modern emission spectroscopy in the soft x-ray...

Modern Emission Spectroscopy Modern Emission Spectroscopy in the soft Xin the soft X--ray rangeray range

INFMCNR

Alberto TagliaferriINFM – Politecnico di Milano

[email protected]

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


SummarySummary

Soft X-ray Emission SpectroscopyWhat is it? What’s it useful for?

Basics: Introduction to main featuresCase stories


What is it? What is it? What’s it useful for?What’s it useful for?


TheThe XX--ray Emission processray Emission process

ExcitationIons, electrons, photons

⇒

⇑

De-excitationElectrons (80 – 99%),

photons (20 – 1 %)


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


Single particle picture:Single particle picture:an oversimplified modelan oversimplified model

Valenceemission

Inner shellemission

Elasticscattering

and and

De-excitation=

EmissionExcitation


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


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!


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


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)


Basics: Basics: Introduction to main featuresIntroduction to main features


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 −−∝∑


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



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


3d 3dε ε


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


3d 3dε ε


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



Resonant Inelastic XResonant Inelastic X--ray Scattering ray Scattering (RIXS)(RIXS)


Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital character selectivity


Bulk sensitive (~103 Å).Magnetic field compatible.Well suited for insulators.More selective than electrons


Intensity and Intensity and tunabilitytunability::Need ofNeed of

synchrotron synchrotron radiation!!


RIXS cross sectionRIXS cross sectionII order process ⇒ Kramers – Heisenberg formula


RIXS cross sectionRIXS cross sectionPhoton in – photon out ⇒ 2D representation


RIXS cross sectionRIXS cross sectionTransition matrix elements:

from G.S. | g ⟩ to Intermediate State | i ⟩


RIXS cross sectionRIXS cross sectionTransition matrix elements:

from Intermediate | i ⟩ State to Final state | f ⟩


RIXS cross sectionRIXS cross sectionRESONANT!

Γ≈ ħ/TLarge energy resonance


RIXS cross sectionRIXS cross sectionEnergy conservation

Tranferred energy T = Ef – Eg = hνin - hνout

The Intermediate state lifetime doesn’t affect the energy

resolution!


RIXS RIXS –– single pathsingle pathSimplest case: a single scattering path

T = hυin- hυout


RIXS RIXS –– single pathsingle pathSimplest case: a single scattering path

hυout = hυin- T

T = hυin- hυout


RIXS RIXS –– Electronic correlationElectronic correlationElectron-electron interaction, single particle picture is no more valid

(e—hole interaction, exchange, configuration interaction, …)


RIXS RIXS –– double pathdouble path

⎮ Σi⟨f⎮T(e)⎮i⟩ ⟨i⎮T(a)⎮f⟩ ⎮2 = AA*+BB* + AB*+BA*

Interferenceterm


RIXS RIXS –– InterferenceInterference

⎮ Σi⟨f⎮T(e)⎮i⟩ ⟨i⎮T(a)⎮f⟩ ⎮2 = AA*+BB* + AB*+BA*

Interferenceterm


RIXS RIXS –– Multiple final statesMultiple final states


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)


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


RIXS RIXS –– ReReality is even more ality is even more complex!complex!Intermediate state relaxation

Relaxation matrix element


Case storiesCase stories


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).


Case: Case: Gd Gd metal polycrystallinemetal polycrystalline

A.Tagliaferri et al., Phys. Rev. B 60, 5728 (1999).

4p 4f5 8

4d 4f8 9


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)




100






Case: Case: CoOCoO

Collaboration:INFM

ESRF – ID08University of Tokyo

L.Braicovich et al., Phys. Rev. B 63, 245115 (2001).


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)




100






Case: layered Case: layered cupratescuprates

G. Ghiringhelli et al., Phys. Rev. Lett. 92, 117406 (2004).


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




100






Polarised excitationPolarised excitation


RIXSRIXS--XMCDXMCD


Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital characterselectivity


Bulk sensitive.Magnetic field compatible.Well suited for insulators.More selective than electrons


{

Intensity and Intensity and tunabilitytunability::need ofneed of

synchrotron synchrotron radiation!!


RIXSRIXS--XMCDXMCD


Resonant excitationEnormous cross-section difference ⇒ Chemical selectivitySelection of the absorption edge (J, l)⇒ orbital characterselectivity


Polarised excitationMagnetic propertiesAnisotropic properties

Bulk sensitive.Magnetic field compatible.Well suited for insulators.More selective than electrons


{

Polarisation,Polarisation,Intensity and Intensity and tunabilitytunability::

need ofneed ofsynchrotron synchrotron radiation!!

Even more Even more


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*


53d 6→ 3d 6L

L. Braicovich et al., submitted Phys. Rev. Lett.


ESRF, GrenobleUniversity of TokioErel = -T = hυout- hυin


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*


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.


ESRF, GrenobleUniversity of Tokio




100






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)


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


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


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


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.


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)


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).


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


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



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




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


L. Braicovich et al., submitted Phys. Rev. Lett.A. Tagliaferri et al., unpublished.


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




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


10-4Magnetic dipole-dipole interaction

now

futu

re


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!


PPerspectiveserspectives

Higher resolutionAngular dependence ⇒ Sum rulesPolarisation analysis of the scattered photons


ConclusionsConclusionsResonant inelastic soft X-ray scattering can be really attractive!

Instrumentally

Theoretically

Experimentally


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!

modern emission spectroscopy in the soft x-ray...

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