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Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 1Freie Universität Berlin
Klaus BaberschkeKlaus Baberschke
Institut für ExperimentalphysikInstitut für ExperimentalphysikFreie Universität BerlinFreie Universität Berlin
Arnimallee 14 DArnimallee 14 D--14195 Berlin14195 Berlin--Dahlem GermanyDahlem Germany
1. Introduction.
2. Element specific magnetizations in trilayers.
3. Determination of orbital- and spin- magnetic moments;XMCD sum rules.Magnetic Anisotropy Energy (MAE) and anisotropic µL.
4. Induced magnetism at interfaces.
5. New developments, outlook
Magnetic dichroism in XASMagnetic dichroism in XASand its applicationand its application
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 2
1. Introduction: XAS
L3,2 edges of 3d elements
Note: the intensity of the 2p → 3d dipole transitions (E1) is proportional to the number of unoccupied final state (i.e. 3d- holes).
X-ray Absorption Spectroscopy is the most appropriate technique for element specific investigations.
Fe
Co
Ni
Cu
Photon energy (eV)
X-r
ay a
bsor
ptio
n cr
oss
sect
ion
(arb
. uni
ts)
0
100
650 700 750 800 850 900 950 1000
200
300
400
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 3
Appendices/References
• In this lecture we will not discuss the equipment/apparatus,but rather focus on application of XAS in magnetism.
• Concerning XAS-technique there exist many review articles e.g.J. Stöhr: NEXAFS Spectroscopy, Springer Series in SurfaceScience 25, 1992; H. Wende: Recent advances in the x-ray absorption spectroscopy, Rep. Prog. Physics 67, 2105 (2004).
• See also lectures A13 J. Vogel; A14 Y. Joly;A’15 (Trieste) F. Sirotti; A”15 (Saclay) M. Sacchi.
• In the soft X-ray regime (VUV) one needs to work in vacuum.For nanomagnetism one wants to prepare and work anyway inUHV (in situ experiments).
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 4
X-ray Magnetic Circular DichroismFaraday – effect in the X-ray regime (Gisela Schütz, 1987)
XMCD signal is a measure of the magnetization
Many Reviews, e.g. H. Ebert Rep. Prog. Phys. 59, 1665 (1996)
0
1
2
3
4
5
6
700 710 720 730 740-3
-2
-1
0
Photon Energy (eV)
Nor
m. X
MC
D (a
rb. u
nits
)N
orm
. XA
S (a
rb. u
nits
)
µ−+
µµ
0
(E)(E)(E)
L2
3L
=µ+ −−µ(E)∆µ
Fe
M
continuum
Spin “up” Spin “down”
EF
2p
2p
left right
L 2
L 3
3d
12
32
+h −h
kM
2p12
2p 32
3d 3 23d 5 2
1 2−3 2−5 2− 1 2+ 3 2+ 5 2+1 2−3 2− 1 2+ 3 2+
1 2−3 2− 1 2+ 3 2+1 2− 1 2+
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 5
The origin of MCD (after K. Fauth, Univ. Würzburg)
Reviews e.g.: Lecture Notes in Physics Vol. 466 by H. Ebert, G. Schütz
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 6
2. Element specific magnetizations in trilayers
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 ⇒ ?
substrate
CoTC
Co CuNi
TCNi
M
M
J int
er
853 eV(L )3 e -e-778 eV(L )3
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 7
Ferromagnetic 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
XM
CD
(ar
b.uu
nits
)
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
TC
Co = 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
. abso
rptio
n (
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)
XM
CD
(arb
.uun
its)
h (eV)ν
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 8
P. Poulopoulos, K. B., Lecture Notes in Physics 580, 283 (2001)
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 (µe
V/a
tom
)d (ML)Cu
FMR / / / /
/ / /
→
→XMCD / / /→
Cu Cu Cu(001)
Cu Cu(001)Cu Cu(001)
FMR
Ni Ni
NiNiCoCo
a)b)c)
Interlayer exchange coupling
T*Ni
M (a
rb. u
nits
)
TCNi = 275K
2.8 ML Cu4.8 ML Ni
Cu(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
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 9
C. Sorg et al.,XAFS XII, June 2003Physica ScriptaT115, 638 (2005)
e_
IP
+HV
hνHstatisch
-0.2
-0.1
0.0
0.1
0.2
Mag
net
izat
ion (
arb. units)
Magnetic Field (Oe)-40 -20 0 20 40
281 K
265 K184 K
5 ML Cu
6 ML NiCu (100)
0 50 100 150 200 250 3000.0
0.1
0.2
0.3
0.4
0.5
Temperature (K)
Mag
net
izat
ion (
arb. units)
Remanence and saturation magnetization
M (
kA/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,Ni∆T
2D
3D0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
T / TC,Ni
2.1 2.6 3.1 4.2 4.0
d (ML)Ni
1 2 3 4 5 6
Theory / Experiment
C,N
iM
C,N
iM
/(T
= 0
)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 10
J.H. Wu et al. J. Phys.: Condens. Matter 12 (2000) 2847
-0.02
0.00
0.02
EFM2
ENM
EFM1
ETOT
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)
χ
χ
T (
o K)
∆
∆
∆∆∆∆
E=E
AFM
EFM
(eV
/ML)
∆-
+
+
Single band Hubbard model: Simple Hartree-Fock (Stoner) ansatz is insufficientHigher 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 nanostructures S 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)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 11
FM1 (Ni)
FM2 (Co)
NM (Cu)
IEC ~ 1dNM
2
dNM
dFM1
Jinter
2D sp
in
fluctu
ation
s
∆TC, Ni
Evidence for giant spin fluctuations PRB 72, 054447, (2005)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 12
3. Determination of orbital- and spin- magnetic moments
Which technique measures what?
µL , µS in UHV-XMCD
µL + µS in UHV-SQUID
µL / µS in UHV-FMR
per definition:
1) spin moments are isotropic
2) also exchange coupling J S1·S2 is isotropic
3) so called anisotropic exchange is a (hidden)projection of the orbital momentum intospin space
For FMR see: J. Lindner and K. BaberschkeIn situ Ferromagnetic Resonance:An ultimate tool to investigate the coupling in ultrathin magnetic filmsJ. Phys.: Condens. Matter 15, R193 (2003)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 13
−≡−−≡ −− 222)2( 2/1
2ψ
Orbital magnetism in second order perturbation theory
The orbital moment is quenched in cubic symmetry
⟨2- LZ 2-⟩ = 0,
but not for tetragonal symmetry
effective Spin Hamiltonian
L± • S
LZ • SZ
+λL • S +_
d1
W.D. Brewer, A. Scherz, C. Sorg, H. Wende, K. Baberschke, P. Bencok, and S. Frota-PessoaDirect observation of orbital magnetism in cubic solidsPhys. Rev. Lett. 93, 077205 (2004)andW.D. Brewer et al. ESRF – Highlights, p. 96 (2004)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 14
Orbital and spin magnetic moments deduced from XMCD
H. Ebert Rep. Prog. Phys. 59, 1665 (1996)
860 880 900
L2 edgeL
µLµS
3 e dge
Ninorm
.XM
CD
(arb
.uni
ts)
Photon Energy (eV)
µLµS
dELL )2( 23 µµ ∆−∆∫
dELL )( 23 µµ ∆+∆∫
?
??
/µ
µL
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
µSµ L
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 µ L
L3 L2
XM
CD
Inte
gral
(ar
b. u
nits
)( ) ( )( ) d
Zdh
2L3L
dZ
dZd
h2L3L
L2NN
dE
T7S23N
NdE2
∫
∫
=+
+=⋅−
? µ? µ
? µ? µ
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 15
Enhancement of Orbital Magnetism at Surfaces: Co on Cu(100)
λ
λλ
/10
/)2(3
/)1(
expnDd
n
nDdn
dD
S
L
eCeBAe
MM
−−=
−−=
−−
Σ+Σ+
=
M. Tischer et al., Phys. Rev. Lett. 75, 1602 (1995)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 16
Giant Magn. Anisotropy of SingleCo Atoms and Nanoparticles
P. Gambardella et al., Science 300, 1130 (2003)
Induced magnetism in molecules
n = number of atoms
T. Yokoyama et al., PRB 62, 14191 (2000)
XMCD
XMCD
CO
~531 eV e-
∼10ML NiCu
µ
µL
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 17
1. Magnetic anisotropy energy = f(T)
2. Anisotropic magnetic moment ≠ f(T)
≈ 1µeV/atom is very small compared to≈ 10 eV/atom total energy but all important
B (G)
100
100 20000
500
300
300
M (G
)
[111]
[100]
Ni[100]
[111]
0.1 G∆µL ~~
Characteristic energies of metallic ferromagnets
binding energy 1 - 10 eV/atom
exchange energy 10 - 103 meV/atom
cubic MAE (Ni) 0.2 µeV/atom
uniaxial MAE (Co) 70 µeV/atom
K. Baberschke, Lecture Notes in Physics, Springer 580, 27 (2001)
anisotropic µL ↔ MAE
ξLSMAE ∝ ∆µL4µB
Bruno (‘89)
g|| - g⊥ = geλ(Λ⊥-Λ||)
D= ∆gλge
MAE = ?M·dB ˜ ½ ?M·?B ˜ ½ 200 · 200 G2
MAE ˜ 2·104 erg / cm3 ˜ 0.2 µeV / atom
Magnetic Anisotropy Energy (MAE) and anisotropic µL
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 18
O. Hjortstam, K. B. et al. PRB 55, 15026 (’97)
-0.005 0.000 0.005 0.010
-100
0
100
200
α =1α =0.05
Ni
c/a=1.08
c/a=0.69c/a=0.79
K (µ
eV)
V
∆ Orbital moment (µ )B
K(µ
eV
/ato
m)
VO
rbita
l mo
me
nt
B(
/ato
m)
µ
0.75 0.85 0.95 1.05
0.05
0.06
0.07
SO (001] SO+OP [110] SO+OP [001]
SO[110]
bcc fcc
-100
0
100
200
300
400
500
exp.
c/a
Magnetic Anisotropy Energy MAE and anisotropic µL
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 19
Ni and Pt carry a magnetic moment
No ‘dead’ Ni layers F. Wilhelm et al. PRL 85, 413 (2000) and ESRF Highlights 2000
Magnetic momentprofile for a Ni6/Pt5 ML
Ni
Pt
4. Induced magnetism at interfaces
1 2 3 4 5 6 7 8 9 10 110.0
0.2
0.4
0.6
theory
(b)bulk Ni TB-LMTO
Monolayers
0.0
0.2
0.4
0.6
experiment
(a)bulk Ni
Ni Pt
Mag
net
ic M
om
ent
(µ /
ato
m)
B
Ni
Ni
NiPt
Pt
Pt
Unitcell
PtNi
N
825 850 875 900
-2
0
2
4
(b)
x2 XANES XMCD
Energy (eV)
L 2
L3
Inte
nsi
ty (a
.u.)
Ni L-edgesNi2/Pt2
11.5 11.6 13.2 13.3
-0.4
0.0
0.4
0.8
(a)
x10
x10
L2
L3
XANES
XMCD
Energy (keV)
Inte
nsi
ty (a
.u.)
Pt L-edges
Ni2/Pt2
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 20
Induced magnetism in 5d-transition metals breakdown of 3rd Hund’s rule ?
F. Wilhelm et al.,Phys. Rev. Lett. 87, 207202 (2001)
alternatively: details of SP-DOS; hybridization
Fe
WλinterSZ LZ
.. Fe WJinterSZ SZ
.. Fe W
µS
µS λintra SZ LZ.. W W µL
Jinter SZ SZ.. Fe W λ interSZ LZ
.. Fe Wλintra SZ LZ
.. W W> >
10.16 10.20 10.24 11.52 11.56 11.60-5
0
5
10
15
mS
Sm Lm
Lm
W
x 2
x 50
L2
x 50
L3
XA
S,X
MC
D(a
rb.u
nits
)
Photon Energy (keV)
XMCD-Integral
Experiment
Expected from3 Hund’s rulerdFe/W interface
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 21
Fe/V/Fe(110)Trilayer
L 3,2
x 15
V FeL 3,2
µ+
µ
µ - µ (highlighted)+
520 540 700 720 740-2
0
2
4
norm
.XA
S,X
MC
D(a
rb.u
nits
)
Photon Energy (eV)
Advantages:controlable growth
• annealing to reduce surface roughness• preparation at 300 K
In-situ experiment, i.e. no capping layers
XMCD measurements:• BESSY II, third generation
synchrotron source inBerlin
• Newly developed ‘gapscan’mode: High degree ofcircularly polarized lightand high photon flux
5 MLFe
Fe
1< <8 MLn
~50ML
Cu(001)
µS
µS
µL
µL
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 22
510 520 530 540
-0.1
0.0
0.1
0.2
0.3
x2.23
C
B
A
norm
. XM
CD
(arb
. uni
ts)
Photon Energy (eV)
0
2
4
6
norm
. XA
S (a
rb. u
nits
)
V L3,2 edges
Fe/V3/Fe trilayer Fe90V10 alloy
D
E
E
a)
b)
Energy (eV)
V L3,2 edges
XA
S (a
rb. u
nits
)X
MC
D (
arb.
uni
ts) Fe 90V10 alloy: L 3,2 edge
a)
b)-10 0 10 20 30
-0.2
0.0
0.2
0.40
2
4
6
8
L2 edge Fe/V3/Fe trilayer
x6
A
B
C
D
525 530 5351.0
1.2
1.4
1.6
1.8
2.0 no oxygen !
exp.
theory
ExperimentA. Scherz et al.
TheoryJ. Minar, D. Benea, H. Ebert, LMU
PRB 66, 184401 (2002)
5. Full calculation of µ(E)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 23
Sum rules and beyond* Gerrit van der Laan
Daresbury Laboratory ,Warrington WA 4 4AD ,UKAbstractSum rules relate the integrated signals of the spin-orbit split core levels to ground state properties, such as the spin-orbit coupling, magnetic moments and charge distribution. These rules give the zeroth moments of the spectral distribution. It is shown how this can be generalized to higher-moment statistical analysis … .Journal of Electron Spectroscopy and Related Phenomena 101–103 (1999) 859–868
Beyond sum rules: full calculation of µ(E)
Photon Energy (eV)
Nor
mal
ized
XM
CD
(arb
. uni
ts)
510 515 520 525 530-0.25
0.00
0.25
0.50 Fe/V/Fe
experiment
multipole-momentanalysis
SPR-KKR
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 24
single pole double pole
double pole approximation (time-dependent DFT)
Petersilka et al. PRL (1996) 1212 Atoms ( S )
761 →1P
PhD thesis A. ScherzL edges metals3,2
-5 0 5 10 15 20 25
Relative Photon Energy (eV)
Abs
orpt
ion
(arb
. uni
ts)
-5 0 5 10 15 20 25
L
XA
S (
arb.
uni
ts)
Relative Photon Energy (eV)
2,3
L2L3
0
unperturbed
unperturbed
perturbed perturbed
ground-state density
frequency-dependent perturbation
linear response theory
M11 M22
↓
⇓
•
•
perturbed resonances shift to higher energies
spectral weight is shifted L L branching ratio3 2→ ⇒
Ti
• energy shift of perturbed resonances• shift of spectral weight L3 → L2(branching ratio)
),,(|'|
),,(2
ωω r'rr'r xcfrr
eK +
−=
⇓
double pole approximation (time-dependent DFT)
determinematrix elements
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 25
6
8
10
12
14
16
6 8 10 12 14 16unperturbed (eV) ∆ω
Ti
V
Cr
Fe
Co
Ni
statistical branching ratio
Ti V Cr Mn Fe Co Ni
Bra
nchi
ng R
atio
0.4
0.5
0.6
0.7
0.8
L2L3
perturbed
∆ω
∆Ω
pert
urbe
d (
)∆
Ω e
V
experiment: L XAS 3,2••
→ ∆Ω binding energies* → ∆ω
∆ω−∆Ω
∆ω−∆ΩnH
≈ 0.125 eV/hole
⇒ double pole model describes branching ratio quite well
⇒ regime where sum rules fail
Ti: M =1.70 eV, M =0.8 eV11 22
experiment
DPA
experiment
DPA
*Fuggle and Mårtensson, J. Electr. Spectr. Relat. Phenom. (1980) 27521
Ti: M11=3.07 eV, M22=-0.56 eV, M12=0.54 eV
double pole model describesbranching ratio for light 3d’sKohn Sham energies → ∆ω
A. Scherz, et al. Measuring the kernel of time-dependent density functionaltheory with X-ray absorption spectroscopy of 3dtransition metalsPhys. Rev. Lett. 95, 253006 (2005)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 26
1) intergral SR 2) MMA 3) calculation of full µ(E)
• gap-scan technique ⇒ systematic investigation of XAS, XMCD fine structure• development double pole approximation
⇒ correlation energies (Ti: M11=3.07 eV, M22=-0.56 eV, M12=0.54 eV)
• experiment ⇒ failure of spin sum rule ↔ core-hole interaction • theory ⇒ correlation energies as input for theory
⇒ future ab initio calculations must includecore-hole correlation effects
H. Wende, Rep. Prog. Phys. 67 (2004) 2105-2181
ü
Summary
see: Recent advances in x-ray absorption spectroscopy
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 27
• All spectroscopic techniques do not restrict themselves tomeasure the intensity (area under the resonance) only. i.e.: integral sum rules.
• A resonance signal contains a resonance position, a width,an asymmetry profile, etc.
• The optimum is given if theory can calculate the full profileof the resonance, in our case µ(E) i.e. the spectral density.
Recent advances in x-ray absorption spectroscopy H. Wende , Rep. Prog. Phys. 67, 2105 (2004)
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 28
A. Scherz et al., XAFS XII June 2003 Sweden, Physica Scripta T115, 586 (2005)A. Scherz et al., BESSY Highlights p. 8 (2002)
L2,3 XAS and XMCD of 3d TM‘s
450 46 0 470 48 0
-2
0
2
4
510 520 530 540 570 580 590 600
-2
0
2
4
700 720 740
-2
0
2
4
780 800 82 0
norm
aliz
ed X
AS,
XM
CD
(arb
. uni
ts)
840 86 0 880
-2
0
2
4
Ti
Photon Energy (eV)
V Cr
Fe Co Ni
x10 x5x15
Ti V Cr Fe Co NiSc Mn Cu Zn
Freie Universität Berlin Hercules A15 / Grenoble / 16.3.06 29
Conclusion, Future
During last few years: enormous progress in
• calculate µ(E), spin dependent spectral distribution
• full relativistic calculations
• real (not ideal) crystallographic structures
• higher ∆E/E, detailed dichroic fine structure
• undulator, gap-scan technique, constant high PC
• element-selective microscopy, probe of “non-magnetic” constituents
• core hole effects:
→ change of branching ratio for early 3d elements
→ effect on XMCD unknown!
• correct determination of ∆ µL and MAE with XMCD (x30)
• correction for spin- and energy-dependence of matrix elements
Theory:
Experiment:
Future:
Recommended