Auger Line Shapes in Solids

Home , Pierre Victor Auger

Pierre Victor Auger (1899-1993)

who discovered the law of the Auger effect in 1925

who discovered the Auger effect in 1923

1 Core-levels observed in photoemission are resonances and width is large for high binding energies

Core-levels observed in photoemission are resonances and width is large for high binding energies

Fe1s binding energy=7112 eV Width > 5 eV

Decay mechanisms: X-ray emission, Auger electron emission.

Auger electrons are seen by the ESCA apparatus along with photoelectrons. Their energies are independent of the photon energy.

X− ray notation level

Ks1 1/2

Ls1 2 1/2

Lp2 2 1/2

Lp3 2 3/2

Ms1 3 1/2

Mp2 3 1/2

Mp3 3 3/2

Md4 3 3/2

Md5 3 5/2

Ns1 4 1/2

Np2 4 1/2

Np3 4 3/2

Nd4 4 1/2

Nd5 4 3/2

Nf6 4 5/2

Nf7 4 7/2 Meitner-Auger Effect and Spectroscopy

An important spectroscopy is based on the Auger Effect. Actually, this effect was first reported in 1923 in Zeitschrift für Physik by the Austrian Physicist Lise Meitner (1878-1968).

In 1925, the great French physicist Pierre Auger (1899- 1993) rediscovered the effect while investigating in a bubble chamber the emission of an electron from an atom that absorbs a X-ray photon, that is, photoemission. The photoelectrons have kinetic energy Ek = hν − EB, where EB is one of the binding energies of the atom inner levels. However the Auger electrons have ν-indepedent energies given approximately by the empirical Auger law.

B BB EAuger (αβγ )=E ( α ) - E ( β ) -E ( γ ) 7 B BB EAuger (αβγ )=E ( α ) - E ( β ) -E ( γ )

Pierre Victor Auger (1899-1993) X-rays of adequate energy produce a primary hole in the state α of binding energy of EB(α) and a photoelectron; since the ion with a core hole is unstable, the primary holes is filled up by an electron in a less bound level β, and the energy gained in the process is taken by an electron in level γ, than is emitted as the Auger electron. For particular transition to happen, it is necessary that the primary hole is deep enough (its binding energy must exceed the sum of those of β and χ).

γ γ

β β

α α 8 The Auger transitions are denoted by the spectroscopic symbols of the shells (or, more precisely, sub-shells) involved: thus a KL1M2 transition is due to a primary hole in the K shell that decays leaving in the final state L1 and M2 holes and an Auger electron.

Μ2

One speaks about Core-Core-Core, Core-Valence-Valence, etc.,transitions depending on the levels that are involved.

The Auger effect is caused by the Coulomb interaction: two electrons of the system collide and while one fills up the primary hole, the other is shot out as the Auger electron.

The energy of the primary-hole state is shared between the Auger electron

and the ion left behind. 9

AES=Auger Electron Spectrum of Cd vapor (Z=48) X− ray notation level

Ks1 1/2

M4 initial hole Ls1 2 1/2

Lp2 2 1/2

N4,5 final Lp3 2 3/2 holes Ms1 3 1/2

Mp2 3 1/2

Mp3 3 3/2

Md4 3 3/2

Md5 3 5/2

Ns1 4 1/2

Np2 4 1/2

Np3 4 3/2

Nd4 4 1/2

Nd5 4 3/2

Nf6 4 5/2

Nf7 4 7/2 11 KL11 M Auger transition in the simplest electron picture:

L11+→ M Kk +the other electrons are (approximately) spectators

12 KL11 M Auger transition in the hole picture is simplest:

Kk+→ L11 + M hole k is in continuum

13 X decay is faster when the involved levels are distant in energy, because of the ν3 factor in the transition probability due to the density of photon final states.

The Auger decay prevails if the states α, β and γ are near in energy

Auger is the dominant for inner shell holes of light atoms, while in heavy ones X decay is much more likely Wentzel (1927 ) theory: αβγ transition Primary holes  final holes Primary holes: deep level α and free state k final holes : the spin-orbitals β and γ

Two-step model: the photoemission process produces ion in its meta-stable ground state- Deep hole creation and Auger decay are disjoint processes .

15 Wentzel (1927 ) theory: αβγ transition Mechanism: the smoking gun

The Auger transition is a Coulomb collision between two holes and is an energy conserving process.

(in reality the other electrons are also involved in some way)

In the hole picture, the initial state |Φi > and the final state |Φf > of the atom are represented by 2 × 2 Slater determinants; they have the same energy and are coupled by the Coulomb interaction. In a KLM transition,

2π 2 Rate by Fermi golden rule PHif =ΦΦ | i C f | .  16 An alternative mechanism : internal photoemission

Μ Μ2 2 hν L L1 1

Κ Κ

One of electrons in the upper states β, γ could fill up the deep hole via a normal radiative process, emitting a X-ray photon; this photon could then cause the photoemission of the other electron. Would’nt the final state be the same?

Indeed, this alternative process does exist, and has the name of internal photoemission; unlike the Auger effect, it obeys optical selection rules. The transition probability of the internal photoemission can be calculated by perturbation theory, but since it is a second-order process in A.P it turns out to be quite small compared to the Auger effect. 17 Atomic Auger Selection Rules 2 Selection rules arise in the two-step model from the conservation of J , Jz and parity between the initial, core-hole state and the final state including the Auger electron. 2 2 In the L-S approximation, L , Lz and S , Sz are also conserved, while in the jj scheme, the states are labeled by the j quantum numbers. KLL transitions If the spin-orbit interaction is more important than the Coulomb interaction, the jj scheme applies. If the Coulomb interaction dominates, the LSMLMS scheme is OK.

The pure jj scheme one would predict 6 transitions, namely, KL1L1,KL1L2, KL1L3,KL2L2,KL2L3, and KL3L3.

L3 L 3 L3 L L 3 L3 3 L2 L 2 L2 L L 2 L2 2 L1 L 1 L1 L L 1 L1 1 K K 18 K K K K In the pure LS scheme, the 5 possible final states are:

2s22p4 3P is forbidden by 06 1 22sp→ S parity conservation; indeed, the primary hole has L=0 2 4 3 1 and is even, 2s 2p P is 15  P even and has L=1 ; by L 22sp →  3  P allowed conservation the Auger electron must be in a p state, which is odd.Hence  1S the final state is odd.  22sp24→ 3 P  The transition to the odd  1  D 2s12p5 3P atomic final state is allowed, and one predicts 5 lines. LS terms

split by Coulomb interaction 19

When the spin-orbit interaction is introduced, in intermediate coupling the forbidden final-state splits :

2 4 3 3 3 3 2s 2p P → P2, P1, P0;

3 then, states with the same j and different spin mix: P2 mixes with 1 3 1 2 4 D2 and P0 mixes with S0 from the same 2s 2p configuration. Now the decay can occur with d or s Auger electrons.

1  =3 + 2 41  S jPS0 from0 2s 2p mixed parity 33 24 3 P→= jP1 from even and J=1 22sp→  P  1  =3 + 2 41  1  j2 from PD22 2s 2p mixed parity  D

3 P1 even and J=1 requires Auger electron in even state with J=1 − forbidden

21 1  =3 + 2 41  S jPS0 from0 2s 2p mixed parity 33 24 3 P→= jP1 from even and J=1 22sp→  P  1  =3 + 2 41  1  j2 from PD22 2s 2p mixed parity  D

3 P1 even and J=1 requires Auger electron in even state with J=1 − forbidden

3 3 P2 and P0 become more and more allowed as Z grows.

3 Instead, P1 remains purely P and forbidden (as long as one can neglect the mixing with higher configurations). Thus, the number of lines grows to 9.

0 61 Allowed Auger transitions 22spS , in intermediate coupling 1 51 3 3 3 2sp 2 P20, P , P 1, P 2, 2spS2 2 41 , 3P , 3 P , 1 D 0 02 2 22 Resonant Photoemission Example: transition metal like Co, or oxides like CuO

photo Photoemission with electron

hνε=(3 dp ) − ε (3 ) εεk =(3dp ) − ε (3 )

vacuum level

3d band Fermi level

d hole

3p core level

23 If the photon is tuned to the transition 3p  3d the Co is left with one less 3p electron and an excess 3d electron above the Fermi level. Then a two electron (Auger transition ) takes a 3d electron to 3p and a second 3d electron above the vacuum. This final state resonates with the direct 3d photoemission (Fano resonance).

Core-Valence-Valence transitions in solids: Lander independent-particle theory

Level scheme E ε k = kinetic energy of Auger electron ε k

vacuum level ε1 =binding energyof level 1= electron jumps to free state = energyof hole in level 1

NE()=∑ δω ( − εk ) k∈ BZ Auger law: ε1 εεε= ++ ε ε ck12 2 core-hole→ 2 valence holes+Auger electrons

electron jumps to core Auger spectrum: ε−+ εε ε εC ck(12 )= Auger energy

27 CVV transitions in solids: Lander theory (1953) Level scheme εck−+( εε12 )= ε Auger electron energy E All hole pairs such that εε12+= ω ε k ε= εω − vacuum level contribute to spectrum at kc .

electron jumps to free state Auger intensity 2 I()|ω= M | dN ε11 () ε N ( ωε− 1 ) NE()=∑ δω ( − εk ) ∫ k∈ BZ M = Wentzel's matrix element ε1

ε 2 Density of final hole states electron jumps to core ε ε ωε− ∫ dN11()( N 1 ) εC = self-convolution of N

NB in Lander theory the holes are created in Bloch stetes 28 Powell, prl (1973) stressed that spectra can be atomic-like or band-like

29 Milano 4 Luglio 2006 S.P.Kowalczyk et al. Phys Rev (1973)

Quasiatomic CVV spectrum

30 Milano 4 Luglio 2006 31 George A. Sawatzky valence atomic orbitals Closed band theory

closed-shell valence ? band

core-hole

Initial state Final state:do holes delocalize?

Model Hamiltonian HH=++atom H Solid H atom− Solid + H free electrons

H=++εε nˆˆ n Ummmmcccc(, , , )†† atom dh dh ∑m ∑∑ 1234m1243 m m m m mm12 mm 34

Hnfreeelectrons= ∑ε kˆ k

HHSolid+ atom− solid enter through LDOS; one may take Anderson model 33 Take Spin-up core hole in initial state

† ic=deep− hole Ψ  1 = φ φ φφ atomic Auger :Amm ( , ', k )deep− hole (1)k (2)m (1) m' (2) r12

neglect inter-atomic transitions i.e. transitions take to the set of states

†† mnσ = cnσ cm↑ Ψ

with two holes on valence orbitals of the same atom.

34 Milano 4 Luglio 2006 Cross section: from Fermi Golden Rule *  S()ωω= ∑∑Amn() kA pq () kD mnpq () mn pq

where the local density of states (LDOS) for the two final-state valence holes is

Dmnpq ()ω= pq σδ ( ω− H ) mn σ

†† mnσ = cnσ cm↑ Ψ

H is all the interacting Hamiltonian except free Auger electron term

35 Milano 4 Luglio 2006 1 hole analogy :ρωmn ( ) =m δω( −= Hn) ρωnm () −iHt Fourier transformρmn (t ) = me n

Dmnpq ()ω= pq σδ ( ω− H ) mn σ −iHt Fourier transformDmnpq ( t ) = pqσσ e mn

The fact that the LDOS appears, rather than the band DOS, as in Lander theory, is one of the main results, and qualifies Auger spectroscopy as a local probe of valence states.

36 Milano 4 Luglio 2006 Simple limiting cases:

Atomic limit multiplets

Non-interacting case

Two-hole correlation function −iHt †† Dmnpqσσ() t= pqσ e mn σσ, mn= cn cm↑ Ψ U=0 limit, taking primary hole spin ↑

σ=↓,()Dtmnpq↓ = ρρmp( t) nq ( t) spins ↓↑ σ=↑ = ρρ− ρρ ↑↑ ,()Dtmnpq↑ mp( tt) nq( ) mq( tt) np ( ) spins

37 Milano 4 Luglio 2006 To calculate the interacting density of states use the identity

111 1 = + H1 ωω−−HH00 ω − H ω − H

One-body part without Repulsion term free electrons

†† Take matrix elements over mnσ = cnσ cm↑ Ψ

The coupled equations can be easily solved in general.

However, if the solid does not significantly perturb the spherical symmetry of the atom, the the D matrices are diagonal in the |LMLSMS > representation, where Hr is diagonal, and obey uncoupled equations. 38 Trivial example: s band: The two-holes Green’s function is defined as φ0

1 ∞ 0 −=iφω0 ( ) 00 00 0 D (ω ') 00 0 ωδ−+Hi Id()ωω= ' −=−iφω() I () ω iD π () ω 0 ∫−∞ ωω− '

D = two-holes DOS 2 holes on same site

1 1 11 00 00= 00 00+ 00 H1 00 ω−H ω − H00 ωω −− HH 1111 00 00= 00 00+ 00 00U 00 00 ωω−−HH00 ω − H ω − H φω(0) ( ) Exact solution φω( ) = 1+ iUφω(0) ( ) φωD0 () D(ω )= Re = π[1−+UI0 ()] ωπ 2 220 U D () ω 2

two-hole resonances

Hole binding by repulsion: a purely quantum effect 39 Example: rectangular band

1 ρω( ) = θα( − | ω |) 2α

−α α ω

⊗ =

1 ω TriangularDOS : D0 (ω )=−− θαω (2 )( ) 24αα2 40 1 ω D0 (ω )=−− θαω (2 )( ) Triangular dos 24αα2

∞ Dy0 () I0 ()ω = dy ∫−∞ ω − y

12ωα+− ω ω22 4 α I 0 (ω )= log | |+ log | | 2α ωα− 24 α22 ω

φωD0 () D(ω )= Re = π[1−+UI0 ()] ωπ 2 220 U D () ω 2 shows the distortion of band-like lineshapes as U grows.

For U>1.44 α the intensity of the continuous line shape drops and tends to zero for large U.

The overall intensity cannot drop, however.

41 φωD0 () D(ω )= Re = π[1−+UI0 ()] ωπ 2 220 U D () ω 2

The missing intensity is into split-off the two-hole resonances, that however come into the theory as 0 over 0 singularities.

D00=0, 1 −= UI 0 To clarify the situation, a trick is in order. Start from two-body GF 1 −=iφω0 ( ) 00 00 ωδ−+Hi0 −=−iφ00() ω I () ω i π D 0 ().From1 ω −body ρω () computeD0 ()ω ∞ Dy0 () FromD00 (ωω ) computeI ( ) = dy ∫−∞ ω − y The mathematics is the same as in the Lehmann representation of G Axx( , ',ω ') ω= δ= ωµδ − Gxx( , ', ) ∫ ,ω ' sign( ' ) * ωω−+' i δω ' 1 Axx( , ',ω ') =− Im(G ) sign(ωµ−>) 0 spectral functio n π 42 G causal, real and imaginary parts are Hilbert transform pairs Letting zi=ω + δ −=iφ (0)( z ) Iz 0 ( ),

In the same way, we automatically get a broadened D0 as the imaginary part, keeping δ small 12ωα+− ω ω22 4 α I 0 (ωω )=+→ log | | log | | with z yields 2α ωα− 24 α22 ω 12z+−αα zz22 4 −=izφδ0 ( ) log( ) + log( ) as→ 0, 2αzz− 24 αα22 →−I00()ωπ iD () ω

This is equivalent to convolving the line shape with a Lorentzian of width δ , which, incidentally, is always appropriate to describe lifetime broadenings which are present in reality even if they are not considered in the model.

43 43 Applications to desorption theory (Knotek Feibelman mechanism) γ = U α steparameter the is 44 Hole binding by repulsion: a purely quantum effect

Band continuum

I called them resonances because they must eventually decay, since they are excited states Strong correlation means bound states, new frequencies, failure of mean field

W=0 pairing yields bound states from repulsion in the presence of

high enough symmetry (Cini and Balzarotti 1995) but this is 45 another topic! Theory of the APECS spectra of Antiferromagnetic Transition Metal Oxides Auger and Auger-photoelectron coincidence spectra of open bands: featureless and uninformative Co solid lines: singles AES

dotted: in coincidence with 2 p3 2

L3 core-hole

M 4,5

from Lund,Thurgate and Wedding, PRB 1997 Coster Kronig dotted: in coincidence with 2 p 1 L2→ LM 3 45 2 LM3 45→ MMM 45 45 45 L2 core-hole

M 4,5

Auger L2→ MM 45 45

L2 Coster Kronig

L2→ LM 3 45 from Lund,Thurgate and Wedding, PRB 1997 LM3 45→ MMM 45 45 45 Ni solid lines: singles AES

coincidence with 2 p3 coincidence with 2 p1 2 2 core-hole core-hole

from Lund,Thurgate and Wedding, PRB 1997 CoO: No info on magnetism from XPS No info on magnetism from AES Photoemission: no change across T N M23M45M45 Auger: para antiferro no change across TN

Finding: Info on magnetism from APECS!

Angle integrated

Evident difference between antiferro and para- Further info on magnetism from angle resolved APECS

Angular configurations NN

photoelectron Auger electron

photoelectron E

Auger electron

X-Ray E polarization NN AN

DEAR APECS E E photoelectron

photoelectron Auger electron Auger electron Theory: X-ray Photoemission

Photoemission: combination of Local Density of states on Co and O

Octahedral cluster- Group Oh Co orbitals→ irreps 1 dee(1) = dY2 = 2,0 d(2) = d22 =() YY2,2 + 2,− 2 ggz xy− 2 i dt (1)= dxy = ( −+ YY2,2 2,− 2 ) 2 g 2 i dt (2)= dyz = ( YY2,1 + 2,− 1 ) 2 g 2 1 dt (3)= dzx = ( −+ YY2,1 2,− 1 ) 2 g 2 Among the 18 states of the ligand Oxygens only those linear combinations with the same symmetry must be taken into account in the Hamiltonian. We get 5 Oxygen orbitals 2 for Eg ant 3 for T2g. These are given by 1 p(1)==− p2 2 pA () −++ pB () pC () 2 pD () +− pE () pF () eg z zxy z xy 12

pp(1) = t2 g xy 1 =−++pB() pC () pE () − pF () 2 yxyx

1 p(2) == p p()()()() A +−− pC pD pF t2 g yz y z y z 1 2 p(2)== p22  pB() +−− pC () pE () pF () eg xy− 2 xyxy 1 p(3)== p[ pA () −−+ pB () pD () pE ()] t2 g zx2 x z x z Slater-Koster matrix elements: all hopping integrals in terms of τσ,τπ

21 22 2 E( l , m , n )=−+ l [ n ( l m )]ττσπ − 3 ln exg 1, 2

21 22 2 E( l , m , n )= m [ n −+ ( l m )]ττσ − 3 mn π eyg 1, 2

21 22 22 E(,,)[()]3() lmnnnlm=−+ττσ + nlm +π ezg 1, 2 3 E(,,)()(1) lmn= ll22 − mττ + l −+ l 22 m exg 2, σ π lmn, , direction cosines 2

3 22 22 E( lmn , , )= mlm ( − )ττσ − m (1 +− lm ) π eyg 2, 2

3 22 22 E (,,)()()lmn= nl − mττσπ −− nl m eg 2,z 2 E(,,) lmn=−−=−= E ( mln ,,) E ( nml , ,) 3 lm22ττ +− m (12) l tx222ggg1, ty1, t2, z σπ E(,,) l m n=−−=−−= E ( m ,,) l n E ( n , m ,) l 3 lmnττ − 2 lmn t22gg2, x t3, y tz 2 g1, σπ E(,,) lmn=−=−−= E ( mln ,,) E ( nml , ,) 3 ln22ττ +− n (12) l tx22gg3, ty2, tz 2 g3, σπ

For CoO, τσ =1.3 τπ =0.6 and the hopping integrals to symmetry adapted combinations

Tepd( g 1)≡=− T pd (1) 2.25166Tepd ( g 2)≡ T pd (2) =− 2.25166

Ttpd(2 g 1)≡=− T pd (3) 1.2Ttpd ( 22 g 2) ≡=− T pd (4) 1.2 Ttpd ( g 3) ≡=− T pd (5) 1.2 We start with10 orbitals and write the one-body part of the Hamiltonian of the cluster (diagonal in the spin indices that are therefore omitted) as

NI =†† ++†† + H0 ∑∑Ed() I d Ii d Ii E p () I p Ii p Ii T pd ( Ii )( d Ii p Ii p Ii d Ii ) Iet=gg,12 i =

∆−6D irrep=eg EI() = ,∆= 5.5, 10D = 0.7 d ∆+  4D irrep=t 2g

−−(εεσπ )irrep =eg EI()=  A p εε−  (σπ ) irrep=t 2g

εεσπ=0.55, = − 0.15 F E B C

This produces 10 molecular orbitals D ′′ˆˆ† † ˆˆ Interaction Hamiltonian Hint = ∑∑ Umm(, ,, nn ) dmmσσ d'' d nσσ' d n′ mm′′ nn σσ ′

ϕϕ∗∗()r () rr ϕϕ () () r ′′= mm1′′ 221 n n For free atoms Umm(, ,, nn ) ∫ drr12 d ||rr12−

U(m,n,n,m) = direct integral, U(m,n,m,n) = exchange integral.

∞∞ r k Slater integralsfk ( n L , n L ) = dr dr R()() r2 R r2 r 22 r < a a b b ∫∫1 2naa L 1 nb Lb 2 12 k +1 −∞ −∞ r> in terms of the Racah parameters A, B, C. 63 1 441 5 f4==+=+ Cf0 A f 42 f B f4 5 9 99

Here A=1.08 (affected by screening, only parameter of theory obtained by fit to XPS spectrum) B=0.14 and C=0.54 free atom values. CoO XPS spectrum – Thy vs expt Note strong dependence on photon energy Theory: Auger profiles

Meitner-Auger effect due to: †† HMeitner− Auger =∑ TA c2' pσσ c k + hc..  Tmq(,)= Amqmmcc (,,,) A core ∑ core 12m12σσ m ' mm1, 2 Auger matrix elements  1 Am( , qm , , m )= (ψ (1) ψ (2) | | ψψ (1) (2)) core 12 2pmcore q 3dm12 3 dm r12

Simplified Physical picture: we assume the cluster valence band is in maximum spin lowest-energy state (Hund’s rule) with equilibrium configuration

33 HΨ==Ψ=(, dS7 ) Ed ()77 (, dS ) gs 22gs gs We neglect all relaxation effects due to a) sudden creation of core-hole b) the transient core-hole screening

 7 3 Tm( , q ) creates 2 holes on Ψ= (dS , ) A core gs 2 Unrelaxed current (up to a constant) 33 J=Ψ=−Ψ=(, dS7† ) Tδω ( HT ) (, dS7 ). A gs 22A A gs This reduces to Cini-Sawatzky theory in the limit of closed bands. (See Cini-Drchal 1-2-3 theory)

CoO 20 5 holes in 10 orbitals := 15504 states. 5 H (3↑↓ 2 ) 252 sextets, 1848 quartets, 3300 doublets dim(H (3↑↓ 2 ))=5400 H (4↑↓ 1 ) 252 sextets, 1848 quartets dim(H (4↑↓ 1 ))=2100 H (5↑↓ 0 ) 252 sextets dim(H (5↑↓ 0 ))=252 6*252+4*1848+2*6600=15504 Calculation of Auger M23M45M45 Matrix elements

ψ 3dm1 ψ 3dm2

iqz  ψ q ≈ e ψ 3 pmcore  ψ q

 1 Am( , qm , , m )= (ψ (1) ψ (2) | | ψψ (1) (2)) core 12 3pmcore q 3dm12 3 dm r12

∞ K ∞∞ K r − θ = 1 dr r22 dr r< R()()() r R r R r dΩ Y** () Ω Y () Ω Y () ΩΩ d eiKr12cos Y()() Ω Y Ω ∑∑21K + ∫∫1122K +1 3p 1313 d d 2∫ 11mcore 1KmK 12m12 1∫ 2 KmK 22m 2 K=0 mK =− 00 r> The angular integral is analytic. We took radial functions from the Clementi-Roetti Tables.

No free parameters Racah A fixed by visual fit of XPS spectrum 5 main peaks observed

5 main peaks predicted and assigned

AN A C S=5/2

C’ S=5/2 photoelectron E

Auger electro

NN E D C’ S=1/2 B S=3/2 E photoelectron Auger

0.00003 D High spin 0.00002 C’ A E B prefers AN

0.00001 C

0 30 35 40 45 50 55 A NiO F Neel temperature 525 K E B C 2h ground state d8 configuration spin S=1 D

εεdg(et )=−=− 7.1,d (2 g ) 6.0,

εεpg(et )= 1.2, p (2 g ) = 1.2,

tepd( g )=−=− 1.6, ttpd (2 g ) 2.8 Racah A= 3.1 NiO 20 4 holes in 10 orbitals := 4585states . 4 H (2↑↓ 2 ) 210 quintets, 990 triplets, 825 singlets H (3↑↓ 1 ) 210 quintets, 990 triplets H (4↑↓ 0 ) 210 quintets

 1 Am( , qm , , m )= (ψ (1) ψ (2) | | ψψ (1) (2)) core 12 3pmcore q 3dm12 3 dm r12

computed using radial functions from the Clementi-Roetti Tables.

No free parameters Racah A fixed by visual fit of XPS spectrum AN

photoelectron E

Auger electron

E photoelectron Auger electron T>Neel Red:high spin Blue: Low spin

Quintets Triplets Singlets peaks are not separated in energy like in Co 0.12 0.12

0.10 0.10 NN AN NN AN 0.08 0.08

0.06 0.06

0.04 0.04

0.02 0.02

0.00 0.00 35 40 45 50 55 60 65 70 35 40 45 50 55 60 65 70 Black: Normalized singlet profile Black: Normalized triplet profile

0.12 NN AN 0.10 NN AN 0.08

0.06 E photoelectron E

photoelectron Auger electron Auger electro 0.04

0.02

0.00 35 40 45 50 55 60 65 70 Best fit Black: Normalized quintet profile AN =0.24*singlet ++ 0.7*triplet 0.06*quintet NN =0.53*singlet ++ 0.36*triplet 0.11*quintet

NN is more low-spin, as in Co. Spins are more intermixed in NiO Open question: what is the mechanism producing the effect?

Evident difference between antiferro and para AN predominantly

photoelectron E

Auger electron

NN predominantly E photoelectron Auger electron

Why?