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