X-ray Absorption Spectroscopy

X-ray Absorption Spectroscopy
Introduction to XAS XAS detection techniques XAS spectral shape 2p XAS multiplet calculations RIXS experiments & calculations

Element specific Sensitive to low concentrations Applicable under extreme conditions SPACE: Combination with x-ray microscopy TIME: femtosecond XAS RESONANCE: RIXS, RPES, R diffraction XAS is element specific because each element has specific binding energies for its core levels. The XAS edge energy is essentially given by the core level binding energy.

Energy  Spectroscopy Direction  Structure Polarization  Magnetism I’(’,k’,q’) I(,k,q) I”(Ek,k”,)

Energy  Spectroscopy Direction  Structure Polarization  Magnetism I’() I(,q)

XAS: spectral shape Excitations of core electrons to empty states
The XAS spectra are given by the Fermi Golden Rule exciton edge jump

3d O2p O2s 3p Excitation of 2p to 3d state Lifetime of excitation is short Lifetime broadening ~200 meV 6

X-ray absorption & x-ray emission X-ray Absorption Spectroscopy Decay of 3d electron to 3p core state X-ray emission 7

X-ray absorption & Auger X-ray Absorption Spectroscopy Decay of 3d/valence electron to 3p core state Energy used to excite a 3d/valence electron Auger electron spectroscopy 8

What is the main decay process
Question: What is the main decay process of a core hole? Electronic (Auger) Radiative (X-ray emission) Soft x-rays: Electronic & Hard x-rays Radiative Soft x-rays: Radiative & Hard x-rays Electronic 9

What is the main decay process
Question: What is the main decay process of a core hole? Electronic (Auger) Radiative (X-ray emission) Soft x-rays: Electronic & Hard x-rays Radiative Soft x-rays: Radiative & Hard x-rays Electronic 10

1s core state 11

XAS: detection techniques

Use decay channels as detector XAS: detection techniques Uniform thickness Uniform concentration of absorbing element Thin enough for photons (CXRO numbers 5 times too large at the edge)

X-ray penetration lengths & electron escape depths
XAS: detection techniques X-ray penetration lengths & electron escape depths nm (CXRO, but 20 nm for L edges) 1-5 nm

Use decay channels as detector XAS: detection techniques X-ray penetrate 1000 nm (λX) Electrons escape from 5 nm (λE) Number of core holes created in first 5 nm is proportional to μ and angle of incidence (α) ITEY ~ λE / (λE + λX cos α) ITEY ~ 1 / λX = μX

Fluorescence Yield XAS: detection techniques saturation & self-absorption

Transmission (pinhole, saturation > thin samples) Electron Yield (surface sensitive) Fluorescence Yield (saturation & self-absorption: > dilute samples) [L edges are intrinsically distorted; discussed in RIXS]

Interpretation of spectral shapes
XAS: spectral shape Interpretation of spectral shapes 18

XAS: spectral shape Excitations of core electrons to empty states
The XAS spectra are given by the Fermi Golden Rule exciton edge jump

X XAS: spectral shape (O 1s) O 1s Fermi Golden Rule 
Excitations to empty states as calculated by DFT X O 1s 20

XAS: spectral shape (O 1s)
Phys. Rev. B.40, 5715 (1989)

oxygen 1s > p DOS Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)

Phys. Rev. B. 40, 5715 (1989); 48, 2074 (1993)

XAS: spectral shape TiSi2
Final State Rule: Spectral shape of XAS looks like final state DOS Phys. Rev. B. 41, (1991)

XAS: spectral shape TiSi2 XAS codes:
Multiple scattering: FEFF, FDMNES, etc. Band structure: WIEN2K, Quantumespresso, etc. Real-space DFT: ADF, etc. Phys. Rev. B. 41, (1991)

X Iron 1s XAS 2p XAS of transition metal ions 2p > 3d
exciton edge jump 2p > 3d (3d5 > 2p53d6, self screened) X 2p > s,d DOS [Phys. Rev. B. 42, 5459 (1990)] 26

XAS: multiplet effects
XAS: spectral shape Overlap of core and valence wave functions  Single Particle model breaks down 3d <2p3d|1/r|2p3d> 2p3/2 2p1/2 Phys. Rev. B. 42, 5459 (1990)

Soft x-rays: Electronic & Hard x-rays Radiative
How much progress has there been in the measurement of an XAS spectrum in the last 30 years? Today we can measure much sharper spectra because the experimental resolution has been improved to better than 100 meV Today we can measure a little bit sharper spectra because the experimental resolution has been improved. The spectra we measure today are exactly the same as those measured 30 years ago. Soft x-rays: Electronic & Hard x-rays Radiative Soft x-rays: Radiative & Hard x-rays Electronic 28

Soft x-rays: Electronic & Hard x-rays Radiative
How much progress has there been in the measurement of an XAS spectrum in the last 30 years? Today we can measure much sharper spectra because the experimental resolution has been improved to better than 100 meV Today we can measure a little bit sharper spectra because the experimental resolution has been improved. The spectra we measure today are exactly the same as those measured 30 years ago. (as they are limited by lifetime broadening) Soft x-rays: Electronic & Hard x-rays Radiative Soft x-rays: Radiative & Hard x-rays Electronic 29

XAS: spectral shape XAS 1s DFT pre-edge of 3d system ?? 2p, 3p, 3d, 4d
multiplets

Pre-edges structures in 1s XAS X-ray absorption of a solid
Fe 4p Fe 3d O 2p O 2s Fe 3p 50 Fe 3s O 1s Fe 2p Fe 2s Fe 1s 7115

Pre-edges structures in 1s XAS
exciton edge jump 1s 1 3d N+1 4p 3d N 4p pre-edge

Pre-edges structures in 1s XAS
3d N 4p pre-edge [J. Phys. Cond. Matt. 21, (2009)]

XAS: spectral shape XAS 2p, 3p, 1s 3d, 4d pre-edge DFT of 3d system
multiplets

Multiplet calculations
Iron 1s XAS Multiplet calculations XAS MCD XPS RIXS (Resonant) Auger RPES EELS 35

Charge Transfer Multiplet program
Used for the analysis of XAS, EELS, Photoemission, Auger, XES [of d and f electron systems] ATOMIC PHYSICS  GROUP THEORY MODEL HAMILTONIANS CTM4XAS (semi-empirical) The TT-multiplets program can be used to explain the spectral shapes of all core level spectroscopies. XAFS, photoemission, auger, etc. The program combines three advanced computer codes, an atomic physics code to describe all atomic interactions, a group theory code to describe the local symmetry (think of crystal fields) and model Hamiltonians to describe many body effects correlated systems. AS A SIDE REMARK I WOULD LIKE TO MENTION that the active site in a catalyst is a perfect example of a correlated system. (in biocatalysis this is often realised) The integrated program gives accurate descriptions of core level spectra, from a set of uniform electronic structure parameters. The program is important for all of the new spectroscopies that I will describe. The program is distributed from my homepage and it is used at some 50 institutes worldwide.

3d XAS of rare earths 4f electrons are localized
No effect of surroundings (no crystal field) 3d XAS is self screened > no charge transfer effect Initial state electron-electron interaction. Valence spin-orbit coupling Final state The core hole – valence hole ‘multiplet’ interaction. The core hole spin-orbit coupling

3d XAS of rare earths Nd3+ 4f3 system: ground state is 4I9/2

2p XAS of NiO with atomic multiplets

2p XAS of 3d transition metal oxides
3d electrons are less localized Effect of surroundings (crystal field effect) 3d XAS is self screened > weak charge transfer effect Initial state electron-electron interaction. valence spin-orbit coupling crystal field effect Final state core hole – valence hole ‘multiplet’ interaction. core hole spin-orbit coupling

crystal field effect Crystal Field Effects eg states t2g states

crystal field effect: spin state
High-spin or Low-spin E T2 E T2 High-spin 3d5 Low-spin 3d5

valence e-e interactions Fdd core-valence e-e Fpd Gpd core & valence spin-orbit ζ crystal field 10Dq, Ds, Dt molecular field, M or H e-e screening κ charge transfer Δ, U, Q hopping TΓ ionic 3d (4d, 5d) 4f, 5f covalent 3d mixed valence f ATOMIC SYMMETRY BONDING

valence e-e interactions Fdd core-valence e-e Fpd Gpd core & valence spin-orbit ζ crystal field 10Dq, Ds, Dt molecular field, M or H e-e screening κ charge transfer Δ, U, Q hopping TΓ ionic 3d (4d, 5d) 4f, 5f 3d ions covalent 3d mixed valence f ATOMIC SYMMETRY BONDING

Charge Transfer Effects
Hubbard U for a 3d8 ground state: U= E(3d7) + E(3d9) – E(3d8) – E(3d8) Ligand-to-Metal Charge Transfer (LMCT): = E(3d9L) – E(3d8)

What parameter is most important for an XAS spectrum, U or Δ?
Both U and Δ are important The Hubbard U is much more important The charge transfer Δ is much more important 46

What parameter is most important for an XAS spectrum, U or Δ?
Both U and Δ are important The Hubbard U is much more important The charge transfer Δ is much more important 47

Main screening mechanism in XAS of oxides: Ligand-to-metal charge transfer Charge transfer energy  is important for XAS Hubbard U is NOT very important for XAS

NiO: Ground state: 3d8 + 3d9L Energy of 3d9L: Charge transfer energy  3d9L 3d8 2p53d10L 2p53d9  +U-Q  

Charge transfer effects in XAS and XPS
Transition metal oxide: Ground state: 3d5 + 3d6L Energy of 3d6L: Charge transfer energy  3d6L XPS 2p53d5 XAS 2p53d7L  3d5 -Q Ground State +U-Q   2p53d6L 2p53d6

Charge Transfer Multiplets of Ni2+
Charge transfer effects in XAS =3 =9 =0 =6

Charge transfer effects in XAS

Charge Transfer effects
Charge transfer effects in XAS Charge Transfer effects 3d8 + 3d9L =10 30% 3d8 1A1 =5 NiO =0 30% 3d8 3A2 La2Li½Cu½O4 =-5 =-10 Chem. Phys. Lett. 297, 321 (1998)

LMCT and MLCT:  - bonding
FeIII: Ground state: 3d5 + 3d6L 3d6L 3d5 2p53d7L 2p53d6 +U-Q    with Ed Solomon (Stanford) JACS 125, (2003), JACS 128, (2006), JACS 129, 113 (2007)

FeIII: Ground state: 3d5 + 3d6L + 3d4L 2p53d5L 2p53d7L 2p53d6 3d4L 3d6L 3d5 -U+Q   + 2   +U-Q   - 2 with Ed Solomon (Stanford) JACS 125, (2003), JACS 128, (2006), JACS 129, 113 (2007)

FeIII(tacn)2 FeIII(CN)6 with Ed Solomon (Stanford) JACS 125, (2003), JACS 128, (2006), JACS 129, 113 (2007)

Calculated for an atom/ion Valence and core spin-orbit coupling Core and valence electron-electron interaction. Comparison with experiment Core hole potential and lifetime Local symmetry (crystal field) Spin-spin interactions (molecular field) Core hole screening effects (charge transfer) 57

First Principle Multiplet calculations
Calculated for an atom/ion Valence and core spin-orbit coupling Core and valence electron-electron interaction. Comparison with experiment Core hole potential and lifetime Local symmetry (crystal field) Spin-spin interactions (molecular field) Core hole screening effects (charge transfer) 58

2p XAS first-principle codes
SOLIDS Band structure multiplet (Haverkort, Green, Hariki) Cluster DFT multiplet (Ikeno, Ramanantoanina, Delley) MOLECULES Restricted Active Space CI (Odelius, Kuhn) Restricted Open-shell CI (Neese) TDDFT/BSE Time-Dependent DFT (Joly) Bethe-Salpeter (Rehr, Shirley) Multi-channel Multiple-scattering (Kruger) 59

Resonant Inelastic X-ray Scattering
core-core RIXS core-valence RIXS RIXS

RIXS Resonant Inelastic X-ray Scattering or
Resonant X-ray Raman Scattering (RXRS) Resonant X-ray Emission Spectroscopy (RXES) Resonant X-ray Energy Loss Spectroscopy (R-XELS)

Core-core RIXS 2p 3s electronic dd, CT magnon vibrations Ψ0

Resonant Inelastic X-ray Spectroscopy
2p3s RIXS of CaF2 2p XAS of CaF2 3d0  ’ 3s13d1 2p53d1

2p3s RIXS of CaF2 2p3s RIXS of CaF2 Ground state is 3d0
Excitation (i0) 3d0  (x) 2p53d1 Decay (x) 2p53d1  (f) 3s13d1

Resonant Inelastic X-ray Scattering
2p3s RIXS of CaF2 Resonant Inelastic X-ray Scattering 3d0  ’ 3s13d1 2p53d1 Phys. Rev. B. 53, 7099 (1996)

1s2p RIXS of transition metal ions
electronic dd, CT magnon vibrations Ψ0

1s2p RIXS of transition metal ions
K edge and 1s2p RIXS CoIII(acac) low-spin CoIII 3d6 [1A1] T2g full Eg empty

Only quadrupole peaks visible
Sharper pre-edge structures in 1s XAS Pre-edge and edge CoO high-spin CoII 3d7 [4T2] Only quadrupole peaks visible 3d7  1s13d8  2p53d8

K pre-edge of TM oxides (LiCoO2)
Pre-edges structures in 1s XAS K pre-edge of TM oxides (LiCoO2) Co K edge of LiCoO2 low-spin CoIII 3d6 [1A1] T2g full Eg empty

K pre-edge of TM oxides Pre-edges structures in 1s XAS

K pre-edge of TM oxides Pre-edges structures in 1s XAS
J. Phys. Cond. Matt. 21, (2009); Phys. Rev. B. 81, (2010)

K edge and 1s2p RIXS Hard x-ray RIXS
Reduce lifetime from 1.5 to 0.2 eV (HERFD XANES) Reveal new features at pre-edge Valence specific EXAFS [Inorg. Chem. 41, 3121 (2002)] Spin-polarized XAS Range extended EXAFS Background free FY for low conc. RIXS-MCD

Core-valence RIXS

2p3d RIXS of transition metal ions
core electronic dd, CT magnon vibrations Ψ0

resonant inelastic x-ray spectroscopy
77

NiII 3d8 []  2p53d9[jj]  3d8[]
2p3d RIXS of NiO NiII 3d8 []  2p53d9[jj]  3d8[] Cartoon of a spin-flip transition

2p3d RIXS of NiO dd S MS ‘spin-flip’ spin-flip
Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy Phys. Rev. B. 57, (1998)

2p3d RIXS RIXS1998: 500 meV RIXS 2019: 25 meV polarization, angles
(in, sample, out) eV electron-electron crystal field charge transfer meV spin-orbit, magnetic distortions vibrations RIXS1998: 500 meV RIXS 2019: 25 meV 80

Energy dependence in 2p3d RIXS
Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy In 2p3d RIXS the intensity of charge transfer is smaller than dd-excitations [Ament et al., Rev. Mod. Phys. 83, 705 (2011)]

Energy dependence in 2p3d RIXS
2 eV – 10 eV charge transfer 0.5 eV – 6 eV dd excitations (atomic + crystal field) 0.0 – 0.5 eV spin-flip (magnon) symmetry distortions HS-LS transition point spin-orbit coupling 0.0 – 0.2 eV vibrations (phonon) Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy

Select specific states in 2p3d RIXS (Fe3O4)
exchange Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy spin-orbit + exchange [Huang et al. Nature Comm. 8, (2017) ]

Spin state of LaCoO3 5T2 1A1 E T2 E T2 E T2 3T1 Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy NOTE: Term symbols and orbital occupations are only indications: they are mixed by electron-electron, spin-orbit, etc.

Spin state of LaCoO3 dd-excitations + fluorescence
Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy dd-excitations + fluorescence [Tomiyasu et al. PRL 8, 119, (2017) ]

Spin state of LaCoO3 Spin transition is from low-spin to high-spin,
Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy Spin transition is from low-spin to high-spin, but is it really high-spin? [Tomiyasu et al. PRL 8, 119, (2017) ]

Spin state of LaCoO3 Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy Order of states at zero Kelvin: LS < HS < IS Strong coupling between LS and IS (not with HS) Large dispersion of IS: Excitonic Insulator [Wang et al. 98, (2018) ]

Spin state of LaCoO3 q-dep. RIXS [Wang et al. 98, 035149 (2018) ]
Low-loss region of RIXS in NiO. Ground state: 3A2 Double group: T2, not split without exchange Echange field H splits ground state into three Ms states as H times Ms, So three states at –H, 0, +H. The spin-flip peak in the figure is at 2H. H is related to the superexchaneg energy q-dep. RIXS [Wang et al. 98, (2018) ]

XAS of radiation sensitive sample
Single synchrotron pulselength is too long Mitzner et al, J. Phys. Chem. Lett. 4, 3641 (2013) 89

XAS of radiation sensitive sample
Fluorescence does not measure XAS spectrum Saturation State-dependent decay Mitzner et al, J. Phys. Chem. Lett. 4, 3641 (2013) 90

FY detection: State dependent decay
Yield methods assume a constant ratio between radiative and non-radiative decay If this ratio is state (= energy) dependent then the related yield methods do not measure XAS. The dominant yield method is not visibly affected, thus for soft X-rays only FY is affected, not electron yield.

FY detection: State dependent decay
L3 L2 EY Solid State Comm. 92, 991 (1994)

Mitzner et al, J. Phys. Chem. Lett. 4, 3641 (2013)
XAS: transmission & FY Mitzner et al, J. Phys. Chem. Lett. 4, 3641 (2013) 93

Fluorescence Yield XMCD
XMCD sum rules break down Ni/Co 20%, Fe 30%, Mn > 100% error

Dips and peaks in FY-XAS
Nature Chem. 4, 766 (2012) & Phys. Rev. Letter discussions (2014)

FY detection 3: inverse PFY
ITFY ~ 𝜇(𝜔)∗𝜎 𝜔 𝜇 𝜔 +𝜇𝐵 + 𝜇𝐵∗𝜎𝐵 𝜇 𝜔 +𝜇𝐵 (+ angles, self-absorption) 𝜎 𝜔 = the integrated RIXS INRFY ~ 𝜇𝐵∗𝜎𝐵 𝜇 𝜔 +𝜇𝐵 Invert equation: IIPFY = 1/INRFY~ 𝜇 𝜔 +𝜇𝐵 𝜇𝐵∗𝜎𝐵 1/(1+x) ≈ 1 – x INRFY ≈ 1 – 𝜇 𝜔

FY detection: dips and peaks
ITFY ~ 𝜇 𝜔 ∗𝜎 𝜔 𝜇 𝜔 +𝜇𝐵 + 𝜇𝐵∗𝜎𝐵 𝜇 𝜔 +𝜇𝐵 Calculations as yet: ITFY ~ 𝜇 𝜔 ∗𝜎 𝜔 −𝜇 𝜔 ∗𝜎B

X-ray Absorption Spectroscopy

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