Fingerprints of entangled spin and orbital physics in itinerant ferromagnets

via angle resolved resonant photoemission

F. Da Pieve1

1 Laboratoire des Solides Irradies, UMR 7642, CNRS-CEA/DSM, Ecole Polytechnique,F-91128 Palaiseau, France and European Theoretical Spectroscopy Facility (ETSF)

(Dated: December 5, 2015)

A novel method for mapping the local spin and orbital nature of the ground state of a systemvia corresponding flip excitations is proposed based on angle resolved resonant photoemission andrelated diffraction patterns, obtained here via an ab-initio modified one-step theory of photoemission.The analysis is done on the paradigmatic weak itinerant ferromagnet bcc Fe, whose magnetism, acorrelation phenomenon given by the coexistence of localized moments and itinerant electrons, andobserved non-Fermi liquid behaviour at extreme conditions remain unclear. The combined analysisof energy spectra and diffraction patterns offers a real space imaging of local pure spin flip, entangledspin flip-orbital flip excitations and chiral transitions with vortex-like wavefronts of photoelectrons,depending on the valence orbital symmetry and the direction of the local magnetic moment. Sucheffects, mediated by the hole polarization, make resonant photoemission a promising tool to performa full tomography of the local magnetic properties even in itinerant ferromagnets or macroscopicallynon magnetic systems.

PACS numbers: 78.20.Bh, 78.20.Ls, 78.70.-g, 79.60.-i

I. INTRODUCTION

Spin and orbital degrees of freedom play a relevantrole in many fascinating correlated and/or spin orbit-driven systems, like Mott insulators1–3, non conventionalsuperconductors4–6 and topological materials7–9. How-ever, in the last two decades, it has become clear thatpeculiar orbital textures and coupling between spin andorbital degrees of freedom can be found even withoutrelevant spin orbit and/or without relevant electron-electron correlation, as in the case of low-dimensional ma-terials exhibiting Peierls transitions and charge densitywaves10–12, some lowly correlated insulators doped with3d ions developing long range magnetic order13, corre-lated metals14 and even weak itinerant ferromagnets15,16,whose behaviour might sometimes challenge the standardmodel of the metallic state, the (ferromagnetic) FermiLiquid theory.

Probing simultaneously spin and orbital degrees offreedom with high sensitivity to spatial localization re-mains nevertheless a difficult task. Indeed, the orbitalangular momentum is often quenched by the crystal fieldin many relevant compounds and it does not contributeto the magnetic moment, thus remaining often unacces-sible to direct probes with local sensitivity. Also, inmany relevant systems, the distinction between incoher-ent particle-hole and collective modes in both the spinand orbital channel is often not obvious17,18, making dif-ficult to understand the role of corresponding fluctua-tions in collective phenomena. Although for certain ge-ometries the commonly used angle resolved photoemis-sion (ARPES)19 and resonant inelastic X-ray scattering(RIXS)20 can give information on the angular characterof electronic states, their sensitivity to spatial localiza-tion is limited due to the linear dependence of the dipoleoperator on the spatial coordinate ~r. The situation be-

comes even more critical when localized and delocalizedelectronic states cooperate to determine the propertiesof a material, like for example in the well investigatedweak itinerant ferromagnet bcc Fe. The origin of the fer-romagnetism in this system, nowadays seen as a corre-lation phenomenon given by the coexistence of localizedmoments associated to electrons in a narrow eg band anditinerant electrons in the t2g band, is still unclear. A ten-dency of eg states to a non-Fermi liquid behaviour at bothextreme PT and ambient conditions has been reported16

(paramagnetic phase). Unexplained correlations eventu-ally determine the localization of the eg states15,21 andthe formation of localized moments down to the bcc ferro-magnetic phase. Finding a strategy to improve the capa-bilities of the widely used ARPES and RIXS techniqueswould boost the advance for an atomic-scale mappingof the magnetic properties of both itinerant ferromag-nets and ultimately of disordered or macroscopically nonmagnetic systems.

Orbital-resolved contributions to ARPES spectra areoften studied either analyzing the contributions to theself-energy entering the one-body spectral function de-scribing photoemission22 or analyzing the contributionsto circular or linear dichroism23–26, often via the one steptheory of photoemission. Other more explorative workshave considered Auger emission, in particular in time co-incidence with photoelectrons, and unravelled the two-hole orbital contributions to both energy spectra27 andangular polar scans28,29. Earlier works have also studiedthe orbital-resolved contributions to full two-dimensionalangular patterns in core level photoemission30,31 andAuger spectroscopy32–34, by looking at the anisotropyof the excited ”source wave” at the absorber in termsof its l,m components. Recently, pioneering diffrac-tion patterns have also been reported35–37 for resonantphotoemission (RPES), the so called participator chan-

2

nel of the non radiative decay following X-ray absorp-tion. In this channel, the decay occurrs before the ex-cited electron has delocalized, leading to one-hole finalstates linearly dispersing with photon energy (Ramanshift) before and at the very edge40, degenerate withusual ARPES. However, the existing practical calcu-lation schemes (model hamiltonian-based)38–41 only fo-cus on the spectator channels of the non radiative de-cay, with two-holes-like final states, which cannot bereached by direct photoemission. Also, retrieving in-formation on local magnetic properties remains difficult,and some effects observed in RIXS, like spin flip-orbitalflip excitations18,40,42–45 have never been reported inRPES.

In this work, it is shown that the yet largely unex-plored spin polarized angle resolved RPES (AR-RPES)is a promising tool for performing a full local spin andorbital tomography of the ground state of a system, byproviding access to local spin flip, orbital flip and chiralexcitations. The study is based on a recently presentedab-initio description for extended systems46,47, relying ona modified one-step theory of photoemission. Such ap-proach is here re-analyzed to elucidate matrix elementseffects and mixed with an auxiliary analysis of the par-tial densities of states to show the connection with lo-cal spin and orbital properties. The paradigmatic caseof the weak itinerant ferromagnet bcc Fe is consideredwithin DFT-LSDA. The ab-initio RPES energy spectraand diffraction patterns for excitation at the L3 edge bycircularly polarized light show that: i) exchange transi-tions induce both pure spin flip excitations, occurring farfrom the Fermi level (EF ), and coupled spin flip-orbitalflip excitations, occurring near EF in correspondance ofa narrow peak in the local partial density of states, as-sociated to the elongated eg levels; ii) the occurrence ofsuch excitations for different experimental geometries de-pends on the different localization/delocalization of therelevant t2g and eg states and on the direction of the localmoment. The influence of the orbital degrees of freedomin the low energy physics of the system is in line with ear-lier suggestions about the role of eg orbitals in the devel-opment of local moments64,66 and with recent combinedexperimental ARPES and theoretical studies21. Similar-ities and differences with the capabilities of ARPES andRIXS are discussed, as well as relevant implications con-cerning possible tomographic photoemission experimentsfor mapping local ground state magnetic properties andlow energy excitations in more complex systems.

II. THEORETICAL SECTION

The cross section for resonant photoemission is pro-portional to the Kramers-Heisenberg formula for second

order processes

∂2σ

∂Ωp∂ω∝

∑

f

|〈f |Dq|0〉 +∑

j

〈f |V |j〉〈j|Dq|i〉

E0 − Ej + iΓj

2

|2δ(~ω + E0 − EF )

(Γj is the core level lifetime-induced width).The first term is the dipole matrix elementDvp=〈iǫpLpσp|Dq|iǫLvσv〉 which describes, in an effec-tive single particle approach, direct valence band photoe-mission (v (p) denotes the valence state (photoelectron)and Lp = (lp,mp)). The second term represents theresonant process, described by the product of the core-absorption dipole matrix elements Dck and the decay (di-rect and exchange) matrix elements Vd and Vx, i.e. Rd =Vd · Dck = 〈iǫpLpσp, j

′c′|V |iǫLvσv, j′ǫkLkσk〉 · Dck and

Rx = Vx · Dck = 〈jǫpLpσp, ic′|V |jǫkLkσp, iǫLvσv〉 · Dck

(k denotes the conduction state where the electron getsexcited and c′ the quantum numbers m′

c, σ′c to which

the initial hole c = mc, σc might scatter). For the morelocalized participator decays, the direct term describesthe process in which the core hole is filled by the excitedelectron and a valence electron is emitted, while theexchange term describes the process in which these twoare exchanged. In principle, the energy detuning fromthe absorption edge and a narrow bandwidth of thephotons can act as a shutter between different channels,although only looking at energy spectra exhibitingthe Raman shift (as often done) might not alwaysallow the distinction between localized and delocalizedexcitations48, which remains an open issue for bothRIXS and RPES. All delocalized states can be describedconveniently via real space multiple scattering, whichdescribes the propagation of a wave in a solid as repeatedscattering events49 and which allows to keep explicitdependence on the local quantum numbers. In suchbasis, the cross section can be cast in a compact form:

∂2σ

∂Ωp∂ω=

∑

qq′

εqεq′∗

σqq′

where εq are the light polarization tensors and the her-mitian 3×3-matrix σqq′ is given by

σqq′ =∑

N,N ′

K(N, q)Imτv(N,N ′)K∗(N ′, q′),

(1)

where K(N, q) are the amplitues of the overall process(interfering direct and core-hole assisted photoemission)and Imτv(N,N

′) is the maginary part of the scatteringmatrix for valence states, containing the band structureinformation of the valence region. N labels the atomicsite i and L=l,m. The amplitudes can be written as

3

K(iLvσv, q) =∑

jLp

B∗jLp

(kp)(δijδσvσp(Dvp +Rd) +Rx)

and explicitly contain the photoelectron scattering am-plitudes BjLp

(kp). These can be resumed as B∗jLp

(kp) =

YLp(kp)i−lpeiδlp , i.e., (the source wave) + all the scat-

tering contributions. The orbital and spin contribu-tion to the outgoing electron wavefunction (source wave)are then determined by the parity and Coulomb se-lection rules of the whole process. They impose that|lc−|lv − lk|| ≤ lp ≤ lc + lv + lk, lc + lv + lk + lp=even andmc +mp = mv +mk. For the spin, one has σc = σk = σc′

for the direct term (the spin of the core hole does notflip) and σc = σk = σp, σc′ = σv for the exchange term(allowing also for possible core hole spin flip leading tosimultaneous flip of the orbital projection mc).

It is important to recall that the anisotropy of thecharge density of such source wave and the anisotropyof the charge density of the core hole state (core holepolarization, Pc) are influenced by the polarization ofthe impinging light and the polarization of the valencestates. Such anisotropies can be characterized by evenmultipoles (quadrupole, etc), describing the alignment(i.e., the deviation from sphericity, given by a differentoccupation among the different ml states, with a sym-metry between ±ml), and odd multipoles (dipole, etc),describing the orientation (i.e. the rotation of the chargedensity, given by a preferential occupation of ml statesover -ml states).

The connection with ground state properties is high-lighted via an auxiliary description, obtained by modify-ing an often used expression for normal Auger emission(i.e., a convolution of the density of states for the twofinal holes50). By considering now the density of states(DOS) of the emitted electron D(E − ǫ) and the DOS ofthe electron dropping into the core hole D(ǫ), weightedby the core hole polarization, the intensity becomes:

I↑(↓)(E) = M↑↑(↓↓)P+(−)

∫

D↑(↓)(E − ǫ)D↑(↓)(ǫ)dǫ+

M↑↓(↓↑)P−(+)

∫

D↑(↓)(E − ǫ)D↓(↑)(ǫ)dǫ

where P± = (1±Pc)/2 takes into account the modi-fications of the DOS of the electron filling the hole bythe core hole polarization, and M↑↑(↓↓) and M↑↓(↓↑) arerespectively the sum of the modulus squares of the spinconserving (direct and exchange) decay matrix elementsand the modulus square of the spin flip (exchange) decaymatrix element:

M↑↑(↓↓) = |Vd,↑↑(↓↓)|2 + |Vx,↑↑(↓↓)|

2,

M↑↓(↓↑) = |Vx,↑↓(↓↑)|2

Pc ranges from -1 (as in a ferromagnet withspin down holes, and light impinging parallel to the

magnetization51) to some other values < 1 when the holeflips its spin or the photon polarization and the local va-lence polarization form a generic angle (in this latter case,both even and odd multipoles contribute to Pc

52, and di-croism occurs in both absorption and decay).

The important theoretical prediction can then be madethat the occurrence of spin flip transitions and theirentanglement with orbital ones are determined by the(geometry-dependent) core hole polarization, the wayit affects excited states of different degree of localiza-tion/delocalization, and how it weights the decay ex-change matrix elements. Also, orbital flips should bemore visible when perturbing a highly symmetric (withrespect to relevant quantization axis) intermediate-stateorbital population (alignment), rather than an asymmet-ric one. Given the influence of matrix elements on differ-ent allowed source waves and the high energy of the pho-toelectrons (which reduces the importance of final-stateeffects), it can be expected that a selective real-spacemapping of (local) spin and spin-orbital excitations ispossible by looking at two-dimensional angular patterns.

III. COMPUTATIONAL DETAILS

Excitation at the 2p 3

2

edge of the itinerant weak fer-

romagnet Fe by circularly polarized light is investigatedto proof the unique capabilities of AR-RPES. DFT-localspin density approximation (LSDA) potentials obtainedby a scalar relativistic LMTO53 calculation for the bulkand a semispherical Fe(010) cluster (with 184 atoms andin-plane magnetization along <001>) are used as inputfor a multiple scattering code developed by the author,which can calculate ARPES and AR-RPES from clus-ter type objects. The calculated magnetic moment of2.26 µB from the self-consistent calculation is in goodagreement with experiment. Core states are calculatedatomically by solving the Dirac equation, while delocal-ized (bound and unbound) states are developed, as men-tioned before, via multiple scattering. For the opticaltransitions, the dipole approximation in the accelerationform is used, since the length form is not well defined fordelocalized state. The weak spin-orbit (SO) coupling ofthe valence and continuum states has been neglected.

From a theoretical viewpoint, non radiative decays arecomplicated dynamical processes which include atomicrelaxation and electron screening in response to the corehole. However, reasonable approximations can be madefor Fe. Electron-core hole interaction is generally weak inmetals because of efficient screening of the Coulomb in-teraction and its only observable effect is the reducedbranching ratio between the L3 and L2 edges of theisotropic x-ray absorption spectra, with respect to whatobtained within the independent particle approximation.However, such reduction is generally smaller for spin-polarized and dichroic spectra, and more importantly,in RPES it only affects the intermediate states, whichare not directly observed. For Fe, the deviation of the

4

-6 -5 -4 -3 -2 -1 0 1 2Energy - E

F (eV)

-6000

-4000

-2000

0

2000

4000

6000

d-D

OS

clu

ster

(a

rb. unit

s)

all d-statest2g

eg

a)

-5 -4 -3 -2 -1 0Energy - E

F (eV)

0

100

200

300

400

5000

100

200

300

400

500

inte

nsity

(ar

b. u

nits

)

ARPES (x 5)AR-RPES (left)AR-RPES (right)

spin down

spin up

b)

FIG. 1: Color online a) DOS of the Fe(010) cluster; b) ARPES and AR-RPES spectra (from47) for parallel geometry andnormal emission. Rest of the panel: PED, RPED for initial binding energy corresponding to the main peak and the spin flippeak in the spin up AR-RPES spectrum, and “source waves” patterns (the emitter is embedded in the cluster but no scatteringevents take place). (the plotted function is χ = I[θ, φ, ǫ]/I0[θ, ǫ]−1, I0 being the intensity averaged over all φ-dependent values.Scans are around the surface normal.)

branching ratio from the statistical value is actually verysmall54, indicating a reasonable single particle descrip-tion. Also, as a consequence of being a weak ferromagnet,both minority and majority spin states can be populatedto screen the core hole, leading to no drastic change inthe local moment56. When the decay takes place, with avalence electron filling the hole and the excited electronemitted, either the effective potential seen by the valenceelectrons is restored to its initial form or, as the electronis emitted with high kinetic energy, a sudden responseof the valence electrons occurrs due to the destructionof the core hole, with no time for electrons to readjust.Thus the spin polarization of the emitted electron re-sults to be approximately the one of the intermediatestate, very similar to the one of the initial ground statein case of Fe55. Dipole and Auger-like matrix elementsare then calculated here using ground state scalar rela-tivistic wave functions. The robustness of the approach isdemonstrated by earlier successful comparisons betweencalculated spin polarization, energy spectra and photoe-mission diffraction patterns and experiments46,57.

IV. RESULTS

A. AR-RPES spectra and diffraction patterns for

parallel geometry

Fig. 1a, 1b show the d-DOS of the whole cluster andthe ARPES and AR-RPES spectra for a photon energy atthe maximum of the resonance for normal emission andparallel geometry (light impinging along the magnetiza-tion, along which spin is measured). Each spin polarizedARPES spectrum shows one main peak and absence ofother sharp features, in agreement with experiments58

and in line with the genuine lowly correlated nature of thesystem. The dichroism is null, due to non chiral geometryand neglected SO in delocalized states. In contrast, theresonant spectra exhibit dichroism (in this geometry onlyrelated to the absorption step, as the orientation of thecore hole is unaffected by reversal of helicity59) and, moreimportantly, new peaks. Going towards higher bindingenergies, the spin up RPES spectra show a first (second)

peak for emission from e↑g (t↑2g) states, while the spin

down spectra exhibit a first peak for emission from t↓2g

states and then an unexpected peak at an energy where

5

TABLE I: Exchange transitions at core states with mixed spincharacter, for left (right) polarization ∆m = +1(−1).

∆m edge mc; σc mk; σk m′

c; σ′

c mp; σp mv; σv

+1 3

2;- 1

20;- 1

21;- 1

2-1; 1

23,4,2,1,0;− 1

21,2,0,-1,-2; 1

2

+1 3

2; 12

1;- 1

22;- 1

20; 1

23,4,2,1,0;− 1

21,2,0,-1,-2; 1

2

-1 3

2;- 1

20;- 1

2-1;- 1

2-1; 1

21,2,0,-1,-2;− 1

21,2,0,-1,-2; 1

2

-1 3

2; 12

1;- 1

20;- 1

20; 1

21,2,0,-1,-2;− 1

21,2,0,-1,-2; 1

2

there are almost no spin down states in the DOS, andwhich thus corresponds to spin up valence states. Thismeans that the spin of the photoelectron is opposite tothe one of the final valence hole, and thus it is a spin fliptransition. Such (exchange-induced) spin flip can onlyoccur for 2p3/2 eigenstates withmixed spin character dueto SO (the mj = ±1/2 sublevels, |3/2, 1/2(−1/2) >=√

2/3|Y ↑10(Y

↓10) > +

√

1/3|Y ↓11(Y

↑1−1) >).

We now move to the more explorative resonant diffrac-tion patterns. Ab-initio spin polarized resonant and di-rect photoemission diffraction patterns (RPED, PED)are reported in Fig. 1, for initial energies correspond-ing to the two peaks in the spin up AR-RPES spectra(the main peak near EF and the one at higher bindingenergy, corresponding to the spin flip excitations in thespin down channel). It is clear that, while almost allRPED patterns resemble the corresponding direct ones,a net 90o twist occurrs for right circular polarization forthe RPED pattern of the spin down channel, the one al-lowing for spin flip transitions, a clear signature of anaccompanying orbital flip of the photoelectron wave. In-terestingly, the effect is actually mainly visible at themain peak, revealing spin flip transitions hidden by dom-inating spin-conserving ones in the quasiparticle peak.

This orbital flip phenomenon can be understood viathe two models described in the theoretical section, byanalyzing the exchange matrix elements and the localpartial DOS. The selection rules dictate lp=1,3,5 (with3 numerically found as the most probable wave, in linewith previous works on similar transitions34,60). Table Ireports the exchange transitions occurring at core holestates with mixed spin character (at their spin downcomponents, as core hole states will be mainly spindown due to the major availability of spin down emptystates). These are mixed spin flip-orbital flip transi-tions, in which both the ml and σz components of thesame mj substate flip. Transitions mixing different mj

states, like mj = 1/2 flipping to mj = −1/2, are alsopossible, being the mj sublevels separated by 0.32 eV,but these imply only spin flip. We recall that the rel-evant irreducible representations here are: t2g: dxy =1√2(ψ2 −ψ−2), dyz = 1√

2(ψ1 −ψ−1), dzx = 1√

2(ψ1 +ψ−1);

eg: dx2−y2 = 1√2(ψ2 + ψ−2), d3z2−r2 = ψ0. Their contri-

bution to the partial DOS around a central absorber ionin the the cluster is shown in Fig. 2.

For left-handed light (∆m = +1 here), the excitation

FIG. 2: (Color online) Local partial DOS (l, m- resolved)around a Fe central ion in the cluster

to a mk = 1, ↓ state (t↓2g) (first row in Table I) is moreprobable than photoexcitation of the other spin downcomponent of the other sublevel59. The numerical evalu-ation of the decay matrix elements for different orbitalcontributions, similarly to earlier investigations56,61,62,allows to select the dominant transitions (in bold in Ta-ble I), and it partially reflects the reasonable result thatthe decay is more favourable if the two involved valenceand conduction electrons have the maximum number ofequal quantum numbers, as in this case they will repeal

more. The decay leading to a t↑2g final hole with mv = ±1

(dxz,dyz) gives the strongest contribution, making a dis-tinction between different orbitals in the DOS aroundthe absorber ion. Indeed, considering the localized na-ture of the recombination, such DOS unravels the or-bital character of the decaying states better than theDOS of the whole cluster, revealing narrow and prou-nounced peaks from different orbitals of the two irre-ducible representations in the spin up main peak, remind-ing of Van Hove singularities in the extended electronicstructure63,64. Angular momentum conservation rules

then dictate a Y ↓33 emitted wave, with strong intensity

reduction along the quantization axis, similarly to theone expected in direct valence band photoemission froma d-shell. and in line with previous reports on alignedf±3 emitted waves for different compounds33. For right-handed light (∆m = −1), the absorption is equally prob-able at the two spin down components of the two mixedspin character sublevels59. However, again the numericalevaluation of the product of the matrix elements suggestsdistinct contributions to the decay, notably a decreasingcontribution from the dxz valence states and a strongerone from the e↑g states with mv = 0 (d3z2−1). This leads

to a ∼ Y ↓30 emitted wave, which is indeed twisted by 90o

with respect to the ∼ Y3±3 behaviour expected in usualdirect valence band photoemission by left/right polariza-tion. At the spin flip energy, the effect seems absent, due

to a stronger e↑g-t↑2g hybridization and the contribution

6

from more than one orbital of the same irreducible rep-

resentation (the dxz, dyz orbitals of the t↑2g). This leadsto more balanced contributions of ml waves and to apetal-like structure.

The results are the first demonstration that RPES issensitive to the very orbital nature of the ground state.Indeed, for elongated orbitals (d3z2−1) a different typeof spin-flip transitions (mixed with an orbital flip) areallowed, contrary to the planar x2 − y2 and interaxialt2g orbitals. This is similar to what previously observedin RIXS in cuprates65. The phenomenon indeed doesremind of the (local) orbital excitations (local dd excita-tions) often studied by RIXS via changes in the polariza-tion of the scattered light. Here such excitations manifestthemselves as deviations from the anisotropy expected inusual photoemission and can accompany spin flip satel-lites in the spectra, even when hidden in the quasiparticlepeak. Contrary to ARPES, the photoelectron wave thenreflects exactly the orbital character of the valence state,allowing to map the valence orbital symmetries via mon-itoring the angular distribution of the resonant currentof opposite spin.

Importantly, the spin flip-orbital flip excitations in-volve an e↑g hole which, being in a completely filled ma-jority spin band, is more localized than those in the par-tially filled minority spin. These more localized valenceflip excitations are then transferred to the photoelectron.The visible orbital flip effect in the anisotropy of the an-gular distributions is thus a manifestation of a differentcorrelation in the two bands with different spin, also high-lighted by recent experimental and theoretical studies onAuger emission27, and of different orbital character, asearlier suggested66. Orbitals appear quenched far fromEF , where only spin flip excitations are clear, while spinand orbital degrees of freedom are entangled and bothactive at low energy in correspondance of a narrow eg

peak near EF , reminiscent of a Van Hove singularity inthe electronic structure63,64. The results thus suggestthat traces of higher correlation in the relevant eg band,possibly at the origin of the non Fermi liquid behaviourobserved at extreme PT 15 and ambient16 conditions, canbe identified even in the phase with long range magneticorder, often thought of insignificant correlations.

These findings have further fundamental andapplication-oriented implications: i) despite the lo-cal crystal field description used here, the counterpartcollective excitations (magnons and orbital waves) occur-ring in a general more complex superexchange scenariomight also be accessed, possibly allowing to distinguishincoherent particle-hole excitations from collectivemodes via their dependence on the photon energy17;ii) spin flip transitions are in principle not expected toremember of the photon angular momentum, at leastin the normal Auger decay in a two step process. Theyshould be always balanced by an orbital flip to conservethe total angular momentum ∆Jz = 0, due to the scalarnature of the Coulomb interaction. The results hereshow that, at resonance and in a one-step approach, spin

FIG. 3: Spin polarized PED and RPED patterns for paral-lel geometry, for excitation at the L3 edge for paramagneticFe(010), photon energy at the maximum of the resonance andinitial state energy corresponding to the main peak in the spinup channel for the ferromagnetic phase.

flip transitions might not be accompanied by orbital flipand that, even when occurring with orbital flip, there is amemory on the photon polarization. This suggests thatboth the Raman shift and the possible memory on thepolarization as seen in the angular distributions shouldbe considered when trying to make a distinction betweenlocalized and delocalized excitations; iii) an importantpractical implication is brought by the fact that theflip effect has an atomic nature, as shown by the spindown source waves patterns (Fig. 1), and disappears forthe spin unpolarized phase (Fig.3). This demonstratesthe sensitivity of RPES to spatial localization, dueto the dominance of on-site transitions46 caused bythe 1/r behaviour of the Coulomb operator, openingthe path for elementally sensitive imaging of magneticdomains. Practical implementations might well involvecutting-edge techniques such as spectromicroscopy67,with energy, angle and high lateral resolution.

B. Diffraction patterns for pependicular geometry

The situation changes drastically when the core holepolarization changes, i.e. when the photon helicity andthe local magnetic moment are oriented differently. Fig. 4reports the patterns for two different perpendicular ge-ometries (light impinging perpendicularly to the magne-tization), for which the dichroism in absorption is nullbut the core hole polarization (now comprising both

7

FIG. 4: PED (P) patterns (first two rows, for left and rightcircular polarization) and RPED (R) patterns (third andfourth rows, for left and right circular polarization) for twoperpendicular geometries.

alignment and orientation) does influence differently theemission for left and right handed light. As the inci-dent light direction is rotated away from the quantiza-tion axis, the selection rules will actually now allow amixture of ∆m = 0,±1 transitions and thus a detailedmicroscopic analysis of orbital contributions is more com-plicated. However, some clear features can be observed.

For grazing incidence, (only the main peak energy isconsidered), the spin down RPED patterns again devi-ate from the direct ones, and exhibit a rotation betweenthe two polarizations, though different from the previ-ous 90o flip. Interestingly, when the light is imping-ing perpendicularly to the surface, and thus the scanaround the surface normal coincides with a scan aroundthe photon incidence direction, vortex-like features, givenby crosses of higher intensity with bending arms follow-ing the counterclockwise (clockwise) rotation of the elec-tric field for left (right) handed light, appear for spe-cific channels. Such effect, called circular dichroism inangular distributions and previously observed in directphotoemission even from non magnetic and non chiralstructures32,68,69, is due to forward scattering peak ”ro-tations” related to the ml of the emitted wave. It is hereunveiled to be correlated with local valence orbital sym-metries. Indeed, emission from the t2g (spin down (up)emission for the main (spin flip) peak energy), differenti-ating from the eg states by non isotropic combinations ofmls, can easily favour non balanced combinations withpreference towards ±ml in the continuum wave, accord-ing to photon’s helicity. Chirality in the patterns thusremains, as the emitted wave is now oriented (the asym-

metries do not cancel when summing over its ml compo-nents). At the spin flip energy, the spin down channelcorresponds to emission from mixed eg-t2g states, andagain a petal-like pattern appears. Overall, for these twoperpendicular geometries, orbital twists are weakened orabsent in the resonant patterns, suggesting smaller con-tributions of spin flip terms and a more delocalized va-lence hole.

V. CONCLUSIONS

In summary, this work presents the exciting prospectof a new generation of resonant photoemission experi-ments, capable to probe simultaneously the spin polar-ization, the local valence orbital symmetries and the ori-entation of local magnetic moments, exploiting the corehole polarization as a prism to access spin and orbitalexcitations.

The results suggest that the analysis of angle-resolvedresonant photoemission energy spectra and diffractionpatterns can give profund insights into the physics ofmany fascinating materials. In case of Fe, orbitals ap-pear quenched far from EF while a coupling between spinand orbital degrees of freedom is found at lower energy,in correspondence of a narrow peak in the local DOS as-sociated to elongated eg states. Such coupling shouldbe considered as a crucial element in the developementof a unified theory of magnetism encompassing both thelocalized moments picture and the itinerant electronicbehaviour for this system, as well as in the attempts ofdescribing the non-Fermi liquid behaviour of such statesat high PT conditions.

More generally, the access to different excitations ac-cording to the local orbital symmetry would allow for ex-ample to probe (metal-oxygen and metal-metal) orbitalhybridizations and the competition between electron lo-calization and delocalization in Mott insulators and cor-related metals. From the theoretical point of view, thework suggests that matrix elements effects have to beconsidered in the description of resonant photoemission,which necessarily has to go beyond interpretations basedon the sole spectral function or estimations of matrix el-ements averaged over the full valence region. Last, forthe experimental side, the results also challenge the con-ventional use of RIXS as the only method to probe spinand orbital physics, opening the doors for possible ex-plorations of both incoherent particle-hole and collectivemagnetic excitations also via the non radiative decay.

Acknowledgments

The author acknowledges fruitful discussions with P.Kruger at the very early stage of this work, the fi-nancial support from the EU (Marie Curie Fellowship,FP7/2007-2013, Proposal No 627569) and the COST ac-

8

tion MP1306: Modern Tools for Spectroscopy on Ad- vanced Materials.

1 Y. Tokura and N. Nagaosa, Science 288, 462 (2000)2 K.I. Kugel and D.I. Khomskii, Sov. Phys. JETP 52, 501

(1981)3 W. Brzezicki, J. Dziarmaga and A.M. Oles Phys. Rev. Lett.

109, 237201 (2012)4 Z.P. Yin, K. Haule and G. Kotliar, Nature Physics 10, 845

(2014)5 R.B. Laughlin, Phys. Rev. Lett. 112, 017004 (2014)6 V. Aji and C.M. Varma, Phys. Rev. B 75, 224511 (2007)7 W. Witczak-Krempa, G. Chen, Y.-B. Kim and L. Balents,

Annual Review of Condensed Matter Physics 5, 57 (2014)8 H. Zhang, C.-X. Liu, and S.-C. Zhang Phys. Rev. Lett.

111, 066801 (2013)9 I. Zeljkovic, Y. Okada, C.-Y. Huang et al., Nature Physics

10, 572 (2014)10 J. van Wezel, Europhys. Lett. 96, 67011 (2011)11 T. Ritschel, J. Trinckauf, K. Koepernik, B. Bchner, M.v.

Zimmermann, H. Berger, Y.I. Joe, P. Abbamonte and J.Geck, Nature Physics 11, 328 (2015)

12 P.A. Bhobe et al. Phys. Rev. X 5, 041004 (2015)13 F. Da Pieve, S. Di Matteo, T. Rangel, M. Giantomassi,

D. Lamoen, G.-M. Rignanese, and X. Gonze, Phys. Rev.Lett. 110, 136402 (2013)

14 A. Georges, L. de’ Medici, J. Mravlje, Annual Reviews ofCondensed Matter Physics 4, 137-178 (2013)

15 A.A. Katanin, A.I. Poteryaev, A.V. Efremov et al., Phys.Rev. B 81, 045117 (2010)

16 L.V. Pourovskii et al., Phys. Rev. B 87, 115130 (2013)17 M. Minola, G. Dellea, H. Gretarsson, Y.Y. Peng, Y. Lu, J.

Porras, T. Loew, F. Yakhou, N.B. Brookes, Y.B. Huang,J. Pelliciari, T. Schmitt, G. Ghiringhelli, B. Keimer, L.Braicovich, and M. Le Tacon, Phys. Rev. Lett. 114, 217003(2015)

18 D. Benjamin, I. Klich and Eugene Demler, Phys. Rev. Lett.112, 247002 (2014)

19 A. Damascelli, Z. Hussain and Z.-X. Shen, Rev. Mod. Phys.75, 473 (2003)

20 L.J.P. Ament, M. van Veenendaal, T.P. Devereaux, J.P.Hill and J. van den Brink, Rev. Mod. Phys. 83, 705 (2011)

21 J. Sachez-Barriga, J. Fink, V. Boni, I. Di Marco, J. Braun,J. Minar, A. Varykhalov, O. Rader, V. Bellini, F. Manghi,H. Ebert, M. I. Katsnelson, A. I. Lichtenstein, O. Eriks-son, W. Eberhardt, and H. A. Durr, Phys. Rev. Lett. 103,267203 (2009)

22 M. Aichhorn, S. Biermann, T. Miyake, A. Georges, and M.Imada, Phys. Rev. B 82, 064504 (2010)

23 C.-Z. Xu, Y. Liu, R. Yukawa, L.-X. Zhang, I. Matsuda,T. Miller, and T.-C. Chiang Phys. Rev. Lett. 115, 016801(2015)

24 Z.-H. Zhu, C. N. Veenstra, G. Levy, A. Ubaldini, P. Syers,N. P. Butch, J. Paglione, M. W. Haverkort, I. S. Elfimov,and A. Damascelli Phys. Rev. Lett. 110, 216401 (2013)

25 J. Sanchez-Barriga, A. Varykhalov, J. Braun, et al., Phys.Rev. X 011046 (2014)

26 C.-H. Park and S.G. Louie, Phys. Rev. Lett. 109, 097601(2012)

27 R. Gotter, G. Fratesi, R.A. Bartynski et al,. Phys. Rev.Lett. 109, 126401 (2012)

28 R. Gotter, F. Offi, F. Da Pieve, A. Ruocco, G. Stefani, S.Ugenti, M. Trioni, et al., Journ. Electr. Spectr. Rel. Phen.161, 128 (2007)

29 F. Da Pieve, D. Sebilleau, S. Di Matteo, R. Gunnella, R.Gotter, A. Ruocco, G. Stefani and C.R. Natoli, Phys. Rev.B 78, 035122 (2008)

30 J. Wider, F. Baumberger, M. Sambi, et al. Phys. Rev. Lett.86, 2337 (2001)

31 T. Greber and J. Osterwalder, Chem. Phys. Lett. 256, 653(1996)

32 H. Daimon, T. Nakatani, S. Imada and S. Suga, J. Electr.Spectr. Rel. Phen. 76, 55 (1995)

33 D. E. Ramaker, H. Yang and Y.U. Idzerda, J. Electr.Spectr. Rel. Phen. 68, 63 (1994)

34 T. Greber, J. Osterwalder, D. Naumovic, A. Stuck,S.Hufner and L. Schlapbah, Phys. Rev. Lett. 69, 1947(1992)

35 P. Kruger, J. Jupille, S. Bourgeois, B. Domenichini, A.Verdini, L. Floreano and A. Morgante, Phys. Rev. Lett.108, 126803 (2012)

36 H. Magnan et al., Phys. Rev. B 81, 085121 (2010)37 M. Morscher, F. Nolting, T. Brugger and T. Greber, Phys.

Rev. B 84, 140406 (2011)38 A. Tanaka and T. Jo, J. Phys. Soc. Jpn. 63, 2788 (1994)39 A. Kotani, J. Appl. Phys. 57, 3632 (1985)40 F.M.F de Groot, J. Electr. Spectr. Rel. Phen. 92, 207

(1998)41 G. van der Laan and B.T. Thole, J.Phys. Condens. Matter

7, 9947 (1995)42 L. Ament, G. Ghiringhelli, M. Moretti Sala, L. Braicovich

and J. van den Brink, Phys. Rev. Lett. 103, 117003 (2009)43 M. van Veenendaal, Phys. Rev. Lett. 96, 117404 (2006)44 F.M.F. de Groot, P.Kuiper and G.A. Sawatzky, Phys. Rev.

B 57, 14584 (1998)45 M.W. Haverkort, Phys. Rev. Lett. 105, 167404 (2010)46 F. Da Pieve and P. Kruger, Phys. Rev. Lett. 110, 127401

(2013)47 F. Da Pieve and P. Kruger, Phys. Rev. B 88, 115121 (2013)48 P. Glatzel, A. Mirone, S. G.Eeckhout, M. Sikora, and G.

Giuli, Phys. Rev. B 77, 115133 (2008)49 D. Sebilleau, R. Gunnella, Z.-Y. Wu, S. Di Matteo and C.

R. Natoli, J. Phys.: Condens. Matter 18, R175 (2006)50 see G. Fratesi, et al., Phys. Rev. B 78, 205111 (2008) and

references therein51 B. Sinkovic, E. Shekel, and S.L. Hulbert, Phys. Rev. B 52,

R15703(R) (1995)52 F. Da Pieve, S. Fritzsche, G. Stefani, N.M. Kabachnik,

Journ. Phys. B: At. Mol. Opt. Phys. 40, 329 (2007)53 O.K. Andersen and O. Jepsen, Phys. Rev. Lett. 53, 2571

(1984)54 J. Schwitalla and H. Ebert, Phys. Rev. Lett. 80, 4586

(1998)55 T. Wegner, M. Potthoff, and W. Nolting, Acta Physica

Polonica A 97, 567 (2000)56 Yu Kucherenko and P. Rennert, J. Phys. Condens. Matter

9, 5003 (1997)57 P. Kruger, F. Da Pieve, and J. Osterwalder, Phys. Rev. B

83, 115437 (2011)

9

58 A.K. See and L.E. Klebanoff, Surf. Sci. 340, 309 (1995)59 G. van der Laan, Appl. Phys. A 65, 135 (1997) The oppo-

site convention for polarization is used in this work.60 L.J. Terminello and J.J. Barton, Science 251, 1218 (1991)61 R. Gotter, F. Da Pieve, F. Offi et al., Phys. Rev. B 79,

075108 (2009)62 R. Gotter, F. Offi, A. Ruocco, F. Da Pieve, R. Bartynski,

M. Cini, G. Stefani, Europhys. Lett. 94, 37008 (2011)63 R. Maglic, Phys. Rev. Lett. 31, 546 (1973)64 V.Y. Irkhin et al., J. Phys. Cond. Matt. 5, 8763 (1993)

65 P. Marra, AIP Conference Proceedings 1485, 297 (2012)66 J.B. Goodenough, Phys. Rev. 120, 67 (1960)67 J. Avila and M.C. Asensio, Synchrotron Radiation News

27, 24 (2014)68 F. Matsui, T. Matsushita, F.Z.Guo and H. Daimon, Surf.

Rev. Lett. 14, 1 (2007)69 N. Mannella, S.-H. Yang, B.S. Mun, L. Zhao, A.T. Young,

E. Arenholz, and C.S. Fadley, Phys. Rev. B. 74, 165106(2006)