Magnetism as seen with X Rays
Elke Arenholz Lawrence Berkeley National Laboratory and Department of Material Science and Engineering, UC Berkeley
1 What to expect:
+ Magnetic Materials Today + Magnetic Materials Characterization Wish List + Soft X-ray Absorption Spectroscopy – Basic concept and examples + X-ray magnetic circular dichroism (XMCD) - Basic concepts - Applications and examples - Dynamics: X-Ray Ferromagnetic Resonance (XFMR) + X-Ray Linear Dichroism and X-ray Magnetic Linear Dichroism (XLD and XMLD) + Magnetic Imaging using soft X-rays + Ultrafast dynamics
2 Magnetic Materials Today
Magnetic materials for energy applications
Magnetic nanoparticles for biomedical and environmental applications
Magnetic thin films for information storage and processing
3 Permanent and Hard Magnetic Materials
Controlling grain and domain structure on the micro- and nanoscale
Engineering magnetic anisotropy on the atomic scale
4 Magnetic Nanoparticles
Optimizing magnetic nanoparticles for biomedical Tailoring magnetic applications nanoparticles for environmental applications
5 Magnetic Thin Films
Magnetic domain structure on the nanometer scale
Magnetic coupling at interfaces
Unique Ultrafast magnetic magnetization phases at reversal interfaces dynamics GMR Read Head Sensor
6 Magnetic Materials Characterization Wish List
+ Sensitivity to ferromagnetic and antiferromagnetic order + Element specificity = distinguishing Fe, Co, Ni, … + Sensitivity to oxidation state = distinguishing Fe2+, Fe3+, …
+ Sensitivity to site symmetry, e.g. tetrahedral, Td; octahedral, Oh + Nanometer spatial resolution + Ultra-fast time resolution
Soft X-Ray Spectroscopy and Microscopy
7 Spectroscopy
Light/Photon Source
Monochromator Sample
sample intensity
wavelength, photon energy intensity
wavelength, photon energy
8 Soft X-Ray Spectroscopy ( h 500-1000eV, 1-2nm)
0 / I t 1.0
0.9
0.8
Electron Storage Ring Monochromator 0.7
Sample 0.6 EY_TM.opj
transmitted intensity I intensity transmitted 770 780 790 800 photon energy (eV)
9 X-Ray Absorption Detection Modes
0 / I t 1.0
0.9 Photons
0.8 absorbed 0.7
0.6 EY_TM.opj
transmitted intensity I intensity transmitted 770 780 790 800 photon energy (eV) mean 6
free 0 / I path e 5nm 4 Electrons
generated
2 electron yield I yield electron
0 EY_TM.opj 770 780 790 800 photon energy (eV) J. Stöhr, H.C. Siegmann, Magnetism (Springer) Electron yield: + Absorbed photons create core holes subsequently filled by Auger electron emission + Auger electrons create low-energy secondary electron cascade through inelastic scattering + Emitted electrons probability of Auger electron creation absorption probability
10 Soft X-Ray Absorption – Probing Depth
Element 10eV below L3 at L3 40 eV above L3 1/ [nm] 1/ [nm] 1/ [nm] Fe 550 17 85 Co 550 17 85 Ni 625 24 85
// // // 3nm Mn Fe Co Ni Ru 1.0 NiFe 15nm
0 3nm
/ I
t Ru
I
0.8 CoFe 15nm
MnIr 15nm // // // luminescence_BL402_Apr2012.opj 640 660 700 720 780 800 860 880 5nm photon energy (eV) Ru
10-20 nm layer thick films supported by substrates transparent to soft X rays
11 X-Ray Absorption Detection Modes and Probing Depth
Mn Fe Co Ni e
1.0 1.0 1.0 1.0
0 Ru 3nm
/ I
t
I
0.8 0.8 0.8 0.8 NiFe 15nm Ru 3nm 1.1 1.0 CoFe 15nm 1.0 1.4 MnIr 15nm
1.0 1.2 0.9 Ru 5nm 1.0 0.9
luminescence_BL402_Apr2012.opj
electron yield (arb. units) 640 650 660 710 720 780 790 850 860 870 photon energy (eV) photon energy (eV) photon energy (eV) photon energy (eV)
+ Electron sample depth: 2-5 nm in Fe, Co, Ni 60% of the electron yield originates form the topmost 2-5 nm
12 X-Ray Absorption Fundamentals
Experimental Concept: Monitor reduction in X-ray flux transmitted through sample as function of photon energy
E Charge state of absorber Fe2+, Fe3+ Valence Symmetry of lattice site of absorber: Oh, Td states Sensitive to magnetic order
Absorption probability: X-ray energy, X-ray polarization, experimental geometry
2p L 3/2 3 Core level Atomic species of absorber Fe, Co, Ni, …. 2p1/2 L2
13 X-Ray Absorption Fundamentals
Experimental Concept: Monitor reduction in X-ray flux transmitted through sample as function of photon energy
E Charge state of absorber Fe2+, Fe3+ Valence Symmetry of lattice site of absorber: Oh, Td states Sensitive to magnetic order
Absorption probability: X-ray energy, X-ray polarization, experimental geometry
2p L 3/2 3 Core level Atomic species of absorber Fe, Co, Ni, …. 2p1/2 L2
14 ‘White Line’ Intensity
Fe valence states
2p L 3/2 3 core level 2p1/2 L2
Intensity of L3,2 resonances is proportional to number of d states above the Fermi level, i.e. number of holes in the d band.
15 ‘White Line’ Intensity
Fe valence states
2p L 3/2 3 core level 2p1/2 L2
Intensity of L3,2 resonances is proportional to number of d states above the Fermi level, i.e. number of holes in the d band.
16 ‘White Line’ Intensity
Co valence states
2p3/2 L3 core level 2p1/2 L2
Intensity of L3,2 resonances is proportional to number of d states above the Fermi level, i.e. number of holes in the d band.
17 ‘White Line’ Intensity
Ni valence states
core level 2p3/2 L3 2p1/2 L2
Intensity of L3,2 resonances is proportional to number of d states above the Fermi level, i.e. number of holes in the d band.
18 ‘White Line’ Intensity
Cu valence states
core level 2p3/2 L3 2p1/2 L2
Intensity of L3,2 resonances is proportional to number of d states above the Fermi level, i.e. number of holes in the d band.
19 X-Ray Absorption Fundamentals
Experimental Concept: Monitor reduction in X-ray flux transmitted through sample as function of photon energy
E Charge state of absorber Fe2+, Fe3+, … Valence Symmetry of lattice site of absorber: Oh, Td states Sensitive to magnetic order
Absorption probability: X-ray energy, X-ray polarization, experimental geometry
2p L 3/2 3 Core level Atomic species of absorber Fe, Co, Ni, …. 2p1/2 L2
20 X-ray Absorption – Valence State
Influence of the charge state of the absorber
N. Telling et al., Appl. Phys. Lett. 95, 163701 (2009)
J.-S. Kang et al., Phys. Rev. B 77, 035121 (2008)
21 X-Ray Absorption – Configuration Model
Ni2+ in NiO: 2p6 3d8 → 2p5 3d9 Configuration model, e.g. L edge absorption : + Excited from ground/initial state configuration, 2p63d8 to exited/final state configuration, 2p53d9 + Omission of all full subshells (spherical symmetric) + Takes into account correlation effects in the ground state as well as in the excited state + Leads to multiplet effects/structure
http://www.anorg.chem.uu.nl/CTM4XAS/ 2S+1L
J. Stöhr, H.C. Siegmann, Magnetism (Springer)
22 X-Ray Absorption Fundamentals
Experimental Concept: Monitor reduction in X-ray flux transmitted through sample as function of photon energy
E Charge state of absorber Fe2+, Fe3+ Valence Symmetry of lattice site of absorber: Oh, Td states Sensitive to magnetic order
Absorption probability: X-ray energy, X-ray polarization, experimental geometry
2p L 3/2 3 Core level Atomic species of absorber Fe, Co, Ni, …. 2p1/2 L2
23 4+ Sensitivity To Site Symmetry: Ti L3,2
PbZr Ti O 3d orbitals 0.2 0.8 2
e e t2
t2
XA (arb. units)
J. Stöhr, H.C. Siegmann,
+ Electric dipole transitions: d02p53d1 Magnetism (Springer) PZT_XA.opj 455 460 465 470 + Crystal field splitting 10Dq acting on 3d orbitals: photon energy (eV) Octahedral symmetry: Tetragonal symmetry:
e orbitals towards ligands higher energy e orbitals b2 = dxy, e = dyz, dyz 2 2 2 2 t2 orbitals between ligands lower energy t2 orbitals b1 = dx y , a1 = d3z r
24 X-Ray Absorption Lattice Symmetry
TiO2
rutile Influence of lattice site symmetry at the absorber
Oh
anataseTiO2
ray absorption ray
- x
D2h G. Van der Laan Phys. Rev. B 41, 12366 (1990)
25 X-Ray Absorption Fundamentals
Experimental Concept: Monitor reduction in X-ray flux transmitted through sample as function of photon energy
E Charge state of absorber Fe2+, Fe3+ Valence Symmetry of lattice site of absorber: Oh, Td states Sensitive to magnetic order
Absorption probability: X-ray energy, X-ray polarization, experimental geometry
2p L 3/2 3 Core level Atomic species of absorber Fe, Co, Ni, …. 2p1/2 L2
26 X-Ray Absorption Fundamentals
Experimental Concept: Monitor reduction in X-ray flux transmitted through sample as function of photon energy
E Charge state of absorber Fe2+, Fe3+ Valence Symmetry of lattice site of absorber: Oh, Td states Sensitive to magnetic order
Absorption probability: X-ray energy, X-ray polarization, experimental geometry
2p L 3/2 3 Core level Atomic species of absorber Fe, Co, Ni, …. 2p1/2 L2
27 Stoner Model For Ferromagnetic Metals
+ Magnetic moments in Fe, Co, Ni
spin-down well described by Stoner model: spin-up d-bands containing up and down empty states, “holes” spins shifted relative to each other empty states, “holes” by exchange splitting + Spin-up and spin-down bands filled exchange splitting according to Fermi statistics + Magnetic moment |m| determined by difference in number of electrons in majority and minority bands J. Stöhr, H.C. Siegmann, Magnetism (Springer) 3d shell maj min |m| μB (ne ne )
28 Origin of X-ray Magnetic Circular Dichroism
2-Step Model for photoexcitation of electrons
from 2p3/2, 2p1/2 to 3d states by absorption 3d of circularly polarized X rays: + Transfer of angular momentum of incident circular polarized X rays to excited electrons (angular momentum conservation, selection rules) + Spin polarization of excited electrons opposite for incident X rays with opposite helicity. + Unequal spin-up and spin-down populations in exchange split valence shell acts as detector for spin of excited electrons.
29 Origin of X-ray Magnetic Circular Dichroism
+ Calculate transition probabilities
from filled 2p3/2 and 2p1/2 states to empty states in d-band for circularly polarized X rays using Fermi’s Golden Rule
30 Origin of X-ray Magnetic Circular Dichroism
+ Wave functions describe electronic and photon states final state |f Energies include electronic and photon energies final state energy f + Calculate transitions probabilities Tif considering photon as time-dependent perturbation, i.e. an electromagnetic (EM) field
Fermi’s Golden Rule
ρ(εf ) = density of final states per unit energy
−1 Tif Dimension [time ] initial state |i
initial state energy i
31
Origin of X-ray Magnetic Circular Dichroism ↓
↓ ↓
↓ + Consider strong ferromagnet with one filled spin band: All spin down d states filled Spin up d states partially filled X-ray absorption of + This specific case: circularly polarized Only spin up electron excited photons with angular momentum q = ±1 in units of ħ
J. Stöhr, H.C. Siegmann, Magnetism (Springer)
32 Origin of X-ray Magnetic Circular Dichroism
q = +1 q = 1 q = 0 q=+1 q=1 q=0
50 30 10 30
L3
L2 J. Stöhr, H.C. Siegmann, Magnetism (Springer)
L3: X rays with q = +/1 excite 62.5%/37.5% of the spin up electrons L2: X rays with q = +/1 excite 25%/75% of the spin up electrons
33
Origin of X-ray Magnetic Circular Dichroism ↓
↓ ↓
↓
= 25% = -50%
Taking into account 2x higher
population of 2p3/2 state as compared to 2p1/2 state:
Identical magnitude XMCD
at L3 and L2 with opposite sign
J. Stöhr, H.C. Siegmann, Magnetism (Springer)
34 X-Ray Magnetic Circular Dichroism (XMCD)
Co 1.0
L Magnitude of XMCD depends on 3 L 0.5 2 + expectation value of 3d magnetic moment XA (arb. units) + degree of circular photon
0.0 polarization, Pcirc + geometry 0.0
-0.2
XMCD -0.4 IXMCD = I I
(arb. units)
FeCo_GaAs_XMCD.opj 770 780 790 800 photon energy (eV)
35 X-Ray Magnetic Circular Dichroism (XMCD)
CoFe O 1.0 2 4
L3 Fe L3 Co
0.5
H XA (arb. units) L2 L2
0.0
3+ circularly Fe , Td
polarized 0.0 XMCD 3+ Fe , Oh (arb. units) -0.2 2+ 2+ Co
Fe ,Oh CoFe2O4.opj 700 710 720 730 780 790 800 J. Stöhr, H.C. Siegmann, photon energy (eV) Magnetism (Springer) + XMCD provides magnetic information resolving elements Fe, Co, … valence states: Fe2+, Fe3+, …
lattice sites: octahedral, Oh, tetrahedral, Td,
36 Magnetic Bionanospinels
3+ Fe , Td + Geobacter sulfurreducens bacteria Fe3O4 form magnetite nanocrystals (15nm) via extracellular reduction of 3+ amorphous Fe(III)-bearing minerals Fe , Oh Fe2+,O h Co-ferrite-1
6 at% Co XMCD
Co-ferrite-2 23 at% Co
60
)
1
0 M (emu g M +60 photon energy (eV)
V. Cocker et al., 2 0 +2 Eur. J. Mineral. 19, 707–716 (2007) H (T)
37 Magnetic Bionanospinels
+ Geobacter sulfurreducens bacteria form magnetite nanocrystals (15nm) via extracellular reduction of amorphous Fe(III)-bearing minerals
2+ Co Oh
60
)
1
0 M (emu g M +60
V. Cocker et al., 2 0 +2 Eur. J. Mineral. 19, 707–716 (2007) H (T)
38 Co-doped TiO2
Co-doped TiO2 Co2+ in CoFe O
2 4
dilute magnetic XA 0
semiconductors XMCD
XA, XMCD
XA (arb. units) (arb. XA
Co metal
XA
0 Co_Co2+.opj
XMCD
XA, XMCD
XMCD (arb. units) (arb. XMCD
780 790 800 810 780 790 800 photon energy (eV) photon energy (eV) J.-Y. Kim et al., Phys. Rev. Lett. 90, 017401 (2003)
+ Comparing XMCD spectra with model compounds and/or calculations Identifying magnetic phases
39 Induced Moments At Co/Cu Interfaces
Co Cu Co
Cu …
+ The element-specificity makes XMCD measurements an ideal tool to determine induced moments at interfaces between magnetic and non-magnetic elements. M. G. Samant et al., Phys. Rev. Lett. 72, 1112 (1994)
40 Magnetic Interfaces
20 Å Co / 200 Å Ir20Mn80 + Weak Mn XMCD signal H = +/-0.5T Uncompensated Mn at FM Co Co/IrMn interface AFM IrMn Co L3,2
+ Same sign of XMCD signal
for Co and Mn XA (arb. units) Mn L3,2 Parallel coupling of Co and Mn moments x20 + Nominal thickness of 0 uncompensated interface moments: (0.50.1)ML
XMCD (arb. units) 630 640 650 660 770 780 790 800 810 photon energy (eV) H. Ohldag et al., Phys. Rev. Lett. 91, 017203 (2003)
41 Band Filling In GaxFe1−x
1.0 0.00 GaxFe1−x Fe L 3,2 (eV) -0.25
3
L
Fe
0.5
-0.50
XA (arb. units) 0.0 0.2 0.4 0.6 x
0.0 0.02 0.25
0.00 0.00
-0.25 XMCD (arb. units) J. Stöhr, H.C. Siegmann, XMCD (arb. units) -0.02 Magnetism (Springer) -0.50 710 712 photon energy (eV) 705 710 715 720 725 photon energy (eV) 0.00 + Fe majority-spin filled for x=0.3 -0.25 + x 0.3: Fe moment decrease strongly,
XMCD
3
L Formation of D03 precipitates
(arb. units) E. Arenholz et al., Fe Fe -0.50 Phys. Rev. B 82, 180405 ( 2010) 0.0 0.2 0.4 0.6 x
42 Composition Dependence of Fe moment in Fe1-xMnx
Drop of magnetic moment
in bcc Fe1-xMnx, i.e. independent of structural transition
43 Sum Rules
+ Theoretically derived sum rules correlate XMCD spectra with spin and orbital moment providing unique tool for studying magnetic materials.
B > 0
A < 0
Nh = IL3 + IL2 /C mL = –2BA + B / 3C m = –A + 2B / C S B J. Stöhr, H.C. Siegmann, Magnetism (Springer)
44 Orbital Moment Of Co Nanoparticles
+ Strong variation of orbital and spin magnetic moment observable as change in
relative L3 and L2 intensity in XMCD spectrum. + Co atoms and nanoparticles on Pt have
enhanced orbital moments up to 1.1 B
P. Gambardella et al., Science 300, 1130 (2003)
45 Element-specific Magnetization Reversal
Co L 3,2 +/- circ. pol.
H = -0.5T
XA (arb. units) (arb. XA
0
(arb. units) (arb.
-
- I -
+
I
780 800 photon energy (eV)
+ Monitoring field dependence of XMCD Element-specific information on magnetization reversal in complex magnetic nanostructures.
46 Element-specific Magnetization Reversal
Co L Co L 3,2 3,2 +/- circ. pol. +/- circ. pol.
H = -0.5T H = +0.5T
XA (arb. units)
XA (arb. units) (arb. XA
0 0
(arb. units)
(arb. units) (arb. -
- - I
- I - +
+ I
I
780 800 780 800 photon energy (eV) photon energy (eV)
+ Monitoring field dependence of XMCD Element-specific information on magnetization reversal in complex magnetic nanostructures.
47 Element-specific Magnetization Reversal
Co L Co L 3,2 3,2 +/- circ. pol. +/- circ. pol.
H = -0.5T H = +0.5T
XA (arb. units)
XA (arb. units) (arb. XA
0 0 0
XMCD (arb. units)
(arb. units) (arb. -
- - I
- I - +
+ I
I
780 800 -0.4 -0.2 0.0 0.2 0.4 780 800 photon energy (eV) magnetic field (T) photon energy (eV)
+ Monitoring field dependence of XMCD Element-specific information on magnetization reversal in complex magnetic nanostructures.
48 Element-specific Magnetization Reversal
Ni H=+0.2 T Fe H=-0.2 T
Co 18 ML Ni
XA (arb. units) x3 8,10 ML Fe
5 ML Co 0
XMCD
700 750 800 850 photon energy (eV)
10 Ni Fe 5 Co
0
XMCD (%) -5
-10 8 ML Fe -40 -20 0 20 40 field (mT)
49 Element-specific Magnetization Reversal
Ni H=+0.2 T Fe H=-0.2 T
Co 18 ML Ni
XA (arb. units) x3 8,10 ML Fe
5 ML Co 0
XMCD
700 750 800 850 photon energy (eV)
10 Ni 10 Ni Fe Fe 5 5 Co Co
0 0
XMCD (%) -5 XMCD (%) -5 8 ML Fe 10 ML Fe -10 -10 -40 -20 0 20 40 -200 -100 0 100 200 field (mT) field (mT)
50 X-Ray Ferromagnetic Resonance
Co 1.0 + XMCD is the difference in X-ray H absorption between antiparallel L 3 L 0.5 2 and parallel orientation of magnetic moment and photon spin.
XA (arb. units) circularly + The XMCD magnitude reflects the polarized 0.0 magnetic moment aligned parallel to the X ray beam. 0.0
-0.2
XMCD -0.4
(arb. units)
FeCo_GaAs_XMCD.opj 770 780 790 800 photon energy (eV)
51 X-Ray Ferromagnetic Resonance
+ In fact: Co Magnetic moments are not 1.0 fully aligned with applied fields H L but precess around them. 3 L 2 0.5 M(t)
XA (arb. units) circularly polarized 0.0
0.0
-0.2
XMCD -0.4
(arb. units)
FeCo_GaAs_XMCD.opj 770 780 790 800 photon energy (eV)
52 X-Ray Ferromagnetic Resonance
+ In fact: Co Magnetic moments are not 1.0 fully aligned with applied fields H L but precess around them. 3 L 0.5 2 H
XA (arb. units) circularly polarized 0.0
0.0 M x H
-0.2
XMCD -0.4 M(t)
(arb. units)
FeCo_GaAs_XMCD.opj 770 780 790 800 photon energy (eV)
+ Is it possible to measure the pression of magnetic moments making use of the pulsed nature of synchrotron radiation and XMCD? (!)
53 X-Ray Ferromagnetic Resonance
Pulsed nature of synchrotron radiation Example: Advanced Light Source Pulse length 70 ps bunch + 256-320 bunches for spacing 500mA beam current + Bunch spacing: 2 ns (500MHz) + Pulse length 70ps
54 X-Ray Ferromagnetic Resonance
Dynamic XMCD measurement, i.e. synchronize X-ray pulses with FMR precession
2 ns H ~70 ps B Mz(t)
M(t) X-ray pulses X-ray pulse repetition signal, ~500 MHz microwave driving field f = n500 MHz
55 X-Ray Ferromagnetic Resonance
Static XMCD Dynamic XMCD M(t) Co X-rays L3 1.0 4
L2
0.5 2
XA (arb. units)
0
0.0 -2 0.0 M
M XMCD (arb. units) -0.2 -4 XMCD -0.4 0 200 400 600 800 1000
(arb. units) FeCo_GaAs_XMCD.opj Microwave delay (ps) 770 780 790 800 photon energy (eV)
56 X-Ray Ferromagnetic Resonance
+ Precession is resonantly excited in the NiFe layer with an 4 GHz RF field. + The resonance field of the CO layer is higher, i.e. no precession is excited in the Co layer.
+ Precession in Py, Cu75Mn25, and Co layers are probed by XMCD using left- and right- circularly polarized X-rays at Ni, Mn, and Co edges, respectively.
+ The Cu75Mn25 spin precession is a direct indicator of the AC spin current through the structure.
57 X-Ray Linear Dichroism
O Cu L3 La1.85Sr0.15CuO4
Cu
L2
E units) (arb. XA XA
C. T. Chen et al. PRL 68, 2543 (1992) 920 940 960 photon energy (eV)
X-Ray Linear Dichroism: + Difference in X-ray absorption for different linear polarization direction relative to crystalline and/or spin axis. + Due to the anisotropic charge distribution about the absorbing atom caused by bonding and/or magnetic order. + “Search Light Effect”: X-ray absorption of linear polarized X rays proportional to density of empty valence states in direction of electric field vector E.
58 Structural Changes In PbZr0.2Ti0.8O3
1.0 t e 2 e 0.5 t2
XA
+ (arb. units) 0.0
//
// 0.2
0.0
difference (arb. units) -0.2
//
// Pb2+ O2 Ti4+, Zr4+ 1.0
as grown 0.5
XA
(arb. units) 0.0
// ferroelectric // polarization reversed 0.00
-0.05
difference + Spontaneous electric polarization due to (arb. units) 455 460 465 470 4+ 4+ off-center shift of Ti , Zr associated with photon energy (eV) E. Arenholz et al., tetragonal distortion linear dichroism Phys. Rev. B 82, 140103 (2010) + Reversing ferroelectric polarization changes XA Change in tetragonal distortion
59 X-Ray Magnetic Linear Dichroism
// 1.0 CoFe2O4
Fe Co Isotropic d electron charge density 0.5 L3 No polarization dependence L3 L2 XA (arb. units) XA (arb. L2 → L → [001] S 0.0 0.02 // = 0 H
Magnetically aligned system 0.00
Spin-orbit coupling distorts -0.02 = 45 charge density H
Polarization dependence CoFe2O4_110_Sept.opj XMLD (arb. units) XMLD (arb. // 700 710 720 730 780 790 800 photon energy (eV) 2 2 + IXMLD = I|| I m , m = expectation value of square of atomic magnetic moment + XMLD allows investigating ferri- and ferromagnets as well as antiferromagnets + XMLD spectral shape and angular dependence are determined by magnetic order and lattice symmetry
60 X-Ray Magnetic Linear Dichroism
1.0 antiferromagnetic NiO
L3
CoNiO_4.0.2_Ni_XMLD.opj Isotropic d electron charge density 0.5 No polarization dependence
XA (arb. units) → L3 L → S 0.0 0.05
= 0 Magnetically aligned system 0.00 [001] Spin-orbit coupling distorts -0.05
charge density = 45
Polarization dependence
XMLD (arb. units) 850 855 860 865 870 875 [001] photon energy (eV)
2 2 + IXMLD = I|| I m , m = expectation value of square of atomic magnetic moment + XMLD allows investigating ferri- and ferromagnets as well as antiferromagnets + XMLD spectral shape and angular dependence are determined by magnetic order and lattice symmetry
61 Magnetic Coupling At Interfaces
1.0 H La Sr MnO (LSMO) Mn XMCD H 0.7 0.3 3 ferromagnet 0.5 LSMO La0.7Sr0.3FeO3 (LSFO) antiferromagnet
XA (arb. units)
LSFO Fe 0.0
L 1.0 1.0 3,2 0.0 1.0 XMLD H
XMCD XMCD
(arb. units) (arb. (arb. units) 0.5 0.5 0.5 3,2
-0.2 L
640 650 (arb. units) photon energy (eV) Mn XA (arb. units) 0.0 0.0 0.0 1.0 1.0 Fe XMLD 0.2 0.0
0.5 XMLD XMLD
0.5
3,2 (arb. units)
-0.2 expt. calc. L (arb. units)
XA (arb. units) Fe 0.0 710 720 0.1 photon energy (eV) 0.0 0 100 200 300 400 temperature (K) 0.0 Perpendicular coupling
XMLD
(arb. units) -0.1 at LSMO/LSFO interface 710 720 E. Arenholz et al., photon energy (eV) Appl. Phys. Lett. 94, 072503 (2009)
62 Planar Domain Wall
1.0 Co/NiO
L3 Co FM Co 2
AFM
NiO XA H 1 H Ni
L (arb. units) (arb. units) 2 0.5 L3 L XA 2
, 0.0 NiO
x50
XMCD
0.0 XMLD
-0.2 Co/NiO (arb. units)
CoNiO_6.3.1.opj 770 780 790 850 860 870 868 870 872 photon energy (eV) photon energy (eV) 50o H 10 1.2 40o
wall angle wall Co 1.1 30o
ratio
0 2
L o 1.0 20
Ni o EH 10
Co XMCD (arb. units) -10 0.9 E||H 0o -0.5 0.0 0.5 0.0 0.2 0.4 0.6 NiO field (T) applied field (T) A. Scholl et al., Phys. Rev. Lett. 92, 247201 (2004)
63 Magnetic Microscopy
64 Magnetic Microscopy
J. Stöhr, H.C. Siegmann, 10-50 nm spatial resolution Magnetism (Springer)
65 Imaging Magnetic Domains Using X-Rays
left circ. right circ.
A B i070725_046.jpg
Co/NiO(001) 1.0
(arb. units) 0.5 i070725_050.jpg
XA A / B , A / B 0.0
XMCD
070727_Co_XMCD.opj 780 790 800
photon energy (eV) i070725_049_050_div.jpg E. Arenholz et al.,
Appl. Phys. Lett. 93, 162506 (2008) i070725_046_047_div.jpg + Images taken with left and right circularly polarized X-rays at photon energies
with XMCD, i.e. Co L3 edge, provide magnetic contrast and domain images.
66 Magnetic Coupling At Co/NiO Interface
X rays Co XMCD
+ Taking into account the geometry 5 m dependence of the Ni XMLD signal Ni XMLD Perpendicular coupling of Co and NiO moments at the interface.
5 m E. Arenholz et al., Appl. Phys. Lett. 93, 162506 (2008) probing in-plane
67 Magnetic Vortices
+ First direct observation of vortex state in antiferromagnetic CoO and NiO disks in Fe/CoO and Fe/NiO bilayers using XMCD and XMLD. + Two types of AFM vortices: - conventional curling vortex as in ferromagnets - divergent vortex, forbidden in ferromagnets - thickness dependence of magnetic interface coupling
conventional curling divergent vortex vortex
J. Wu et al., Nature Phys. 7, 303 (2011)
68 Nanoscale Magnetic Phases
AFM
T R
AFM
2m + BiFeO3 – multiferroic = ferroelectric + antiferromagnetic + Compressive strain on rhombohedral phase (R-phase) induced by substrate tetragonal-like phase (T-phase) + Partial relaxation of epitaxial strain Formation of a nanoscale mixture of T- and R-phases 2m
Q. He et al., Nature Comm. 2, 225 (2011)
69 Nanoscale Magnetic Phases
AFM PFM
XMCD PEEM XMCD-PEEM
2m
+ Highly distorted R-phase is the source of 2m enhanced magnetic moment in the XMCD
Q. He et al., image. Nature Comm. 2, 225 (2011)
70 Ultrafast Magnetism
+ Energy reservoirs in a ferromagnetic metal + Deposition of energy in one reservoir Non-equilibrium distribution and subsequent relation through energy and angular momentum exchange
Electron-phonon relaxation time
el-lat
Electron-spin el-sp lat-sp relaxation time Spin-lattice J. Stöhr, H.C. Siegmann, Magnetism (Springer) relaxation time
71 Ultrafast Dynamics Of Spin And Orbital Moments
Co0.5Pt0.5 + Orbital (L) and spin (S) magnetic moments can change with total angular momentum is conserved. + Efficient transfer between L and S through spin–orbit interaction in solids + Transfer between L and S occurs on fs timescales.
+ Co0.5Pt0.5 with perpendicular magnetic anisotropy + 60 fs optical laser pulses change magnetization + Dynamics probed with XMCD using 120fs X-ray pulses
C. Boeglin, et al., + Linear relation connects Nature 465, 458 (2010) Co L3 and L2 XMCD with Lz and Sz using sum rules
72 Ultrafast Dynamics Of Spin And Orbital Moments
+ Thermalization: Faster decrease of orbital moment + Theory: Orbital magnetic moment strongly correlated with magnetocrystalline anisotropy + Reduction in orbital moment Reduction in magnetocrystalline anisotropy + Typically observed at elevated temperatures in static measurements as well
Electron-phonon relaxation time
el-lat
Electron-spin el-sp lat-sp
C. Boeglin, et al., relaxation time Spin-lattice Nature 465, 458 (2010) relaxation time
73 References And Further Reading
J. Stöhr, H.C. Siegmann Magnetism From Fundamentals to Nanoscale Dynamics Springer
74