Freie Universität Berlin Hercules A15 / Trieste / 17.3.05 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 µorb.
4. Induced magnetism at interfaces.
Magnetic Magnetic dichroismdichroism in XASin XASand its applicationand its application
Freie Universität Berlin Hercules A15 / Trieste / 17.3.05 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
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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.
• 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).
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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 (
arb.
uni
ts)
Nor
m. X
AS
(arb
. uni
ts)
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
1 2
32
+h −h
kM
2p12
2p 32
3d 32
3d 52
1 2−3 2−5 2− 1 2+ 3 2+ 5 2+1 2−3 2− 1 2+ 3 2+
12−3
2− 12+ 3
2+12− 1
2+
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The origin of MCD (after K. Fauth, Univ. Würzburg)
There are many reviews e.g.: Lecture Notes in Physics Vol. 466 by H. Ebert, G. Schütz
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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
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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
(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
TC
Co = 340 K
T*C
Ni = 308 K
T (K)M
(arb
. uni
ts)
0
200
400 Ni L3,2Co L3,2
x 1.72
no
rm.
ab
sorp
tion
(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
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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 (µ
eV/a
tom
)
d (ML)Cu
FMR / / / /
/ / /
→
→XMCD / / /→
Cu Cu Cu(001)
Cu Cu(001)Cu Cu(001)
FMR
Ni Ni
NiNiCo
Co
a)b)c)
Interlayer exchange coupling
T*Ni
M (
arb.
uni
ts)
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
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C. Sorg et al.,XAFS XII, June 2003Physica Scripta 2005
e_
IP
+HV
hνHstatisch
-0.2
-0.1
0.0
0.1
0.2
Mag
net
ization (
arb.
unit
s)
Magneti c Field (Oe)-40 -20 0 20 40
281 K
265 K184 K
5 ML Cu6 ML Ni
Cu (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 (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,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
)
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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 /
TC
Ni
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)
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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 (to be published)
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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)
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−≡−−≡ −− 2}22{)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
Freie Universität Berlin Hercules A15 / Trieste / 17.3.05 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 dg e
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
µSµL
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
)( ) ( )( ) d
Zdh
2L3L
dZ
dZd
h2L3L
L2N
NdE
T7S23N
NdE2
∫
∫
=+
+=⋅−
? µ? µ
? µ? µ
Freie Universität Berlin Hercules A15 / Trieste / 17.3.05 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 / Trieste / 17.3.05 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
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anisotropic µL ↔ MAE
ξLSMAE ∝ ∆µL4µBBruno (‘89)
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
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/atomK. Baberschke, Lecture Notes in Physics, Springer 580, 27 (2001)
B (G)
100
100 20000
500
300
300
M (G
)
[111]
[100]
Ni[100]
[111]
0.1 G∆µL ~~
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 µorb
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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(
/a
tom
)
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
500ex
p.
c/a
Magnetic Anisotropy Energy MAE and anisotropic µorb
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Quadrupolar effects (E2)
Rare earth metals:
(5d)
• highly localized 4f states • ordering by exchange interaction via magnetized conduction band
XMCD at L edges:3,2 electric dipolar transitions E1: 2p ( l=1) ( l=2)
∆∆
5d4fand electric quadrupolar transitions E2: 2p
Literature: rare earth compounds (3d,4f) Bartolomé, Tonnerre et al., Phys. Rev. Lett. , 3775 (1997) Giorgetti, Dartyge et al., Appl. Phys. A, , 703 (2001)• •
7973
µ ρ(E) |M (E)| (E)fi2
∝
Tb foil: G. Schütz et al: Z. Phys. B: Condens. Matter (1988) 6773
but: E2 contributions neglectedTheory: • H. Ebert et al., Solid State Comm. (1990) 475
• Xindong Wang, P. Carra et al., Phys. Rev. B (1993) 9087
76 47
⇒”simple model for interpretation in terms of spin-polarization of the d-band - in contrast to transition metals - ”is not justified
5d
4f
2p3/2
2p1/2
7512.5
7517.5
8249.0
8254.0~5 eV
~736.5 eV
L3 L2
{
{
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Tb XMCD at L3,2-edges
7500 7520 7540 8240 8260 8280
-0.01
0.00
E2
E2
XMC
D(a
rb.u
nits
)
Photon Energy ( eV )
0.0
0.5
1.0 µ+
µ-
Abso
rptio
n(a
rb.u
nits
)
10 K, 7 T
L3
L2
µ
µ
C
0/
E (eV)
0
0.02
0.04
-0.0 4
-0.02
Abs
orpt
ion
• XMCD of single element magnetTb single crystal
• High resolution at ESRF (ID 12A):
fine structurefree of noise
Pioneer experiment:G. Schütz et al.Z. Phys. B:Condens Matter73 (1988) 67
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Separation E1 ↔ E2 contributions
• FEFF8*: - self-consistent- full multiple scattering in real-space
details of5d spin polarized DOS
H. Wende et al., and J.J. Rehr et al., J. Appl. Phys. 91, 7361 (2002)and Highlights ESRF p. 84 (2003)
• Separation of E1 and E2 contributionsby switching on/off the E1,2 contributionin the calculation
7500 7520 7540 8240 8260 8280
-0,01
0,00
0,01
Experiment Theory E1 Theory E2
Nor
mal
ized
XMC
D(a
rb.u
nits
)
Photon Energy ( eV )
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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 /a
tom
)B
Ni
Ni
NiPt
Pt
Pt
Unitcell
PtNi
N
825 850 875 900
-2
0
2
4
(b)
x2 XANES XMCD
Energy (eV)
L2
L3
Inte
nsity
(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
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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 WJi nterSZ SZ
.. Fe W
µS
µS λintra SZ LZ.. W W µL
JinterSZ SZ.. Fe W λ interSZ LZ
.. Fe W λint ra 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
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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
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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 al loy: 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 !
ex p.
theory
ExperimentA. Scherz et al.
TheoryJ. Minar, D. Benea, H. Ebert, LMU
PRB 66, 184401 (2002)
Beyond sum rules: full calculation of µ(E)
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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 / Trieste / 17.3.05 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)
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A. Scherz et al., XAFS XII June 2003 Sweden, Physica Scripta;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 59 0 600
-2
0
2
4
700 720 740
-2
0
2
4
780 800 82 0
norm
aliz
ed X
AS,
XM
CD
(ar
b. u
nits
)
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 / Trieste / 17.3.05 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: