modern emission spectroscopy in the soft x-ray...
TRANSCRIPT
Modern Emission Spectroscopy Modern Emission Spectroscopy in the soft Xin the soft X--ray rangeray range
INFMCNR
Alberto TagliaferriINFM – Politecnico di Milano
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 2
CoworkersCoworkersINFM-CNR - Politecnico di Milano
Lucio BraicovichClaudia Dallera
Giacomo Ghiringhelli
Francesca FracassiKatia Giarda
Andrea Piazzalunga
ESRF – ID08
Nick Brookes
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SummarySummary
Soft X-ray Emission SpectroscopyWhat is it? What’s it useful for?
Basics: Introduction to main featuresCase stories
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What is it? What is it? What’s it useful for?What’s it useful for?
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TheThe XX--ray Emission processray Emission process
ExcitationIons, electrons, photons
⇒
⇑
De-excitationElectrons (80 – 99%),
photons (20 – 1 %)
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Energy scalesEnergy scales∆E (eV) Topic
101-102Chemical sensitivity (Core level separation) Core level Spin-Orbit interaction (10 – 50 eV)Configuration interaction (10 – 50 eV)
100
Chemical bond and inter atomic excitationsInsulator and semiconductor gapValence band separationHigh energy intra-shell excitations (spin flip)Electron correlation effectsCrystal field (1-2 eV)Collective excitations (plasmons)
10-1 Multiplet splittingIntra-shell excitations
10-2 (RT)Valence band dispersionSpin-orbit interaction in valence band and orbitalsExchange interaction in valence band and orbitals
10-4 Magnetic dipole-dipole interaction
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Single particle picture:Single particle picture:an oversimplified modelan oversimplified model
Valenceemission
Inner shellemission
Elasticscattering
and and
De-excitation=
EmissionExcitation
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Interaction of radiation with matterInteraction of radiation with matterAtomic n. Element K L-I L-II L-III M-I M-II M-III M-IV M-V N-I N-II N-III N-IV N-V N-VI N-VII O-I
1s 2s 2p1/2 2p3/2 3s 3p1/2 3p3/2 3d3/2 3d5/2 4s 4p1/2 4p3/2 4d3/2 4d5/2 4f5/2 4f7/2 5s
1 H 13.62 He 24.63 Li 54.74 Be 111.55 B 1886 C 284.27 N 409.9 37.38 O 543.1 41.69 F 696.7
10 Ne 870.2 48.5 21.7 21.611 Na 1070.8 63.5 30.4 30.512 Mg 1303 88.6 49.6 49.2113 Al 1559 117.8 72.9 72.514 Si 1839 149.7 99.8 99.215 P 2145.5 189 136 13516 S 2472 230.9 163.6 162.517 Cl 2822 270 202 20018 Ar 3205.9 326.3 250.6 248.4 29.3 15.9 15.719 K 3608.4 378.6 297.3 294.6 34.8 18.3 18.320 Ca 4038.5 438.4 349.7 346.2 44.3 25.4 25.421 Sc 4492 498 403.6 398.7 51.1 28.3 28.322 Ti 4966 560.9 460.2 453.8 58.7 32.6 32.623 V 5465 626.7 519.8 512.1 66.3 37.2 37.224 Cr 5989 696 583.8 574.1 74.1 42.2 42.225 Mn 6539 769.1 649.9 638.7 82.3 47.2 47.226 Fe 7112 844.6 719.9 706.8 91.3 52.7 52.727 Co 7709 925.1 793.2 778.1 101 58.9 59.928 Ni 8333 1008.6 870 852.7 110.8 68 66.229 Cu 8979 1096.7 952.3 932.7 122.5 77.3 75.130 Zn 9659 1196.2 1044.9 1021.8 139.8 91.4 88.6 10.2 10.131 Ga 10367 1299 1143.2 1116.4 159.51 103.5 100 18.7 18.732 Ge 11103 1414.6 1248.1 1217 180.1 124.9 120.8 29.8 29.233 As 11867 1527 1359.1 1323.6 204.7 146.2 141.2 41.7 41.734 Se 12658 1652 1474.3 1433.9 229.6 166.5 160.7 55.5 54.635 Br 13474 1782 1596 1550 257 189 182 70 6936 Kr 14326 1921 1730.9 1678.4 292.8 222.2 214.4 95 93.8 27.5 14.1 14.137 Rb 15200 2065 1864 1804 326.7 248.7 239.1 113 112 30.5 16.3 15.338 Sr 16105 2216 2007 1940 358.7 280.3 270 136 134.2 38.9 21.6 20.139 Y 17038 2373 2156 2080 392 310.6 298.8 157.7 155.8 43.8 24.4 23.140 Zr 17998 2532 2307 2223 430.3 343.5 329.8 181.1 178.8 50.6 28.5 27.141 Nb 18986 2698 2465 2371 466.6 376.1 360.6 205 202.3 56.4 32.6 30.842 Mo 20000 2866 2625 2520 506.3 411.6 394 231.1 227.9 63.2 37.6 35.543 Tc 21044 3043 2793 2677 544 447.6 417.7 257.6 253.9 69.5 42.3 39.944 Ru 22117 3224 2967 2838 586.1 483.3 461.5 284.2 280 75 46.3 43.245 Rh 23220 3412 3146 3004 628.1 521.3 496.5 311.9 307.2 81.4 50.5 47.346 Pd 24350 3604 3330 3173 671.6 559.9 532.3 340.5 335.2 87.1 55.7 50.947 Ag 25514 3806 3524 3351 719 603.8 573 374 368.3 97 63.7 58.348 Cd 26711 4018 3727 3538 772 652.6 618.4 411.9 405.2 109.8 63.9 63.9 11.7 10.749 In 27940 4238 3938 3730 827.2 703.2 665.3 451.4 443.9 122.9 73.5 73.5 17.7 16.950 Sn 29200 4465 4156 3929 884.7 756.5 714.6 4g3.2 484.9 137.1 83.6 83.6 24.9 23.951 Sb 30491 4698 4380 4132 940 812.7 766.4 537.5 528.2 153.2 95.6 95.6 33.3 32.152 Te 31814 4939 4612 4341 1006 870.8 820.8 583.4 573 169.4 103.3 103.3 41.9 40.453 I 33169 5188 4852 4557 1072 931 875 630.8 619.3 186 123 123 50.6 48.954 Xe 34561 5453 5107 4786 1148.7 1002.1 940.6 689 676.4 213.2 146.7 145.5 69.5 67.5 - - 23.355 Cs 35985 5714 5359 5012 1211 1071 1003 740.5 726.6 232.3 172.4 161.3 79.8 77.5 - - 22.756 Ba 37441 5989 5624 5247 1293 1137 1063 795.7 780.5 253.5 192 178.6 92.6 89.9 - - 30.357 La 38925 6266 5891 5483 1362 1209 1128 853 836 274.7 205.8 196 105.3 102.5 - - 34.358 Ce 40443 6548 6164 5723 1436 1274 1187 902.4 883.8 291 223.2 206.5 109 - 0.1 0.1 37.859 Pr 41991 6835 6440 5964 1511 1337 1242 948.3 928.8 304.5 236.3 217.6 115.1 115.1 2 2 37.460 Nd 43569 7126 6722 6208 1575 1403 1297 1003.3 980.4 319.2 243.3 224.6 120.5 120.5 1.5 1.5 37.561 Pm 45184 7428 7013 6459 - 1471.4 1357 1052 1027 - 242 242 120 120 - - -62 Sm 46834 7737 7312 6716 1723 1541 1419.8 1110.9 1083.4 347.2 265.6 247.4 129 129 5.2 5.2 37.463 Eu 48519 8052 7617 6977 1800 1614 1481 1158.6 1127.5 360 284 257 133 127.7 0 0 3264 Gd 50239 8376 7930 7243 1881 1688 1544 1221.9 1189.6 378.6 286 271 - 142.6 8.6 8.6 3665 Tb 51996 8708 8252 7514 1968 1768 1611 1276.9 1241.1 396 322.4 284.1 150.5 150.5 7.7 2.4 45.666 Dy 53789 9046 8581 7790 2047 1842 1676 1333 1292 414.2 333.5 293.2 153.6 153.6 8 4.3 49.967 Ho 55618 9394 8918 8071 2128 1923 1741 1392 1351 432.4 343.5 308.2 160 160 8.6 5.2 49.3
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 9
Traditional FluorescenceTraditional FluorescenceBinary alloy AxBy, species A and B have comparable cross-section
hνout
EF EF
hνout
EF
hνout
+ ⇒
Excitation well above any absorption edge!
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Traditional FluorescenceTraditional FluorescenceMain features:
Photon in – Photon outBulk sensitive.Magnetic field compatible.Well suited also for insulators.
Optical transitionsMore selective than photoemission
Soft X-ray (E < 2 keV) ⇒ el. dipole (E1)Hard X-ray ⇒ dipole (E1) + quadrupole (E2)
Well suited for chemical analysisAlthough Not chemically selective in the
excitation step!
EF
hνout
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Resonant SpectroscopyResonant SpectroscopyResonant emission spectroscopy, also known as
Resonant Inelastic X-ray Scattering (RIXS) adds to the traditional fluorescence:
Selectivity– chemistry– crystal site– oxidation state– orbital character
Intensity (sometime)
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Basics: Basics: Introduction to main featuresIntroduction to main features
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Interaction of el.Interaction of el.--magnmagn. radiation with matter. radiation with matterAbsorption cross section
10 100 1000 10000 100000
Cros
sse
ctio
n(A
.U.)
Energy (eV)
))(2)(ingf
f
a hEEfTg νδσ −−∝∑
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Interaction of el.Interaction of el.--magnmagn. radiation with matter. radiation with matterAbsorption cross section
10 100 1000 10000 100000
Cros
sse
ctio
n(A
.U.)
Energy (eV)
EF
3d5/2
4f
3d3/2
))(2)(ingf
f
a hEEfTg νδσ −−∝∑
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Absorption Fine StructureAbsorption Fine StructureDetailed Absorption cross section at
an absorption edgeChemical and site selectivity
No buried structures (TEY measurements)Resolution limited by the final state lifetime
2p63dn → (2p53dn+1, 2p53dnε)
EF
2p3/2
2p1/2
EF
2p3/2
2p1/2
))((2)(ingf
f
a hEEfTg νδσ −−∝∑
3d 3dε ε
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Absorption Fine StructureAbsorption Fine StructureDetailed Absorption cross section at
an absorption edgeChemical and site selectivityOrbital character selectivity
∆l = ±1, ∆s = 0, ∆j = 0, ±1No buried structures (TEY measurements)Resolution limited by the final state lifetime
2p63dn → (2p53dn+1, 2p53dnε)
EF
2p3/2
2p1/2
EF
2p3/2
2p1/2
))((2)(ingf
f
a hEEfTg νδσ −−∝∑
3d 3dε ε
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Resonant Inelastic XResonant Inelastic X--ray Scattering ray Scattering (RIXS)(RIXS)
Main features:Photon in – Photon out
Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital character selectivity
Chemical shift ⇒ Site and oxidation state selective
Bulk sensitive (~103 Å).Magnetic field compatible.Well suited for insulators.More selective than electrons
Soft X-ray (E < 2 keV) ⇒ el. dipole (E1)Hard X-ray ⇒ dipole (E1) + quadrupole (E2)
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Resonant Inelastic XResonant Inelastic X--ray Scattering ray Scattering (RIXS)(RIXS)
Main features:Photon in – Photon out
Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital character selectivity
Chemical shift ⇒ Site and oxidation state selective
Bulk sensitive (~103 Å).Magnetic field compatible.Well suited for insulators.More selective than electrons
Soft X-ray (E < 2 keV) ⇒ el. dipole (E1)Hard X-ray ⇒ dipole (E1) + quadrupole (E2)
Intensity and Intensity and tunabilitytunability::Need ofNeed of
synchrotron synchrotron radiation!!
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RIXS cross sectionRIXS cross sectionII order process ⇒ Kramers – Heisenberg formula
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RIXS cross sectionRIXS cross sectionPhoton in – photon out ⇒ 2D representation
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RIXS cross sectionRIXS cross sectionTransition matrix elements:
from G.S. | g ⟩ to Intermediate State | i ⟩
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RIXS cross sectionRIXS cross sectionTransition matrix elements:
from Intermediate | i ⟩ State to Final state | f ⟩
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RIXS cross sectionRIXS cross sectionRESONANT!
Γ≈ ħ/TLarge energy resonance
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RIXS cross sectionRIXS cross sectionEnergy conservation
Tranferred energy T = Ef – Eg = hνin - hνout
The Intermediate state lifetime doesn’t affect the energy
resolution!
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RIXS RIXS –– single pathsingle pathSimplest case: a single scattering path
T = hυin- hυout
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RIXS RIXS –– single pathsingle pathSimplest case: a single scattering path
hυout = hυin- T
T = hυin- hυout
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RIXS RIXS –– Electronic correlationElectronic correlationElectron-electron interaction, single particle picture is no more valid
(e—hole interaction, exchange, configuration interaction, …)
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RIXS RIXS –– double pathdouble path
⎮ Σi⟨f⎮T(e)⎮i⟩ ⟨i⎮T(a)⎮f⟩ ⎮2 = AA*+BB* + AB*+BA*
Interferenceterm
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RIXS RIXS –– InterferenceInterference
⎮ Σi⟨f⎮T(e)⎮i⟩ ⟨i⎮T(a)⎮f⟩ ⎮2 = AA*+BB* + AB*+BA*
Interferenceterm
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RIXS RIXS –– Multiple final statesMultiple final states
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RIXS cross section calculationsRIXS cross section calculationsAb initio ionic calculation of the KH formula
good for localised shells (TM 3d, RE 4f)
2p63d n → 2p53d n+1 → (2p63d n, 2p63s13d n+1)3d104f n → 3d94f n+1 → (3d104f n, 3d104p54f n+1)
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RIXS RIXS –– Reality is complex!Reality is complex!Excitation into the Continuum of states ε
1) Elasticscattering
2) Valencescattering
3) Inner shellscattering
3
2
1
1 2 3
EF
2p3/2
2p1/2
EF
3d
3s
EF
3s
εε ε
3s
3d 3dEF
3s
ε
3dEF
3s
ε
3d
2p3/2
2p1/2
2p3/2
2p1/2
2p3/2
2p1/2
2p3/2
2p1/2
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RIXS RIXS –– ReReality is even more ality is even more complex!complex!Intermediate state relaxation
Relaxation matrix element
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Case storiesCase stories
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Case: Case: Gd Gd metal polycrystallinemetal polycrystalline
Collaboration:INFM, Milano and TASC Trieste
Daresbury Lab.ESRF – ID08
Freie Universität Berlin
A.Tagliaferri et al., Phys. Rev. B 60, 5728 (1999).
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 36
Case: Case: Gd Gd metal polycrystallinemetal polycrystalline
A.Tagliaferri et al., Phys. Rev. B 60, 5728 (1999).
4p 4f5 8
4d 4f8 9
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 37
Case:Case: GdGd metal polycrystallinemetal polycrystalline
Coster-Kronig
relaxation
3d5/2
4fEF
2p1/2
2p3/2
3d
3d3/2
3d3/244f n → (3d3/2
34f n+1, 3d3/234f nε) → (3d3/2
44p 54f n+1, 3d3/244p 54f nε)
3d3/244f n → (3d3/2
34f n+1, 3d3/234f nε) → (3d5/2
54f n+1 ε, 3d5/254f nε2) → (3d5/2
64f n+1 ε, 3d5/264f nε)
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Energy scalesEnergy scales∆E (eV) Topic
101-102Chemical sensitivity (Core level separation) Core level Spin-Orbit interaction (10 – 50 eV)Configuration interaction (10 – 50 eV)
100
Chemical bond and inter atomic excitationsInsulator and semiconductor gapValence band separationHigh energy intra-shell excitations (spin flip)Electron correlation effectsCrystal field (1-2 eV)Collective excitations (plasmons)
10-1 Multiplet splittingIntra-shell excitations
10-2 (RT)Valence band dispersionSpin-orbit interaction in valence band and orbitalsExchange interaction in valence band and orbitals
10-4 Magnetic dipole-dipole interaction
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Case: Case: CoOCoO
Collaboration:INFM
ESRF – ID08University of Tokyo
L.Braicovich et al., Phys. Rev. B 63, 245115 (2001).
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Case: La compoundsCase: La compounds
Collaboration:INFM, Milano
ESRF, Grenoble
Elastic peak A4f 0 → 3d 94f 1→ 4f 0
Charge transfer excitations B4f 0 → 3d 94f 1→ 4f 1L
Peak C4f 0 → 3d 94f 1 → 5p54f 1
Eloss = -T = hυout- hυin
C. Dallera et al., Phys. Rev. B 64, 153104 (2001)
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 41
Energy scalesEnergy scales∆E (eV) Topic
101-102Chemical sensitivity (Core level separation) Core level Spin-Orbit interaction (10 – 50 eV)Configuration interaction (10 – 50 eV)
100
Chemical bond and inter atomic excitationsInsulator and semiconductor gapValence band separationHigh energy intra-shell excitations (spin flip)Electron correlation effectsCrystal field (1-2 eV)Collective excitations (plasmons)
10-1 Multiplet splittingIntra-shell excitations
10-2 (RT)Valence band dispersionSpin-orbit interaction in valence band and orbitalsExchange interaction in valence band and orbitals
10-4 Magnetic dipole-dipole interaction
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Case: layered Case: layered cupratescuprates
G. Ghiringhelli et al., Phys. Rev. Lett. 92, 117406 (2004).
Collaboration:INFM, Milano
ESRF, GrenobleEPFL, Lausanne
d-d excitations3d 9 → 2p3/2
53d10→ 3d 9*
Charge transfer excitations3d 9 → 2p3/2
53d10→ 3d 10L
Important for HTc supercondutivity
CuO: no apical Oxygen
Resolution ∆E ~ 800 meV,
Cu L3 edge
∆E 300 meV
Erel = -T = hυout- hυin
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 43
Energy scalesEnergy scales∆E (eV) Topic
101-102Chemical sensitivity (Core level separation) Core level Spin-Orbit interaction (10 – 50 eV)Configuration interaction (10 – 50 eV)
100
Chemical bond and inter atomic excitationsInsulator and semiconductor gapValence band separationHigh energy intra-shell excitations (spin flip)Electron correlation effectsCrystal field (1-2 eV)Collective excitations (plasmons)
10-1 Multiplet splittingIntra-shell excitations
10-2 (RT)Valence band dispersionSpin-orbit interaction in valence band and orbitalsExchange interaction in valence band and orbitals
10-4 Magnetic dipole-dipole interaction
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 44
Polarised excitationPolarised excitation
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RIXSRIXS--XMCDXMCD
Main features:Photon in – Photon out
Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital characterselectivity
Chemical shift ⇒ Site and oxidation state selective
Bulk sensitive.Magnetic field compatible.Well suited for insulators.More selective than electrons
Soft X-ray (E < 2 keV) ⇒ el. dipole (E1)Hard X-ray ⇒ dipole (E1) + quadrupole (E2)
{
Intensity and Intensity and tunabilitytunability::need ofneed of
synchrotron synchrotron radiation!!
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 46
RIXSRIXS--XMCDXMCD
Main features:Photon in – Photon out
Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital characterselectivity
Chemical shift ⇒ Site and oxidation state selective
Polarised excitationMagnetic propertiesAnisotropic properties
Bulk sensitive.Magnetic field compatible.Well suited for insulators.More selective than electrons
Soft X-ray (E < 2 keV) ⇒ el. dipole (E1)Hard X-ray ⇒ dipole (E1) + quadrupole (E2)
{
Polarisation,Polarisation,Intensity and Intensity and tunabilitytunability::
need ofneed ofsynchrotron synchrotron radiation!!
Even more Even more
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Case: Case: MnO, state of the art resolutionMnO, state of the art resolutionMn L2,3 edge
Very structured d-d excitations (d 5)3d 5 → 2p3/2
53d 6→ 3d 5*
Charge transfer excitations3d 5 → 2p3/2
53d 6→ 3d 6L
L. Braicovich et al., submitted Phys. Rev. Lett.
Collaboration:INFM, Milano
ESRF, GrenobleUniversity of TokioErel = -T = hυout- hυin
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 48
Case: Case: MnO, state of the art resolutionMnO, state of the art resolution
Very structured d-d excitations (d 5)3d 5 → 2p3/2
53d 6→ 3d 5*
Charge transfer excitations3d 5 → 2p3/2
53d 6→ 3d 6LImportant ab initio calculation tuning:
CT energy ∆ = 6.5 eVon site Coulomb int. Udd = 7.2 eVcore hole-valence int. Udc = 8.0 eVCrystal field 10Dq = 0.5 eV
Anderson impurity vs ionic cluster modelTotal Energy resolution ∆E = 300 meV
(Resolving power > 2000)
Data
Calc.
L. Braicovich et al., submitted Phys. Rev. Lett.
Collaboration:INFM, Milano
ESRF, GrenobleUniversity of Tokio
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 49
Energy scalesEnergy scales∆E (eV) Topic
101-102Chemical sensitivity (Core level separation) Core level Spin-Orbit interaction (10 – 50 eV)Configuration interaction (10 – 50 eV)
100
Chemical bond and inter atomic excitationsInsulator and semiconductor gapValence band separationHigh energy intra-shell excitations (spin flip)Electron correlation effectsCrystal field (1-2 eV)Collective excitations (plasmons)
10-1 Multiplet splittingIntra-shell excitations
10-2 (RT)Valence band dispersionSpin-orbit interaction in valence band and orbitalsExchange interaction in valence band and orbitals
10-4 Magnetic dipole-dipole interaction
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XMCDXMCD
l=2
l=1 j=l+s=3/2j=l-s=1/2
left Right
Magnetic propertiesSum rules ⇒ Spin and orbital moment
Increased site selectivity
Sa mpleCPL M
Longitudinal
Sa mpleCPL
M
Perpendicular
2p63dn → (2p53dn+1, 2p53dnε)
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RIXS Circular DichroismRIXS Circular DichroismDichroism in absorption and in emission Magnetic properties
Increased selectivity with respect to absorption spectroscopy
))()(()(..., 2)()(
outingff i iiing
ae
hhEEiEhvEgTiiTf
helicity ννδσ −−−×Γ−−+
∝∑∑
2p63dn → (2p53dn+1, 2p53dnε) → (2p63dn, 2p63dn-1ε)
l=2
l=1 j=l+s=3/2j=l-s=1/2
left Right
l=2
l=1 j=l+s=3/2j=l-s=1/2
left Right
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Circular Dichroism Circular Dichroism –– Geometry Geometry Polarised core hole → angular dependence of
the emissionDichroism in emission even when absent in
absorption (perpendicular geometry)
Sa mpleCPL M
Longitudinal
Sa mpleCPL
M
Perpendicular
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 53
Circular Dichroism Circular Dichroism –– GeometryGeometryPolarised core hole → angular dependence of
the emissionDichroism in emission even when then absent
in absorption
Sa mpleCPL M
Longitudinal
Sa mpleCPL
M
Perpendicular
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Saturation and selfSaturation and self--absorptionabsorptionMin. saturationMax. self-absorption
Max. saturationMin. self-absorption
Spectra need to be corrected for the saturation - self-absorption to compare with calculations
The inner shell scattering limits the effect because the emitted photons do not have the enough energy to excite resonantly the atoms of the emitting species.
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 55
RIXS MCDRIXS MCDExample in longitudinal geometry Example in longitudinal geometry
Magnetic Mn impurities (2%) in polycrystalline NiSaturation and self-absorption are dichroic!
Concentrated systems → heavy correctionsDilute systems → limited self-absorption
Leading step for dichroism: absorption
What’s useful for: Check ab initio calculations → parameters from
ionic model (Crystal field, Exchange interaction, electron screening, …)
optical constantsElectronic excitations (spin flip, charge transfer, …)Local environment (inter-atomic interactions)
2p63dn → (2p53dn+1, 2p53dnε) → (2p63dn, 2p63dn-1ε)
F.Borgatti, P.Ferriani, G.Ghringhelli, A.Tagliaferri, B.De_Michelis, C.M.Bertoni, N.B.Brookes, L.Braicovich, Phys. Rev. B 65, 094406 (2002)
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 56
RIXS MCDRIXS MCDExample in perpendicular geometry Example in perpendicular geometry
Perpendicular geometry → no dichroism in absorptionConcentrated systems
Valence scattering is heavily affected by Saturation and self-absorption
Inner-shell scatteringMuch less affected by self-absorptionStill affected by saturation, but the effect is not
dichroic because XMCD in absorption is zeroDichroism ONLY present in the emission channel
What’s useful for ? Same as longitudinal geometry, but much cleaner!
Atomic properties of the elements in condensed matter
More stringent constraints on the calculationsSum rules in Scattering → higher multipole moment
properties of the Ground State
Ni in ferrite oxide (NiFe2O4) and Co in metal
M
P
ε
x
y
z
θ
2p63dn → (2p53dn+1, 2p53dnε) → (2p63s13dn+1, 2p63s13dn-1ε)
L. Braicovich, G. van_der_Laan, G. Ghiringhelli, A. Tagliaferri, M.A. van Veenendaal, N.B. Brookes, M.M. Chervinskii, C. Dallera, B. De Michelis, H.A. Dürr, Phys. Rev. Lett. 82, 1566 (1999).
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 57
RIXS MCD RIXS MCD -- Symmetry breaking in perpendicular Symmetry breaking in perpendicular geometry due to the emission direction geometry due to the emission direction
M
P
ε
x
y
z
θ
Intermediate state core hole polarization upon excitation with circularly polarised light
Dipole optical transition → the core hole orbital moment tends to be aligned with the exciting photon helicity
Ferromagnetic state → the core hole spin moment tends to be aligned with the sample magnetisation
Spin-orbit interaction → the spin and orbital moment tends to be coaxial
The trade-off is a core hole with a symmetry axis aligned along an intermediate direction with respect to the photon helicity and
the magnetisation
M
P
M
P
P ⇔ -P
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 58
RIXS MCDRIXS MCDIonic Ni in perpendicular geometry Ionic Ni in perpendicular geometry
Ni in ferrite oxide (NiFe2O4): a test caseNi2+ ion (electrons localised on the atom
site, narrow bands).Ferromagnetic stateGood agreement with ab initio calculations
2p63dn → 2p53dn+1 → 2p63s13dn+1
M
P
ε
x
y
z
θ
L. Braicovich, G. van_der_Laan, G. Ghiringhelli, A. Tagliaferri, M.A. van Veenendaal, N.B. Brookes, M.M. Chervinskii, C. Dallera, B. De Michelis, H.A. Dürr, Phys. Rev. Lett. 82, 1566 (1999).
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 59
RIXS MCDRIXS MCDMetallic Co in perpendicular geometry Metallic Co in perpendicular geometry
Co metal: a delocalised system Co has similar 3d shell occupation with
respect to Ni2+ (7 to 8 electrons ).Wide 3d band → delocalisedFerromagnetic stateThe ionic model is not appropriate a priori
FindingsThe measured dichroism is 1/3 of the
theoretical for a Co2+ ionThe dichroism at the L2 edge is zero in
agreement with the theory (J too low)Sizable dichroism in between the two
edges, not compatible with an ionic model
M
P
ε
x
y
z
θ
2p63dn → (2p53dn+1, 2p53dnε) → (2p63s13dn+1, 2p63s13dn-1ε)
L. Braicovich, G. van_der_Laan, G. Ghiringhelli, A. Tagliaferri, M.A. van Veenendaal, N.B. Brookes, M.M. Chervinskii, C. Dallera, B. De Michelis, H.A. Dürr, Phys. Rev. Lett. 82, 1566 (1999).
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 60
RIXS MCDRIXS MCDMetallic Co in perpendicular geometry Metallic Co in perpendicular geometry
New technique (IRRS)Coarse energy resolution on hνoutSensitivity to the linear polarisation of the
emitted photons
FindingsThe circular dichroism appears only for emitted
photons with E perpendicular to the scattering plane.
The dichroism above the L3 and L2 edge depends on the cinetic of the core hole and of the spin spin rearrangement in the valence band
Circular dichroism in IRRSfor scattered light with E vector parallel ( ) and perpendicular ( ) to the scattering plane
ps
Co metal
M
P
ε
x
y
z
θ
Ep
Es
Ep
Es
2p63dn → (2p53dn+1, 2p53dnε) → (2p63s13dn+1, 2p63s13dn-1ε)
L. Braicovich et al., submitted Phys. Rev. Lett.A. Tagliaferri et al., unpublished.
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 61
SoftSoft XX--ray Emission spectrographray Emission spectrograph
Crucial parameters:Resolving power E/∆ECounting rate d(cosα - cosβ) = nλ
E/∆E ∝ 1/d
d
S.M.Butorin et al., PRB 54, 4405 (1996) L. Braicovich et al., submitted to PRL
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 62
Energy scalesEnergy scales∆E (eV) Topic
101-102Chemical sensitivity (Core level separation) Core level Spin-Orbit interaction (10 – 50 eV)Configuration interaction (10 – 50 eV)
100
Insulator gapValence band separationHigh energy intra-shell excitations (spin flip)Electron correlation effectsCristal field (1-2 eV)Collective excitations (plasmons)
10-1Multiplet splittingIntra-shell excitations
10-2 (RT)Valence band dispersionSpin-orbit interaction in valence band and orbitalsExchange interaction in valence band and orbitals
10-4Magnetic dipole-dipole interaction
now
futu
re
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 63
RIXS in the soft XRIXS in the soft X--ray rangeray rangePhoton in – Photon out
Bulk sensitive.Magnetic field compatible.Well suited also for insulators.
Optical transitionsMore selective than electrons ⇒ el. dipole (E1)Well suited for chemical analysis
Resonant excitationChemical selectivitySite selectivityOrbital character selectivity
PolarisationMagnetic propertiesAnisotropic properties
Fluorescence
Need synchrotron
source!
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 64
PPerspectiveserspectives
Higher resolutionAngular dependence ⇒ Sum rulesPolarisation analysis of the scattered photons
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 65
ConclusionsConclusionsResonant inelastic soft X-ray scattering can be really attractive!
Instrumentally
Theoretically
Experimentally
Frascati, 19 october, 2005 VIII Scuola Nazionale di Luce di Sincrotrone 66
ConclusionsConclusionsResonant inelastic soft X-ray scattering can be really attractive!
Instrumentally → is developing!Theoretically → is a stringent test for the most
performant ab initio calculations!Experimentally → is very selective!