NSRRC September 12 program Part 1 CTM4XAS Atomic Multiplet, crystal fields and charge transfer Part 2CTM4RIXS.

NSRRC September 12 program

Part 1CTM4XAS

Atomic Multiplet, crystal fields and charge transfer

Part 2 CTM4RIXS

Charge Transfer Multiplet program

Used for the analysis of XAS, EELS,

Photoemission, Auger, XES,

ATOMIC PHYSICS

GROUP THEORY

MODEL HAMILTONIANS

if EEiffXAS reI

2ˆ~

Excitations of Excitations of core electrons core electrons to empty statesto empty states

The XAS spectrum The XAS spectrum is given by theis given by the

Fermi Golden RuleFermi Golden Rule

X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy

Excitations of Excitations of core electrons core electrons to empty statesto empty states

The XAS spectrum The XAS spectrum is given by theis given by the

Fermi Golden RuleFermi Golden Rule

symmetrysiteXAS MI ,2~


1s1s

22pp22ss

Phys. Rev. B.40, 5715 (1989)Phys. Rev. B.40, 5715 (1989)



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

oxygen 1s > p DOSoxygen 1s > p DOS


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

oxygen 1s > p DOSoxygen 1s > p DOS

1-particle:

1s edges

(DFT + core hole +U)

2-particle:

+ all edges of closed shell systems

(TDDFT, BSE)

many-particle:

open shell systems

(CTM4XAS)

Interpretation of XASInterpretation of XAS

Fermi Golden Rule:IXAS = |<f|dipole| i>|2 [E=0]

Single electron (excitation) approximation:IXAS = |< φ empty|dipole| φcore>|2

22

ˆˆ iqiiqf recre

2

ˆ?? creq

XAS: multiplet effectsXAS: multiplet effects

2p2p3/23/2

2p2p1/21/2

Overlap of core and valence wave functionsOverlap of core and valence wave functions

Single Particle model breaks downSingle Particle model breaks down

3d3d

<2p3d|1/r|2p3d><2p3d|1/r|2p3d>

XAS: multiplet effectsXAS: multiplet effects

Phys. Rev. B. 42, 5459 (1990) Phys. Rev. B. 42, 5459 (1990)

X-ray absorption: core hole effectX-ray absorption: core hole effectXAS: recent first principles XAS: recent first principles developments for L edgesdevelopments for L edges

• DFT to cluster Wannier multiplet (Haverkort)

• Restricted-Active-Space (Odelius, Koch, Broer, Lundberg)

• Extensions of TD-DFT with 2h-2e (Neese, Roemelt)

• ab-initio multiplets [‘RAS-DFT’] (Ikeno, Uldry)

[ See http://www.anorg.chem.uu.nl/FXS2013/]

http://www.anorg.chem.uu.nl/FXS2013/

CTM4XAS (semi-empirical)CTM4XAS (semi-empirical)


Used for the analysis of XAS, EELS,

Photoemission, Auger, XES,

ATOMIC PHYSICS

GROUP THEORY

MODEL HAMILTONIANS

Atomic Multiplet TheoryAtomic Multiplet Theory

Niii

pairsre

NrZe

Nmp slrH

iji

i )(222

2


=E

• Kinetic Energy• Nuclear Energy• Electron-electron interaction• Spin-orbit coupling

Niii

pairsre

NrZe

Nmp slrH

iji

i )(222

2


X X

=E

• Kinetic Energy• Nuclear Energy• Electron-electron interaction• Spin-orbit coupling

2S+1L

Term Symbol

Term Symbols of a two-electron stateTerm Symbols of a two-electron state

1s2s-configuration

Term symbols 1s: 2S

Term symbols 2s: 2S

Term symbols 1s2s: multiply L and S separately

L2p=0, L3p=0 >> LTOT = 0

S2p=1/2, S3p=1/2

Term SymbolsTerm Symbols

1s2s-configuration

S2p=1/2, S3p=1/2

What are the values of the total S (STOT) ?

= 0 or 1

Singlet or triplet: ↑↓ or ↑↑,

but the degeneracies are 1 and 3

Term SymbolsTerm Symbols

Singlet or triplet

N

iiipairs

re

ATOM slrHij

)(2

Spin-orbit couplingSpin-orbit coupling

Valence Spin-orbit coupling

• Couple L and S quantum numbers• L and S loose their exact meaning as quantum

numbers• Only the total moment J is a good quantum number

• Main n 1,2,3,….

• Azimuthal L (orbital moment)

• Spin S

• Magnetic mL (orbital magnetic moment)

• Spin magnetic mS (spin magnetic moment)

• Total moment J

• Total magnetic mJ

Quantum numbersQuantum numbers

• Term symbols of a 2p13d1 configuration

• 2p1 2P1/2, 2P3/2 (S=1/2, L=1))

• 3d1 2D3/2, 2D5/2 (S=1/2, L=2))

• 2p13d1 STOT = 0 or 1

LTOT = 1 or 2 or 3

1P1 + 3P0, 3P1, 3P2

1D2 + 3D1, 3D2, 3D3

1F3 + 3F2, 3F3, 3F4

[[(2J+1)=3+1+3+5+5+3+5+7+7+5+7+9=60]

Term Symbols

• Term symbols of a 2p2 configuration

Term Symbols

Configurations of 2p2

1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1

1 0 -1

1 0 -1 1 0 -1

1 0 -1 1 0 -1

LS term symbols: 1S, 1D, 3PLSJ term symbols:

MS=1 MS=0 MS=-1

ML= 2 0 1 0

ML= 1 1 2 1

ML= 0 1 3 1

ML=-1 1 2 1

ML=-2 0 1 0

Term Symbols of 2p2

1S0 1D2

3P0 3P1 3P2

pairs

reij

H2

The electron-electron interactionThe electron-electron interaction

• Electron-electron interaction acts on 2 electrons• It can couple 4 different wave function a, b, c and d

The electron-electron interactionThe electron-electron interaction

1. Split wave functions into radial and angular part2. Split operator into radial and angular part3. Use series expansion of 1/r12

Coulomb integralCoulomb integral

• Special case: a=c and b=d>> the two electron are in the same shell

• Fk is called a Slater integral• It is a number that is calculated from first principles

N

iiipairs

re

ATOM slrHij

)(2

k

kk

k

kkJ

Sre

JS GgFfLL 1212 ||

12

2


Electron-electron interactions of Valence States

Valence Spin-orbit coupling

CTM4XAS version 5.2

CTM4XAS version 5.2

N

iiipairs

re

ATOM slrHij

)(2

k

kk

k

kkJ

Sre

JS GgFfLL 1212 ||

12

2


Core Valence Overlap

Core Spin-orbit coupling

1s 2s 2p 3s 3p

0.07

0

5

0

8

17

13

0

17

2Core Spin-orbit coupling

Multiplet Effects (NiMultiplet Effects (Ni2+2+))

Core Valence Overlap

2p XAS of TiO2p XAS of TiO22

• Ground state is 3d0

• Dipole transition 3d02p53d1

• Ground state symmetry: 1S0

• Final state symmetry: 2P2D gives

• 1P, 1D, 1F, and 3P, 3D, 3F

• Final state symmetries:

1P, 1D, 1F, and 3P, 3D, 3F

• Transition <1S0|J=+1| 1P1, 3P1 , 3D1>

• 3 peaks in the spectrum

2p XAS of TiO2p XAS of TiO22

Exercise: Calculate the 2p XAS spectrum of a Ti atom

• Term symbols with maximum spin S are lowest in energy,

• Among these terms:

Term symbols with maximum L are lowest in energy

• In the presence of spin-orbit coupling, the lowest term has

• J = |L-S| if the shell is less than half full

• J = L+S if the shell is more than half full

3d1 has 2D3/2 ground state 3d2 has 3F2 ground state3d9 has 2D5/2 ground state 3d8 has 3F4 ground state

Hunds rulesHunds rules

Give the Hund’s rule ground states for 3d1 to 3d9

Fe atom: Ground state:3d6 (4s2) 5D j=4

Exercise: Calculate the 2p XAS spectrum of Fe

Fe atom: Ground state: 3d6 (4s2) Final state: 2p53d7 Dipole transition: p-symmetry

3d6-configuration: 5D, etc. j=42p53d7-configuration: 110 states j’= 3,4, 5p-transition: 1P j=+1,0,-1

ground state symmetry: 5D 5D4

transition: 5D 1P = 5PDFpossible final states: 68 states

Term Symbols and XASTerm Symbols and XAS

Fe atom: Ground state: 3d6 (4s2) 5D j=4


5D

5D0

5D4

NiII ion in NiO: Ground state: 3d8 Final state: 2p53d9 Dipole transition: p-symmetry

3d8-configuration: 1S, 1D, 3P,1G, 3F j=4

2p53d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4p-transition: 1P j=+1,0,-1

ground state symmetry: 3F 3F4

transition: 3F 1P = 3DFGtwo possible final states: 3D, 3F 3D3,3F3,3F4, 1F3


3d3d88 XAS calculation XAS calculation

+LS2p

0+FK, GK: > 3F

+LS3d : > 3F4

Atomic multipletsAtomic multiplets


ATOMIC PHYSICS

GROUP THEORY

MODEL HAMILTONIANS

t2g states

Crystal Field Effects

eg states

Octahedral crystal field splitting

metal ionin free space

in symmetrical field

t2g

yz xz xy

eg

in octahedral ligand field

x2-y2 z2

x2-y2 yz z2 xz xy

0 7 = 2.13 eV

Crystal Field Effects in CTM

SO3 Oh (Mulliken)

S 0 A1

P 1 T1

D 2 E+T2

F 3 A2+T1+T2

G 4 A1+E+T1+T2

Crystal Field EffectsCrystal Field Effects

TiIV ion in TiO2: 3d0-configuration: 1S, j=02p13d9-configuration: 2P2D = 1,3PDF j’=0,1,2,3,4p-transition: 1P j=+1,0,-1

Write out all term symbols:1P1 1D2 1F3

3P0 3P1 3P2

3D1 3D2 3D3

3F2 3F3 3F4

1 3 4 3 1

2p XAS of TiO2 (atomic multiplets)

J in SO3 Deg.

0 1

1 3

2 4

3 3

4 1

12

Crystal Field Effect on XAS

<1S0|dipole|1P1> goes to <A1|T1|T1>

J in SO3 Deg. Branchings

0 1 A1

1 3 3T1

2 4 4E, 4T2

3 3 3A2, 3T1,3T2

4 1 A1, E, T1, T2

12



J in SO3 Deg. Branchings in Oh Deg.

0 1 A1 A1 2

1 3 3T1 A2 3

2 4 4E, 4T2 T1 7

3 3 3A2, 3T1,3T2 T2 8

4 1 A1, E, T1, T2 E 5

12 25



Effect of 10Dq on XAS:3d0

Comparison with Experiment

Comparison with Experiment

CTM4XAS version 5.2

CTM4XAS version 5.2

0.0 0.0 0.0

Turning multiplet effects off

• Term symbols with maximum spin S are lowest in energy,

• Among these terms:

Term symbols with maximum L are lowest in energy

• In the presence of spin-orbit coupling, the lowest term has

• J = |L-S| if the shell is less than half full

• J = L+S if the shell is more than half full

3d1 has 2D3/2 ground state 3d2 has 3F2 ground state3d9 has 2D5/2 ground state 3d8 has 3F4 ground state

Hunds rulesHunds rules

Energy

Symmetries Oh Total symmetry

1S 4.6 eV

1A1

3P 0.2 eV

3T1

1D -0.1 eV

1E + 1T2

3F -1.8 eV

3A2 + 3T1 + 3T2

1G 0.8 eV

1A1+1T1+

1T2+1E

Crystal Field Effects on 3dCrystal Field Effects on 3d88 states states

SO3 Oh (Butler) Oh (Mulliken)

S 0 0 A1

P 1 1 T1

D 2 2 + ^1 E+T2

F 3 ^0+ 1 +^1 A2+T1+T2

G 4 0 + 1 + 2 + ^1 A1+E+T1+T2

Crystal Field EffectsCrystal Field Effects

Energy

Symmetries Oh Total symmetry

1S 4.6 eV

1A1

3P 0.2 eV

3T1

1D -0.1 eV

1E + 1T2

3F -1.8 eV

3A2 + 3T1 + 3T2

1G 0.8 eV

1A1+1T1+

1T2+1E

Double group symmetry Double group symmetry

A1A1=A1

T1T2= T1+ T2+ E+ A2

Crystal Field Effects: Tanabe-SuganoCrystal Field Effects: Tanabe-Sugano

Effect of 10Dq on XAS:3dN

High-spin or Low-spin

10Dq > 3J(d4 and d5)

10Dq > 2J(d6 and d7)

2p XAS of Mn2+

3d spin-orbit coupling

Exercise: Calculate the 2p XAS spectrum of CoO

3d spin-orbit coupling

Ground state of a transition metal system3dN at every site

Charge fluctations

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)



= E(3d9L) – E(3d8)

E(3d10LL‘) – E(3d8)Two times charge transfer: 2 Extra 3d3d interaction: U

2 +U


Charge Transfer Effects in XASE(3d9L) – E(3d8) = E(3d10LL‘) – E(3d8) = 2 +U

2p XAS: 3d8 2p5 3d9

E (2p53d9) = E2p+

2p XAS: 3d9L 2p5 3d10L

E (2p53d10L) = E2p- Q +2+U

Energy difference: E2p- Q +2+U- E2p - = +U-QQ U+2 eV

+U-Q

Charge Transfer Effects in XAS

3d5

MnO: Ground state: 3d5 + 3d6LEnergy of 3d6L: Charge transfer energy

2p53d6


3d6L

3d5


2p53d7L

2p53d6

+U-Q


-Q

Charge Transfer Effects in XPS

3d6L

• Transition metal oxide: Ground state: 3d5 + 3d6L• Energy of 3d6L: Charge transfer energy

XAS

2p53d7L

+U-Q

2p53d6

3d5

2p53d6L

XPS

2p53d5

-Q

Ground State

Charge transfer effects in XAS and XPS

NiO: Ground state: 3d8 (3d8 )

+ 3d9L Charge transfer energy

+ 3d93d7 Hubbard U

+ 3d10L2 2+U

+ 3d7L Metal-ligand CT MLCT


Charge Transfer Multiplets of NiCharge Transfer Multiplets of Ni2+2+

=0

=9=3

=6

Exercise: perform a series of charge transfer calculations changing from +10 to -10.

Spectral shape:

(1) Multiplet effects

(2) Charge Transfer

J. Elec. Spec.J. Elec. Spec.67, 529 (1994)67, 529 (1994)


Charge transferCharge transfer



=10

NiO

La2Li½Cu½O4

30% 3d8

1A1

30% 3d8

3A2=-5

=5

=0

=-10

3d8 + 3d9L

Charge Transfer effects

Chem. Phys. Lett. 297, 321 (1998)

=10

NiO

La2Li½Cu½O4

30% 3d8

1A1

30% 3d8

3A2=-5

=5

=0

=-10

3d8 + 3d9L

Charge Transfer effects

Calculate the 2p XAS spectrum of Cs2KCuF6

3d6L

3d5

2p53d7L

2p53d6

+U-Q

FeIII: Ground state: 3d5 + 3d6L

C NM

filled d-orbital

empty *-orbital

M C N

filled -orbital

empty d or p orbital

(i) -C?C?N distance

C NM

filled d-orbital

empty *-orbital

M C N

filled -orbital


(i) C?

C NM

filled d-orbital

empty *-orbital

M C N

filled -orbital


(i) -C?C?N distance

C NM

filled d-orbital

empty *-orbital

M C N

filled -orbital


(i) C?

(i) donation (ii) back-donation

empty d-orbital

filled orbital

LMCT and MLCT: - bonding - bonding

with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)

3d4L

3d6L

3d5

FeIII: Ground state: 3d5 + 3d6L + 3d4L

2p53d5L

2p53d7L

2p53d6

+U-Q - 2

-U+Q + 2



-2

0

2

4

6

8

10

700 705 710 715 720 725 730

Energy (eV)

No

rmal

ized

Ab

sorp

tio

n

Fit X

Series2

FeIII(tacn)2

FeIII(CN)6



RIXSRIXS

RIXSRIXS

Butorin, J. Elec. Spec. 110, 213 (2000)

Resonant Inelastic X-ray SpectroscopyResonant Inelastic X-ray Spectroscopy

dd excitation


2p XAS of CaF2

3d0

’

3s13d1

2p53d1

Phys. Rev. B.Phys. Rev. B.53, 7099 (1996)53, 7099 (1996)

Resonant Inelastic X-ray ScatteringResonant Inelastic X-ray Scattering

2p3s RIXS of CaF2

3d0

’

3s13d1

2p53d1

Butorin Butorin J. Elec. Spec 110, 213 (2000)J. Elec. Spec 110, 213 (2000)


Exercise: Repeat these calculations

NiII 3d8 [] 2p53d9[jj] 3d8[]Soft x-ray RIXS and magnetismSoft x-ray RIXS and magnetism

Phys. Rev. B.Phys. Rev. B.57, 14584 (1998)57, 14584 (1998)

dd spin-flip‘spin-flip’

MSS

2p3d RIXS of NiO

Soft x-ray RIXS and magnetismSoft x-ray RIXS and magnetism

CTM4RIXSCTM4RIXS

What does the progam do?

What does the program do?

Nothing, really… no multiplets, no group theory, no angular dependence, …)

Takes output of two separate ctm4xas calculations and combines them in Kramers-Heisenberg Formula

CTM4RIXSCTM4RIXS

CTM4RIXSCTM4RIXS

• Load in absorption and emission files → Extract information and save energies, symmetries and transition matrix elements (saved as .sm file).

• >> These matrices are calculated with CTM4XAS if the RIXS option is chosen

AbsorptionTriad

GS → T1 → IS

EmissionTriad

IS → T2 → FS

|g>, Eg

|n>, En

|f>, Ef

CTM4RIXSCTM4RIXS

A first CTM4RIXS calculationA first CTM4RIXS calculation

Choose the name_abs that has been calculated with CTM4XAS


Choose ‘1’ in the pop-up menu


Choose ‘1’ in the pop-up menu


Click button at bottom


Set L intermediate to 0.4 and click button at bottom


Set Delta to 0.1 (two times) and click button at bottomChoose a name in the pop-up window.


Set Delta NOT to a small number >> CTM4RIXS crashes


Start the calculation with the RIXS buttonA pop-up window tracks the progress.

• The RIXS calculation is finished.

• Next the RIXS plane can be plotted with the screen on the right.

CTM4RIXSCTM4RIXS

Plotting a CTM4RIXS calculationPlotting a CTM4RIXS calculation

Select the file button and next the select the file you calculated;GOTO the name_RIXS directoryGOTO the name_matrices directorySELECT name_Ms


This is the 2p3d RIXS plane of Ni2+ with 10Dq=1.0 eV.


Enlarge a region of the 2D map with this button & select the region.


Final state energy to set the vertical axis to energy loss. (& enlarge/select the region).

Selecting a cross-sectionSelecting a cross-section

Choose a vertical cross section & select energy.The screen on the right shows the cross section (= RXES)

• 2D RIXS plane

• Cross sections, including

resonant XESselective XASHERFD

partial FY

What is calculated with CTM4RIXSWhat is calculated with CTM4RIXS

• No interatomic exchange (can be included)

• Only 3dN > 2p5 3dN+1 > 3dN channel• (as yet) no charge transfer

• Fluorescence is not included

What is NOT calculated with CTM4RIXSWhat is NOT calculated with CTM4RIXS


Calculations without the CTM4XAS interface

Calculations without the CTM4XAS interfaceCalculations without the CTM4XAS interface

Calculation of 2p3d RIXS without charge transfer

(note: this is a repetition of CTM4XAS, now with the original DOS commands)

1.Do a CTM4XAS calculation for 2p3d RIXS, for example for Co2+, 10dq=1 eV, using co2 as filename.2.Copy the files co2_ems.rcg, co2_abs.rcg, co2_ems.rac and co2_abs.rac to the directory c:cowan/batch 3.Open the DOS prompt command window, for type cmd in “search programs”4.Goto the directory c:/cowan/batch by typing ‘cd ..’, ‘cd ..’, ‘cd cowan’, ‘cd batch’ 5.type ‘rcg2 co2_ems’ and ‘rac2 co2_ems’. Same for the _abs files.6.Open the ora-files with CTM4RIXS and make a plot (same as with CTM4XAS files)7.(shift the excitation energy and the emission energy to the correct values)


Calculation of 2p3s RIXS (without charge transfer)

1.Do a CTM4XAS calculation for 2p3d RIXS, for example for Co2+, 10dq=1 eV.2.Do a RCN calculation using hco23s.rcn within c/cowan/batch; The output is written in the file hco23s.rcf3.Open the file co2p3s_ems.rcg and change the line P_5__D_8 to P_5__D_8__S_2 (keep the same number of spaces indicated by _). Change the line P_6__D_7 to P_6__D_8__S_1.4.Open the file hco23s.rcf and copy the line starting with “Co2+ 3s01 3d08” and replace in co2p3s_ems the line starting with “Co2+ 2P06 3D07”.5.Change the energy to 0.0000 (from a value around -600).6.Re-run the rcg and rac files for 2p3s RIXS.7.Open the ora-files with CTM4RIXS and make a plot.8.(shift the excitation energy and the emission energy to the correct values)9.(Note that the integrated XES spectrum now gives exactly the XAS spectral shape because it is a core-core channel)


Calculation of 2p3d RIXS with charge transfer (MATLAB is needed)

Step 1: run CTM4XAS•RUN an XAS calculation with CTM4XAS, including charge transfer. •Use any name. I use nitest1, with 10Dq=1, DELTA=3, Udd=6, Upd=7, rest=default.•Copy the files nitest1.rcg and nitest1.ban to cowan/batch•Copy in cowan/batch rni2.rac to nitest1.rac



Step 2: Run the calculations for absorption•Copy BANEX2.BAT to cowan/batch #see below#•Copy banderex.exe to cowan/bin ##•Open the DOS prompt•Change the directory to c:cowan/batch•Type Rcg2 nitest1•Type Rac2 nitest1•Type Banex2 nitest1•The result is in the file nitest1.oba

(## this is a modified executable file using exact diagonalization as created by Robert Green; ask me to send it to you)



Step 3a: Create the inputfiles for the x-ray emission step and run the calculations Copy nitest1.rcg to nitest1x.rcgEdit the file nitest1x.rcg

Invert lines 4 and 5 (line 4 is D08 P06)Invert lines 12 and 13Invert block 4 with block 3.

[Each block starts with 0 80998080 …. and ends with -99999999.]Save the file nitest1x.rcgCopy nitest1.rac to nitest1x.racCopy nitest1.ban to nitest1x.ban



Step 3b: Edit the file nitest1x.banChange the lines def EG2 = 3.000 unity def EF2 = 2.000 unityto def EG2 = 2.000 unity def EF2 = 3.000 unityChange for the triads the first sign from + to – and the last sign from – to +Change erange 0.3 to erange 999Type Rcg2 nitest1xType Rac2 nitest1xType Banex2 nitest1xThe result is in the file nitest1x.oba



Step 4: Run the Kramers-Heisenberg calculation(for the moment use this procedure; all parameters are set in racin.m)•Copy nitest1.oba to rni2.oba•Copy nitest1x.oba to rni2x.oba•Start MATLAB•Type dorixs•The RIXS matrix is saved in rni2_MS•Change the name rni2_MS to rni2_MS.mat

Step 5: Plot with CTM4RIXSLoad the file rni2_Ms.mat

XES calculationsXES calculations

X-ray absorption and X-ray photoemissionX-ray absorption and X-ray photoemission

2p 3/2

2p 1/2

2s

1s

fluorescent radiation

2p 3/2

2p 1/2

2s

1s

Fluorescence Auger

Core Hole DecayCore Hole Decay

X-ray emissionX-ray emission

Resonant X-ray emission spectroscopyResonant X-ray emission spectroscopy

5880 5900 5920 6480 6520 6560Fluorescence Energy [eV]

x 8

x 500

K1,3

K1

K2

K''

K2,5

K'

K

K Main Lines K Satellite LinesMnO

1s X-ray emission1s X-ray emission

Tot

al E

nerg

y

2p53dn

3p53dn

1s13dn

Core Hole

Valence hole

Photoionizationor

K capture

5880 5900 5920 6480 6520 6560Fluorescence Energy [eV]

x 8

x 500

K1,3

K1

K2

K''

K2,5

K'

K

K Main Lines K Satellite Lines

K KMain Lines

K Satellites

3dnGround State

1s X-ray emission1s X-ray emission

Etotal

K Fluorescence

Strong interaction between

unfilled 3p and 3d shells!

3d1s

3d3p

Photoionization

Multiplet effects in 1s3p XES (KMultiplet effects in 1s3p XES (Kββ))

Spin-selectivity in the K line

K1,3

3p

3d

3p

3d

K’

?5P

7P


3p XPS and K XES

Free Mn atom3p XPS

MnF2 K

A

F

B

Identical final state configuration:3p53d5


1s2p and 1s3p XES spectra


Approximations:

- 3dN ground state (+ CT)

- XES only from lowest energy 1s13dN state (+CT)

- Charge transfer energy is -Q

3d6L


Pre-edge

1s13d7L

+U-Q

1s13d6

3d5

1s13d6L

edge

1s13d5

-Q

Ground State

Charge transfer in 1s pre-edge and edge


Approximations:

- 3dN ground state (+ CT)

- XES only from lowest energy 1s13dN state (+CT)

- Charge transfer energy is -Q

- Neglect 1s3d exchange interaction (needed for spin-pol.)

- Neglect of excitation process (a better approximation is to

describe the excitation process with XPS)

Charge transfer in XES spectra

Pieter Glatzel et al. Phys. Rev. B. 64, 045109 (2001)

Charge transfer in XES spectra

Pieter Glatzel et al. Phys. Rev. B. 64, 045109 (2001)

RIXS at metal K edgesRIXS at metal K edges

Fe K pre-edgesFe K pre-edges

Westre et al. JACS 119, 6297 (1997); Heyboer et al. J.Phys.Chem.B. 108, 10002 (2004)


Pre-edge and edge

Only quadrupole peaks visible3d7 1s13d8 2p53d8

Only correct with interference effects ONOnly correct with interference effects ON

CoO

high-spin CoII

3d7 [4T2]


Non-local screening peaks RIXS-MCD at the K pre-edge



Non-local screening peaks RIXS-MCD at the K pre-edge of Fe3O4



XMCD at high-pressureSikora, PRL 105, 037202 (2010)

MCDMCD

X-MCDX-MCD

X-MCDX-MCD

L=2, S=1/2 2DJ=5/2 or 3/2More than half-full2D5/2

Cu2+: 3d9 2p53d10

L=1, S=1/2 2PJ=3/2 or 1/2

2P3/2 or 2P1/2

J= +1 or 0 or -1light polarization q = mJ

X-MCDX-MCD

Cu2+: 3d9

MCD

MCD mJ=-5/2to

mJ’=-3/2

no LS

X-MCDX-MCD


X-MCDX-MCDno LSMCD

+ crystal fieldMCD

X-MCDX-MCD

3F no LS

3F4 LSMCD

XPSXPS

X-ray photoemissionX-ray photoemission

Charge transfer effects in XPS

+U-Q

Charge Transfer Effects in XAS

3d5


2p53d6


3d6L

3d5


2p53d7L

2p53d6

+U-Q


-Q

Charge Transfer Effects in XPS

3d6L


XAS

2p53d7L

+U-Q

2p53d6

3d5

2p53d6L

XPS

2p53d5

-Q

Ground State

Charge transfer effects in XAS and XPS

Charge transfer effects in XPS

Exercise: Calculate the 2p XPS spectrum of NiCl2

NSRRC September 12 program Part 1 CTM4XAS Atomic Multiplet, crystal fields and charge transfer Part 2CTM4RIXS.

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