core-level spectroscopy: basics of xas, xes, xmcd and...
TRANSCRIPT
![Page 1: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/1.jpg)
Core-level spectroscopy:
Basics of XAS, XES, XMCD and alike
Ondrej Sipr
Institute of PhysicsAcademy of Sciences of the Czech Republic
Prague
Introduction to the application of ab-initio method in spectroscopy
EUSpec Hands-on course
Pilsen, 25. February 2015
1
![Page 2: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/2.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
2
![Page 3: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/3.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
2
![Page 4: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/4.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
2
![Page 5: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/5.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
2
![Page 6: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/6.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
3
![Page 7: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/7.jpg)
Why x-ray spectroscopy (one of many why’s . . . )
Only indirect methods are available if you want to study interiourof a material: blackbox techniques.
BlackboxOutputInput
Spectroscopy:Way to investigate ground state of a system by studying itsresponse to a perturbation
Why x-rays?Dimensions of the probe have to be comparable to the dimensionsof the investigated system.
X-rays are useful for a local view.
4
![Page 8: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/8.jpg)
Emission and absorption of light quanta
◮ System is described by a Hamiltonian Hel. Consider its twoeigenstates |ψi 〉 and |ψf 〉 (i.e., stationary states).
◮ The system is perturbed by a Hamiltonian Hint whichrepresents the interaction between electrons and photons,
Hint = −e
mA(x) · p .
A(x) vector potential — quantized electromagnetic fieldp momentum operator acting on electron states
The above Hamiltonian neglects terms proportional to |A|2,
meaning that we cannot describe two-photon transitions in this way.
5
![Page 9: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/9.jpg)
Fermi’s Golden Rule
Probability per unit time that a perturbation Hint causes atransition between states |ψi 〉 and |ψf 〉 of the unperturbedHamiltonian Hel is
wfi =2π
~|Mfi |
2 δ(Ef − Ei ± ~ω)
(“+” for absorption of photons, “-” for emission of photons).
(First order time-dependent perturbation theory.)
Transition matrix element:
Mfi ≈⟨
ψf
∣
∣
∣e±
i
~q·x
ǫ · p∣
∣
∣ψi
⟩
,
where q is the photon wave vector (cq = ~ω), ǫ is the polarizationvector of the radiation.
6
![Page 10: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/10.jpg)
Some definitions and manipulations
Absorption coefficient:
µ(ω) =∑
f
wfi =∑
f
2π
~|〈ψf |Hint|ψi〉|
2 δ(Ef − Ei + ~ω)
µ(ω) = −2
~Im
⟨
ψi
∣
∣
∣
∣
H†int
1
Ei − ~ω − Hel + iεHint
∣
∣
∣
∣
ψi
⟩
◮ Initial and final states |ψi 〉 and |ψf 〉 are in the absence of theinteraction with the electromagnetic radiation but in thepresence of electron-electron interaction.
◮ Hamiltonian Hel is the full many-body Hamiltonian, includingall electron-electron interactions.
◮ Often we can go away with describing the electron-electroninteraction just on the LDA level.
7
![Page 11: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/11.jpg)
Matrix elements: dipole approximation
Transition matrix element: Mfi ≈⟨
ψf
∣
∣
∣e±
i
~q·x
ǫ · p∣
∣
∣ψi
⟩
.
Taylor expansion: e±i
~q·x = 1 ± i
~q · x + 1
2(i~q · x)2 + . . .
If the quantum system is localised within a characteristic length a
(i.e, processes occur at this length scale),
1
~qa ≪ 1 ⇔ a ≪
c
ω⇔ a ≪
λ
2π,
then i~q · x and higher order terms can be neglected.
We thus have just Mfi ≈ ǫ · 〈ψf |p|ψi〉 .
This is called the dipole approximation.
8
![Page 12: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/12.jpg)
Other forms of matrix elements
“Primordial form” of the dipole matrix element:
Mfi ≈ ǫ · 〈ψf |p|ψi 〉 .
Using the coordinate-momentum commutation relations (and fewother tricks), the matrix element can be re-written as
Mfi ≈ ǫ · 〈ψf |p|ψi 〉 = imωǫ · 〈ψf |r|ψi 〉 =i
ωǫ · 〈ψf |∇V |ψi 〉
In most situations, all these forms are equivalent.
9
![Page 13: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/13.jpg)
(Dipole) selection rules: where do they come from?
Dipole transition matrix element is an integral: ǫ · 〈ψf |r|ψi 〉
Analogy:
Integral of a product of an even and an odd functions will beidentically zero.
Likewise:If wave functions |ψi 〉 and |ψf 〉 have certain symmetries, the dipolematrix element will be identically zero.
Transitions for which 〈ψf |r|ψi 〉 is zero are called forbiddentransitions.
Transitions forbidden by the dipole selection rule are accessible via
higher-order terms in the exp(± i~q · x) expansion, their intensity is
usually much smaller than intensity of the dipole-allowed transitions.
10
![Page 14: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/14.jpg)
Density of states: powerful tool for intuition
Density of states (DOS) describes how many electron states arethere at certain energy ε.
n(ε) =∑
n
∫
1BZ
dk
4πδ(ε − εnk) .
Knowing the DOS for a solid is analogous to knowing the energylevels for an atom.
11
![Page 15: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/15.jpg)
How DOS enters spectroscopy
Probability of a radiative transition:
w =2π
~|Mfi |
2 δ(Ef − Ei ± ~ω) .
Recall: n(ε) =∑
n
∫
(1BZ)dk4π δ(ε − εnk).
In spectroscopy, we will integrate over i ’s or f ’s.We are interested in a probability that as a results of interaction with
electromagnetic radiation, either a specific final state is created out of all
possible initial states or that a specific initial state is transferred in any
final state.
If the matrix elements do not depend on i or f , we get
[I (ω)] / [µ(ω)] / [. . .] ≈2π
~|Mfi |
2n(±E[f ,i ] ± ~ω) .
The spectra reflect the DOS weighted by transition matrixelements Mfi .
12
![Page 16: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/16.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
13
![Page 17: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/17.jpg)
X-ray Absorption Spectroscopy (XAS)
◮ X-rays go in, x-rays go out, absorption coefficient is measuredas a function the energy of the incoming x-rays.
x-rays inx-rays out
sample
◮ Most of the absorption goes on account of the photoelectriceffect on core electrons.
14
![Page 18: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/18.jpg)
XAS probes density of unoccupied states
EF
Core hole is left behind the ejected (photo)electron.
15
![Page 19: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/19.jpg)
Comparing photoemission with x-ray absorption
EF
EF
PES: from the valence band tovacuum.
XPS (X-ray photoemissionspectroscopy): from core levels.
XAS: from core levels to theconduction band.
XAS is angle-integrated XPS.
16
![Page 20: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/20.jpg)
Chemical selectivity
EF
absorption coreedge level
K 1sL1 2sL2 2p1/2L3 2p3/2
◮ Generally, absorption coefficient decreases if x-ray energyincreases.
◮ If incoming x-rays energy is large enough to excite anothercore electron, the absorption coefficient increases by a jump.
◮ Transitions of electrons from one core level only dominate thespectrum close to this jump.
17
![Page 21: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/21.jpg)
Angular momentum selectivity
Dipole approximation (recall slides on the matrix element):
Mfi ≈ ǫ · 〈ψf |r|ψi 〉 .
If wave functions |ψi 〉 and |ψf 〉 have certain symmetries, the (dipole)
matrix element will be identically zero.
Only transitions between states with their angular momentumquantum number differing by one are allowed:
ℓf = ℓi ± 1
XAS probes angular-momentum selected DOS as seen from achemically specific site.
18
![Page 22: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/22.jpg)
X-ray emission spectroscopy (XES)
EF
EF
1. Prepare the conditions: create a hole in the core.
2. Measure the intensity of x-rays which are emitted whenelectrons from valence band fill this hole.(Steady-state situation, not a pump-probe experiment.)
19
![Page 23: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/23.jpg)
XES – XAS complementarity
◮ XAS probes density of unoccupied states
◮ XES probes density of occupied states
20
![Page 24: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/24.jpg)
Information from XES (in comparison to PES)
◮ Unlike in photoemission, no information about k-vector.Only DOS is accessible.
◮ However, we know which DOS we are probing:◮ Chemically specific.◮ Angular-momentum-specific.
◮ Calculations: similar formula as in XAS.◮ The core hole is in the initial state, not in the final state.
For final state, there is a valence band hole, which is usuallywell screened.
21
![Page 25: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/25.jpg)
XMCD = XAS − XAS + magnetization + SOCXMCD (X-ray Magnetic Circular Dichroism):
Sample is magnetized, measure the difference between absorptionof left and right circularly polarized x-rays.
magnetization
photon helicity
parallel
antiparallel
x-rays
µXMCD = µ(+) − µ(−)
22
![Page 26: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/26.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
23
![Page 27: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/27.jpg)
Electron-electron interaction in spectroscopy
In many (if not most) circumstances, the electron-electroninteraction in solids can be handeled within the LDA.
However:
◮ Spectroscopy: dynamic highly non-uniform situation.
◮ Core hole is a localized perturbation, strong Coulombinteraction with the excited photoelectron.
◮ Also other electrons are affected. This may be oftendownfolded to
◮ finite core hole lifetime,◮ finite photoelectron lifetime.
◮ Some beyond-LDA interactions may be present among the valenceand/or conduction electrons which whould be there even withoutthe spectroscopic processSee earlier talks of Gian-Marco Rignanese, Jurgen Braun, . . .
Example of LDA+DMFT in PRB 84, 115102 (2011)
24
![Page 28: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/28.jpg)
Core hole: take it seriously or not?
Calculating the spectrum fully accounting for all the ingrediences isoften impossible.
To account for the core hole requires many-body calculations.Such calculations can be done for atoms but not for solids.(Everything is possible in principle but . . . )
The choice is yours:
◮ You may include many-body effects associated with the corehole but then you cannot include the solid-state-like effects(influence of other atoms apart from the photoabsorbing one).
◮ You can fully account for the influence of other atoms(hybridization) but then you cannot include the core hole in atruly many-body fashion.
25
![Page 29: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/29.jpg)
Tailor your approach according to the problem
◮ If the process is delocalized, hybridization is more importantthan the core hole interaction. Use LDA and standardsolid-state-like approaches.E.g. case of K edge of metals [J. Synchr. Rad. 10, 26 (2003)].
◮ If the process is localized, core hole dominates over thehybridization. Use atomic-like approach (model crystal fieldHamiltonian, multiplets).E.g. case of L2,3 edges of 3d elements in oxides [Micron 41,
687 (2010)].
26
![Page 30: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/30.jpg)
What if. . .
If both core hole and hybridization have to be properly accountedfor, then you have a problem.
◮ Time-dependent DFT within the linear response theory [PRL
80, 4586 (1998); PRB 67, 115120 (2003); PRB 21, 215502
(2012)].
◮ Multi-channel multiple scattering [PRB 42, 1944 (1990); PRB
70, 245120 (2004); JPCM 24, 365501 (2012)].
◮ Bethe-Salpeter equation [PRB 64, 165112 (2001); JPCM 21,
104205 (2009); PRB 82, 205104 (2010)].
◮ More sophisticated Hamiltonians with parameters chosen sothat the relevant hybridization and interaction is described[Coord. Chem. Rev. 253, 526 (2009); talk of Maurits Haverkort].
◮ ???
27
![Page 31: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/31.jpg)
Simple treatment of the core hole
If the core hole interaction is not too strong, its effect can bedescribed within the final state rule [PRB 25, 5150 (1982)].
Final state rule:Take LDA wave functions calculated for a system in the final stateof the spectroscopic process.
◮ XAS: calculate it with the core hole.
◮ XES: calculate it without the core hole.
Technically, this means treating the photoabsorbing atom as animpurity: the photoelectron is removed from the core level and putinto the top of the valence band.
Calculational method: embedded impurity (Green’s functionformalism), supercell (band-structure formalism)
“Relaxed and screened model.”
28
![Page 32: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/32.jpg)
Useful many-body cheats (1)
◮ “Diffuse” interaction of the core hole with other electronsresults in finite core hole lifetime. Broaden the spectrum usingFWHM from the tables [At. Data Nucl. Data Tables 77, 1
(2001)].
◮ “Diffuse” interaction of the excited photoelectron with otherelectrons results in finite photoelectron lifetime. Broaden thespectrum employing the universal curve for inelastic mean freepath [SSC 42, 365 (1982); Surf. Interface Anal. 1, 2, 1979].
◮ LDA-like effects beyond the LDA result in energy-dependentexchange-correlation potential:
◮ Hedin-Lundquist,◮ Dirac-Hara.
[PRB 35, 2604 (1987); PRB 51, 13015 (1995)]
29
![Page 33: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/33.jpg)
Useful many-body cheats (2)
Beware:these are cheats, do not hang to tabulated values too literally[J. Synchr. Rad. 6, 236 (1999); PRB 52, 6349 (1995); J. Synchr. Rad.
10, 51 (2003); PRB 76, 104411 (2007)].
However, encouraging attempts to do real calculations in many ofthese respect were done [PRB 65, 064107 (2002); PRB 76, 195116
(2007)].
30
![Page 34: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/34.jpg)
Outline
Spectroscopy: Light and matter
The zoology of x-ray spectroscopies
How big theory enters the business
When spectroscopy may benefit from calculations: case study
31
![Page 35: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/35.jpg)
L2,3 edge of magnetic systems (transition metals)
2p1/2
2p3/2
EF
L2 L3
0
2
4
6
L2,
3-ed
geX
AN
ES
isotropicabsorption
L3
L2
-10 0 10 20 30energy [eV]
-4
-2
0
2
L2,
3-ed
geX
MC
D
difference(+) - (-)
32
![Page 36: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/36.jpg)
L2,3 edge of magnetic systems (transition metals)
2p1/2
2p3/2
EF
L2 L3
0
2
4
6
L2,
3-ed
geX
AN
ES
isotropicabsorption
L3
L2
-10 0 10 20 30energy [eV]
-4
-2
0
2
L2,
3-ed
geX
MC
D
difference(+) - (-)
XMCD sum rules:
By adding, subtracting anddividing the peak areas,chemically-specific µspin, µorband µorb/µspin can be obtained
∫
(∆µL3 − 2∆µL2) dE ∼µ(d)spin + 7T
(d)z
3n(d)h
∫
(∆µL3 +∆µL2) dE ∼µ(d)orb
2n(d)h
32
![Page 37: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/37.jpg)
What can XMCD do for us?
◮ Through the sum rules, XMCD can inform about µspin andµorb separately
◮ For compounds, magnetic state of each element can beexplored separately
◮ Employing sum rules on experimental data may requiresubstantial theoretical input
33
![Page 38: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/38.jpg)
Validity of sum rules
( spin + 7Tz) / nh( spin + 7Tz) / nh
2 4 6 8
number of Fe atoms
0.6
0.7
0.8
(sp
in+
7Tz)
/nh
per
Fe
atom
orb / nhorb / nh
2 4 6 8
number of Fe atoms
0.025
0.03
0.035
0.04
0.045
orb/
n hpe
rF
eat
om
directly
from XAS
orb / ( spin + 7Tz)orb / ( spin + 7Tz)
2 4 6 8
number of Fe atoms
0.04
0.045
0.05
0.055
orb
/(sp
in+
7Tz)
per
Fe
atom
FeN / Ni(001)
◮ Trends of the “effective moments” (µspin + 7Tz)/nh andµorb/nh are reproduced well enough
◮ Applying sum rules to supported clusters in principle makessense
34
![Page 39: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/39.jpg)
Tz term: A feature, not a bug !
3
IA
∫
(∆µL3 − 2∆µL2) dE =µspin + 7Tz
nh
IA integrated isotropic absorption spectrumµspin d component of the local spin magnetic momentnh number of holes in the d bandTz d component of magnetic dipole operator
Tz =⟨
Tz
⟩
=⟨
12 [σ − 3r(r · σ)]
z
⟩
Tz is a measure of the asphericity of spin magnetization
µspin can be obtained only in combination with 7Tz !
35
![Page 40: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/40.jpg)
Does Tz term really matter ?
◮ For bulk systems it is usually negligible
◮ For surfaces, monolayers or wires, absolute value of 7Tz isabout 20 % of µspin
◮ For investigating trends of µspin within a series of systems,what matters is how Tz varies from one system to another
◮ If variations in Tz are small, neglect of Tz causes just anoverall shift of the deduced µspin
◮ Could Tz vary in such a way that the overall trendsof µspin+7Tz and µspin would be quite different ?
EPL 87, 67007 (2009)
36
![Page 41: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/41.jpg)
Results: µspin and [µspin + 7Tz ]/nh(
spin
+7
Tz)
/nh
[B]
1 3 5 7 9
0.7
0.8
0.9
no Tz
with Tz
spin
[B]
1 3 5 7 9no. of Fe atoms N
2.8
3.0
3.2
Fe on Ni
(sp
in+
7T
z)/n
h[
B]
1 3 5 7 9
0.7
0.8
spin
[B]
1 3 5 7 9no. of Co atoms N
1.8
1.9
2.0
2.1
Co on Ni(
spin
+7
Tz)
/nh
[B]
1 3 5 7
0.7
0.8
0.9
spin
[B]
1 3 5 7no. of Fe atoms N
2.8
3.0
3.2
3.4
Fe on Au
(sp
in+
7T
z)/n
h[
B]
1 3 5 70.2
0.4
0.6
0.8
spin
[B]
1 3 5 7no. of Co atoms N
1.8
1.9
2.0
2.1
Co on Au
FeN/Ni(001) CoN/Ni(001) FeN/Au(111) CoN/Au(111)
37
![Page 42: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/42.jpg)
Results: µspin and [µspin + 7Tz ]/nh(
spin
+7
Tz)
/nh
[B]
1 3 5 7 9
0.7
0.8
0.9
no Tz
with Tz
spin
[B]
1 3 5 7 9no. of Fe atoms N
2.8
3.0
3.2
Fe on Ni
(sp
in+
7T
z)/n
h[
B]
1 3 5 7 9
0.7
0.8
spin
[B]
1 3 5 7 9no. of Co atoms N
1.8
1.9
2.0
2.1
Co on Ni(
spin
+7
Tz)
/nh
[B]
1 3 5 7
0.7
0.8
0.9
spin
[B]
1 3 5 7no. of Fe atoms N
2.8
3.0
3.2
3.4
Fe on Au
(sp
in+
7T
z)/n
h[
B]
1 3 5 70.2
0.4
0.6
0.8
spin
[B]
1 3 5 7no. of Co atoms N
1.8
1.9
2.0
2.1
Co on Au
FeN/Ni(001) CoN/Ni(001) FeN/Au(111) CoN/Au(111)
For CoN/Au(111), the Tz changes the picture completely!
37
![Page 43: Core-level spectroscopy: Basics of XAS, XES, XMCD and alikesipr/separaty/intro-to-core-spectra.pdf · (“+” for absorption of photons, “-” for emission of photons). (First](https://reader033.vdocument.in/reader033/viewer/2022043002/5f7e92c18b9d10751d581a62/html5/thumbnails/43.jpg)
Conclusion
Spectroscopy can be very useful but you have to know whatyou are doing.
38