Magnetic Circular Dichroism

18K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Orbital and spin magnetic moments deduced from XMCD

19K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Deconvolution into spin (µS) and orbital (µL) moments

The total magnetic moment (squares) of Co/Cu(001) vs the inverse film thickness and its separation

into spin (down triangle) and orbital (diamonds) contribution. The bulk value is indicated (dashed line).

For comparison experimental results using PND and XMCD are given by the open symbols.

http://www.dissertation.de/PDF/an452.pdf

20K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

FMR in ferromagnetic nanostructureIn situ UHV-FMR set up

pressure: 10-11mbartemperature: 20K - 500K

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

J. Lindner, K.B.J. Phys.: Cond. Matt 15, R193 (2003)

quartzfinger

thermocouple

lHe cryostat

sample

electromagnet

UHV

cavity

7.2 ML Ni/Cu(001)T=297 K

W. Platow,Ph.D. thesis

(1999)

318 K

1.6 ML Gd/W(110)295 K

21K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Landau-Lifshitz-Gilbert-Equation

Magnetic resonance (ESR, FMR)

∂∂

×+×−=∂

∂t

MM

MG

HMt

M

Seff 22)(

1γγ

22K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Determination of g-Tensor components

+−+

+−+=

M

K

MK

MM

K

M

K

MK

MHH||42||4||42

]100[,02

]100[,02]100[||,

2 2242

424 ππ

γ

ω

( )M

KKMH ⊥

⊥⊥

++−= 42

,0]001[,

24π

γ

ω

hBµ

γ⋅

=g

with

C. Kittel, )J.Phys. Radiat. , 291 (195112

22−= g

s

lµµ

0

f2 (GH

z2)

H0 (kOe)0

or f

(GH

z)g||,[100] / [110]

g⊥,[001]

23K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

Ferromagnetic resonance on Fen/Vm(001) superlattices

Fe

MgO[110] MgO

a =3.05 (+0.8%)⊥ Å

a =2.83 (-1.3%)⊥ Å

[100]Fe/V

0 50 100 150 200-2.5

-2.0

-1.5

-1.0

-0.5

0.0MAE=E[001]-E [110]

b)

MA

E(µ

eV/a

tom

)

T (K)

-2

-1

0

1

2

3

4

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4a)

← K2← K

4⊥

K 4II→

K4

II (µeV/atom

)

K2,K

4⊥(µ

eV/a

tom

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2T/TC

Fe V2 5

510 520 530 700 720 740-1

0

1

2

FeV

x5

prop. µL

prop. µS

Photon Energy (eV)

g<2 g>2

µS µL µS µL

L3 L2

XM

CD

Inte

gral

(ar

b. u

nits

)

XMCD

A.N. Anisimov et al.J. Phys. C 9, 10581 (1997)and PRL 82, 2390 (1999)and Europhys. Lett. 49, 658 (2000)

µµ

L/

S

Fe40 Fenm Fe 4 /V4 Fe2/V54 /V2

bulk Fe

0

0.06

0.12/FMR: (Fe+V)

XMCD: (Fe)µ µL / S

XMCD(V)µ µL / S

µSµL

2.09

2.264

g

2.09

2.268

g⊥

0.045

0.133

µ /µL S µ (µ )L B µ (µ )S B

bcc Fe-bulk

bcc (001) Fe /V superlattice2 5

0.10

0.215

2.13

1.62

-1.4

-2.0

MAEµeV/atom

FMR

24K. Baberschke FU Berlin „Lectures on magnetism“ #1, Fudan Univ. Shanghai, Oct. 2005

per definition:1) spin moments are isotropic2) also exchange coupling J S1·S2 is isotropic3) so called anisotropic exchange is a (hidden)

projection of the orbital momentum onto spin space

Summary

Distinguish between: 1. Magnetic anisotropy energy = f(T) 2. Anisotropic magnetic moment ≠ f(T)

Quenching of <LZ> is oversimplified argument