Evidence for weak electronic correlations in Fe-pnictides
W. L. Yang, P. O. Velasco, J. D. Denlinger, A. P. Sorini, C-C. Chen, B. Moritz, W.-S. Lee, F. Vernay, B. Delley, J.-H. Chu, J. G. Analytis, I. R. Fisher, Z. A. Ren, J. Yang, W. Lu, Z. X. Zhao, J. van den Brink, Z. Hussain, Z.-X. Shen, T. P. Devereaux
aa r X i v : . [ c ond - m a t . s up r- c on ] M a y Evidence for weak electronic correlations in Fe-pnictides
W. L. Yang, A. P. Sorini, C-C. Chen,
2, 3
B. Moritz, W.-S. Lee, F. Vernay, P. Olalde-Velasco,
1, 5
J. D. Denlinger, B. Delley, J.-H. Chu,
2, 6, 7
J. G. Analytis,
2, 6, 7
I. R. Fisher,
2, 6, 7
Z. A. Ren, J. Yang, W. Lu, Z. X. Zhao, J. van den Brink,
2, 9
Z. Hussain, Z.-X. Shen,
2, 6, 7, 3 and T. P. Devereaux
2, 7 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 Stanford Institute for Materials and Energy Sciences,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA. Department of Physics, Stanford University, Stanford, California 94305, USA Paul Scherrer Institut, Condensed Matter Theory Group, Villigen PSI, Switzerland Instituto de Ciencias Nucleares, UNAM, 04510 Mexico DF, Mexico Department of Applied Physics, Stanford University, Stanford, California 94305, USA Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA. National Lab for Superconductivity, Institute of Physics,Chinese Academy of Sciences, Beijing, P. R. China. Institute Lorentz for Theoretical Physics, Leiden University,P.O. Box 9506, 2300 RA Leiden, The Netherlands (Dated: October 23, 2018)Using x-ray absorption and resonant inelastic x-ray scattering, charge dynamics at and nearthe Fe L edges is investigated in Fe pnictide materials, and contrasted to that measured in otherFe compounds. It is shown that the XAS and RIXS spectra for 122 and 1111 Fe pnictides areeach qualitatively similar to Fe metal. Cluster diagonalization, multiplet, and density-functionalcalculations show that Coulomb correlations are much smaller than in the cuprates, highlightingthe role of Fe metallicity and strong covalency in these materials. Best agreement with experimentis obtained using Hubbard parameters U . J ≈ . PACS numbers: 74.70.Dd,78.70.Dm,71.10.Fd,71.15.Mb
I. INTRODUCTION
In the new and rapidly developing field of Fe-pnictidesuperconductivity, the question of what constitutes thebasic ingredients for high transition temperatures re-mains largely unanswered. Parallels have been drawnto the cuprate high-temperature superconductors, whichcontain partially filled d -electron spins that in the par-ent phase are aligned antiferromagnetically like the pnic-tides, and high-temperature superconductivity emergeswhen magnetism can be suppressed. Common to manyideas is that superconductivity itself may be emergentfrom the two competing phases, driven by an underlyingquantum critical point.A key question that needs to be addressed to under-stand this framework is whether or not the Fe pnictidesare strongly correlated like the cuprates. Since den-sity functional theory (DFT) calculations have indicatedthat the electron-phonon interaction is too weak to ac-count for high transition temperatures, the strengthof the Coulomb correlations would give some account forthe pairing strength possible in an electronic-based pair-ing mechanism. Recent renormalization group flow andrandom-phase approximation (RPA) calculations of effec-tive tight-binding models fitted to DFT bands indicatethat several pairing instabilities, such as sign-changing s − wave pairing and d − type pairing, all have nearly thesame energy, which depends subtly on Coulomb param-eters U and magnetic exchange J . Therefore pinningdown these numbers would greatly focus the discussion of the physics of the Fe pnictides.Theoretically, the situation is complicated. TraditionalDFT methods, which can be extremely accurate in un-correlated materials, can account for the correct atomicstructure but yield large sublattice magnetic momentsthat have not been observed in experiments. This over-estimation of the magnetic moment is exactly oppositeto the situation in the cuprates, where DFT underesti-mates the moment, and implies that Coulombic effectsare a small part of the story for the pnictides. Howeverit does not provide an explanation as to why the momentsare so much larger than those found in experiments .Recently, theoretical treatments using combinations ofDFT and dynamical mean field theory (DMFT) haveyielded opposite conclusions. One set of cal-culations yield Hubbard parameters U ∼ Another sethowever gives U ∼ Angle-resolved photoe-mission (ARPES) studies have shown strong density ofstates (DOS) near the Fermi level relative to the pnicto-gen valence band. The Fe conduction band states, witha bandwidth W d − level Coulomb interactions, as well as exci-tons and satellites due to strong core-hole interactions. These strong satellites and spread out spectral weightshave not been observed in recent x-ray absorption (XAS)measurements at the oxygen K -edge in 1111, setting anupper bound on the effective Coulomb parameter U ∼ Absorption and emission studies on the Fe L , edges also are in agreement with weak electronic corre-lations, and can be simply matched to the unoccupied d DOS determined from DFT calculations. However cal-culations pertinent to the XAS process, where core holesare created, and the emission process, where photons areemitted from the valence states in the presence of a corehole, have not been carried out. This is crucially neededin order to understand the true role of Coulomb interac-tion in these materials.In this paper we present a comprehensive study ofXAS measurements and resonant inelastic x-ray scat-tering (RIXS) at the Fe L , edges in a variety of Fe-based materials, including the superconducting 1111 Fepnictide SmO . FeAs and the undoped 122 pnictidesBaFe As and LaFe P . It is shown that the XAS spec-tra of Fe pnictides look qualitatively, and in some casesquantitatively, similar to Fe metal and show no featuresresembling the multiple peak structures seen in Fe insu-lators, such as hematite ( α -Fe O ) and other iron oxides.A resonance study of x-ray emission across the L and L edges demonstrates that the RIXS spectra is domi-nated by fluorescence, with no observance of discernableexcitonic or satellite peaks.In addition, we present calculations using three sepa-rate models which specifically include and account for therole of the core hole in x-ray absorption and emission pro-cesses. These calculations are performed using quantumcluster, multiplet, and DFT-based methods, and high-light the roles of Fe metallicity, FeAs covalency, and localCoulomb and Hund’s couplings. DFT calculations using FEFF give quantitative agreement with XAS measure-ments and align absorption peaks to Fe d-DOS above theFermi level, demonstrating the minor role of core hole in-teractions. Cluster calculations of XAS support the roleof strong Fe-As hybridization involving As states belowthe Fermi level, setting an upper bound of U ∼ . FeAs,non-superconducting BaFe As , LaFe P , α -Fe O , andFe metal are presented, comparing and contrasting qual-itative behaviors across these compounds, while in Sec.III calculations are presented for XAS and XES at theFe L , edges. Secs. III A and III B present calculationsfor L -edge XAS in Fe clusters to highlight the expected role of strong Coulomb correlations, and it is shown thatspectral features related to the strong correlations thatare not seen in experiments of Sec. II can be used to setupper limits on Hubbard parameters. Moreover, DFT-based FEFF calculations, which include multiple scatter-ing and core hole effects, are presented in Sec. III C,and are shown to provide excellent agreement with themeasured XAS spectra. Finally, Sec. IV summarizes ourfindings and states our conclusions.
II. XAS AND RIXS MEASUREMENTS
The SmO . FeAs samples with superconducting tran-sition temperature (T c ) of 55K, so far the high-est T c in the family of iron arsenides, were pre-pared by a high-pressure synthesis method . Sam-ple quality was checked by x-ray powder diffractionand T c was confirmed by both transport and mag-netic measurements . We have also measured F-doped samples with the same T c , as well as thenon-superconducting parent compounds SmOFeAs, butfound no obvious difference in the spectra. BaFe As and LaFe P single crystals were prepared by the fluxmethod . Data shown here were collected at roomtemperature with incident beam 45 degrees to samplesurfaces. We noticed serious surface oxidization effectsfor the iron pnictides, and to avoid this surface oxidiza-tion problem all the data were collected on in-situ cleavedsample surfaces.XAS and RIXS measurements were performed atbeamline 8.0 of the Advanced Light Source at LawrenceBerkeley National Laboratory. The undulator and spher-ical grating monochromator supply a linearly polar-ized photon beam with resolving power up to 6000.RIXS data were collected by a Rowland circle geometryspectrometer perpendicular to the incident beam. Thelinear polarization of the incident beam is parallel to thescattering plane. XAS spectra were collected by measur-ing sample current (TEY) and fluorescent yield (TFY).All XAS spectra have been normalized to the beam fluxmeasured by a clean gold mesh. The resolution is betterthan 0.2eV for XAS measurements. For the X-ray emis-sion measurements, the incident beam resolution is about0.9eV and the spectrometer resolution is about 0.7eV.The Fe L , absorption structure of iron pnictides areshown on top of Figs. 1-3. According to dipole selectionrules, iron is a 3d element displaying L , absorption fea-tures from 2 p d to 2 p d transitions. The spin-orbitinteraction splits the 2p states into 2p / and 2p / , lead-ing to two well separated peaks. The intensity ratio ofthe two peaks is largely defined by the high-spin or low-spin ground states related to the crystal field . As the 2 p core levels are featureless and narrow, L and L absorp-tion peaks often provide detailed information on the elec-tronic structure of the unoccupied 3d states. As shownin Figs. 1a-3a, all the iron pnictide samples, includingthe 55K T c SmO . FeAs (Fig.1a), non-superconducting I n t en s i t y ( A r b . U n i t ) I n t en s i t y ( A r b . U n i t ) SmO
FeAs Tc=55K TEY TFY (a) (b)
FIG. 1: (a) X-ray absorption spectra of the 55K T c SmO . FeAs. TEY and TFY intensity of the Fe L , edgesis plotted as a function of incident photon energy. The dif-ference between TEY and TFY data is mainly from the self-absorption effect in TFY. (b) RIXS spectra of SmO . FeAscollected with excitation energy across the Fe L , absorptionpeaks. The number on the left stands for the excitation en-ergy corresponding to the number marked in (a), the value ofwhich is marked with the arrows on the spectra. Inset showsthe prominent Fe L emission peak collected with excitationenergy above the Fe L absorption edge (no.2 to 8), they alloverlap nicely with the nonresonant spectrum (no.8). Notethat RIXS spectra were normalized to the Fe L emissionpeak for emphasizing the similar lineshape. BaFe As (Fig.2a) and LaFe P (Fig.3a), exhibit onlythe two major peaks, L at about 720eV and L at about707eV. There are weak shoulders around 709.5eV, butno peak splitting or intensity ratio change was observed.This result is consistent with that on other 1111 and122 compounds . As XAS has been demonstrated tobe a powerful tool for probing the crystal field and elec-tronic interactions for 3d metals ; the non-splittingXAS structure indicates a weak crystal field effect thatfavors high-spin ground states.Fig.1b shows the RIXS data of the superconductingSmO . FeAs obtained at energies labeled in Fig.1a. Thespectrum on top (No. 8) was collected with an incidentphoton energy of 735eV, which is far above the Fe L and L absorption edges, the so called nonresonant normalemission spectrum. Like all other 3d transition metals,this nonresonant spectrum exhibits two main fluorescentfeatures at about 704eV and 717eV, resulting from therefill of the 2p / and 2p / holes respectively. The 2p / feature is very weak compared to the L edge in the XAS
695 700 705 710 715 720 725Det. Photon energy (eV) I n t en s i t y ( A r b . U n i t ) I n t en s i t y ( A r b . U n i t ) (a) (b)
696 704 712
Photon Energy (eV)700 710 720 730
FIG. 2: (a) Fe L , XAS spectra of a BaFe As single crys-tal. (b) RIXS spectra of BaFe As collected with excitationenergy labeled and marked in (a). Inset shows that all theFe L emission peaks (scaled to the same intensity) collectedwith excitation energy above Fe L absorption edge (no.2 to8) overlap with the nonresonant spectrum (no.8). spectrum, partially due to the Coster-Kronig decay pro-cess of the 2 p / holes to 2 p / .The RIXS spectra collected with resonant energies alsodisplay the strong 704eV peak as seen in the nonreso-nant spectrum. With the excitation energy approachingthe L absorption edge (No.1), the 704eV peak evolvesand stays at the same energy with all the excitationsabove the L edge (No.2-7). This fluorescent featuredoes not track the excitation energy and overlap withthe 704eV peak in the nonresonant spectrum (inset ofFig.1b). No energy loss feature, which is normally asso-ciated with various electron excitations and correlations,was displayed by the RIXS data.RIXS of nonsuperconducting BaFe As (Fig.2b) andLaFe P (Fig.3b) share the same characterization asthat of the 55K superconducting SmO . . Charge excitation features like Kondo peakand lower Hubbard peak are completely absent, and theRIXS data is dominated by a peak at 704eV with theonly difference being the strength of the 701.5eV shoul-der. Again, the prominent peaks collected at differentresonant energies overlap nicely with the fluorescent peakin the nonresonant spectrum (insets of Fig.2b and 3b).The absence of excitation induced energy-loss featuresin the RIXS data for all the iron pnictide samples indi-cates the weak correlation in this system. It is thus desir- I n t en s i t y ( A r b . U n i t ) Photon Energy (eV)700 710 720 730 I n t en s i t y ( A r b . U n i t )
696 704 712
695 700 705 710 715 720 725Det. Photon energy (eV) (a)(b)
FIG. 3: (a) Fe L , XAS spectra of a LaFe P single crystal.(b) RIXS spectra of BaFe P collected with excitation energylabeled and marked in (a). Inset shows that all the Fe L emission peaks (scaled to the same intensity) collected withexcitation energy above Fe L absorption edge (no.2 to 7)overlap with the nonresonant spectrum (no.7). able to compare the iron pnictides with known metallicand insulating iron components, to reveal the importanceof metallicity and to show that this result is not exper-imental resolution limited. In Fig.4, we show the XASand RIXS data collected on pure iron metal. The XAS(Fig.4a) displays non-splitting L and L peaks with a slightly weaker shoulder compared to the ironpnictides. The RIXS data of Fe metal show more sym-metric peaks without shoulders, as well as stronger elasticpeaks tracking the excitation energies. But just like theiron pnictides, the RIXS lineshape is dominated by thepeak at 704eV which overlaps with the fluorescence peakcollected with off resonance excitation energy (inset ofFig.4b), and the iron metal resembles all the iron pnic-tides in the featureless RIXS data without excitation orcorrelation peaks.On the contrary, the α -Fe O powder sample dis-plays very different XAS and abundant features in RIXS.The XAS data (Fig.5a) shows strong splitting struc-ture on both L and L absorption edges due to theinterplay of crystal-field (10 Dq =0.88eV) and electronicinteractions . RIXS data (Fig.5b) show that the spec-tral appearance changes drastically with excitation ener-gies, and obviously do not overlap with the nonresonantspectrum (No. 10). We plotted the energy loss featuresat different resonant energes in Fig.5c. Particular en-ergy loss features, as indicated by the gray lines, were I n t en s i t y ( A r b . U n i t ) Iron Metal TEY TFY I n t en s i t y ( A r b . U n i t ) (a) (b) FIG. 4: (a) Fe L , XAS spectra of Fe metal. (b) RIXS spec-tra of Fe metal collected with excitation energy labeled andmarked in (a). Inset shows that, with the elastic peak track-ing excitation energy, all the Fe L emission peaks collectedwith excitation energy above Fe L absorption edge (no.2 to7) overlap with the nonresonant spectrum (no.7), same asthat of iron pnictides. enhanced at particular resonant energies, leading to verydifferent lineshape. These energy loss features are sig-natures of dd -excitations , details on which is not thetopic of this paper. With better resolution, our RIXSdata revealed more excitation modes than that in previ-ous publications, covering the whole range of the opticabsorption bands .For a direct comparison between all the samples, andfor comparing with the theoretical calculations, Fig.6shows the RIXS data collected with 708eV excitation en-ergy as well as the XAS data on the five different samples.There are only minors difference in the symmetry of thelineshape and strength of the shoulders between the XASdata of iron pnictides and iron metal; while the crystalfield splitting leads to very different XAS spectrum of α -Fe O data (Fig.6b). The RIXS (Fig.6a) of iron pnictidesand iron metal is dominated by the prominent fluores-cent peak with no energy loss feature related to chargeexcitations; while for α -Fe O , RIXS shows strong en-ergy dependence and complex energy loss structure fromelectronic excitations and correlations. The similarity onthe spectra between iron pnictides and iron metal, aswell as the absence of charge excitation features in theRIXS data, suggests that iron pnictides are unlikely to bestrongly correlated systems, which is further elaboratedby theoretical calculations below. I n t en s i t y ( A r b . U n i t ) Photon Energy (eV)
700 710 720 730695 705 715 725Det. Photon energy (eV) I n t en s i t y ( A r b . U n i t ) (a)(b) (c) -8 -4 0Energy Loss (eV)-10 -6 -2 FIG. 5: (a) Fe L , XAS spectra of α -Fe O powder. (b) RIXSspectra of α -Fe O collected with excitation energy labeledand marked in (a). (c) Energy loss features corresponding to dd -excitations marked with gray lines.FIG. 6: (a) Comparison of RIXS data on the noted samplesat 708eV excitation energy. All iron pnictides and iron metalshow only fluorescent peaks same as the nonresonant spec-trum (insets of Fig.1-4b), while α -Fe O displays multiplepeaks as the signature of dd -excitations. (b) Comparison ofXAS data on the same five samples, α -Fe O again displaysvery different lineshape due to the crystal field splitting. III. CALCULATIONS
In order to understand the main features of the ex-perimental spectra, namely that the spectra of the Fepnictides greatly resemble that of Fe metal, we proceedin three steps. First, to determine the importance of cor-relations, we present exact diagonalization calculations ofa Hubbard model cluster which can be solved for eitherstrong or weak Coulomb correlations. These calculationsare used to give a qualitative estimate of the size of theHubbard U and Hund’s J . Knowing the values of theseparameters relative to the band width allows us to deter-mine whether weakly-correlated methods are appropriatefor describing the experimental spectra. Second, to bet-ter understand the relationship between multiplet, spin-orbit, and crystal field effects on the spectra we presentatomic multiplet calculations. And finally, having estab-lished the relatively minor role of correlations in the Fepnictides, we present DFT-based calculations of XAS andXES spectra for comparison with experiment. A. Cluster Diagonalization
In order to see explicitly how correlations affect theXAS profile, we perform a model many-body calculationbased on the exact diagonalization (ED) technique, witha multi-orbital Hubbard model as the effective Hamil-tonian. This approach has been successfully applied tounderstand the correlated physics in materials such asthe high-T c cuprate parent compounds .The Fe pnictides have a tetrahedral FeAs plaquetteserving as the building block of the two dimensionalFe As layer. We have therefore attempted to capturethe essential physics revealed from XAS spectra with aFeAs tetrahedral cluster including the five Fe 3 d levelsand the As 4 p x,y,z orbitals. The energy eigenstates thatare necessary for calculating the XAS cross-sections via Fermi’s golden rule are then obtained by diagonalizingthe multi-orbital Hamiltonian.Our cluster calculations have been carried out in anassumed d high-spin state for the Fe 3 d -levels, whichis energetically preferred over the low-spin configurationdue to Hund’s coupling. While the experimentally mea-sured magnetic moment in Fe pnictides is about 0 . µ B ,LDA predicts a larger magnetic moment . This strengthwould decrease if the system is more delocalized.The multi-orbital Hamiltonian entering the calcula-tions can be written as H = H k + H ǫ + H C + H Q . Here H k is the kinetic energy term: H k = X j,γγ ′ ,σ t pd,γ ( d † γσ p jγ ′ σ + h.c. )+ X jj ′ ,γγ ′ ,σ t pp,jj ′ ,γγ ′ ( p † jγσ p j ′ γ ′ σ + h.c. ) , (1)where d † γσ creates a particle with spin σ in orbital γ atthe Fe site, and p † jγ ′ σ creates a particle with spin σ inorbital γ ′ at As site j . The relations among the multi-orbital hoppings are derived from the the Slater-Kostertable , with the strengths of these Slater-Koster ma-trix elements being | V pdσ | =14.091(eV · ˚ A ) √ r p r d d , and | V pdπ | = √ | V pdσ | . Here d is the Fe-As bond length (inunits of ˚ A ), and the material specific values r p and r d are either given or can be calculated from Ref. . In thiswork we use the values: d = 2 . A , r p = 13 . A , and r d =0 . A . We have further assumed that | V ppσ | = | V pdσ | . H ǫ is the orbital site-energy term: H ǫ = X γσ ǫ d ( γ ) n d,γσ + X j,γσ ǫ p n p,jγσ , (2)with n d,γσ ≡ d † γσ d γσ , and n p,jγσ ≡ p † jγσ p jγσ . The Fe e g and t g orbital site energies are defined with respectto their center of gravity ǫ d by ǫ d ( e g ) ≡ ǫ d − Dq , and ǫ d ( t g ) ≡ ǫ d + 4 Dq . The arsenic p orbital site energy ǫ p is defined by ∆ = ǫ d − ǫ p + nU for the d n con-figuration, where ∆ is the charge transfer gap energy.The subtraction of an average Coulomb repulsion term, U = A − B + C , ensures a d n ground state; A , B ,and C are the Racah parameters.The correlated physics is introduced directly from theCoulomb interaction term, including intra-orbital on-siteCoulomb interactions, Hund’s exchange coupling, andelectron pair hopping processes, written as : H C = U X γ,σ = σ ′ n d,γσ n d,γσ ′ + U ′ X σ,σ ′ ,γ = γ ′ n d,γσ n d,γ ′ σ ′ + J X σ,σ ′ ,γ = γ ′ d † γσ d † γ ′ σ ′ d γσ ′ d γ ′ σ + J ′ X σ = σ ′ ,γ = γ ′ d † γ,σ d † γσ ′ d γ ′ σ ′ d γ ′ σ . (3)The above tight-binding parameters are related via theGoodenough-Kanamori-Anderson relation: U = U ′ + 2 J ,and J = J ′ . Written in terms of the Racah parame-ters, the on-site intra-orbital Coulomb repulsion U is ex-pressed as U = A + 4 B + 3 C . On the other hand, theHund’s coupling J , typically of order ∼ B and C . Later we shall treat A as an adjust-ing parameter, and hence the on-site Coulomb repulsions,seeing how it affects the XAS spectra.For the XAS final states we include an additional core-hole potential term in the Hamiltonian: H Q = X γ,σ U Q n d,γσ n c , (4)where n c ≡ d † c d c , and d † c is the creation operator for ahole in the core-hole orbital. The strength of U Q can bedetermined experimentally from the energy separation ofthe well-/poorly-screened resonances, and is of the sameorder of magnitude as U . Here we use | U Q | = U forsimplicity. In short, the tight-binding parameters usedin the calculations are (in units of eV): V pdσ = − . V pdπ = 0 . V ppσ = 0 .
55, and V ppπ = − . B = 0 . C = 0 .
40 (resulting in a J ( e g ) = 0 . ǫ d ≡ . Dq =0.20, and ∆ = 1 . L -edge XAS spectra fromthe cluster calculation, with varied Coulomb repulsion U .A stronger U suppresses the XAS shoulder peak inten-sity. The shoulder peak is further split into a two-peakstructure for larger Hund’s coupling, as is shown in Fig.8. By either increasing the covalency or reducing thecorrelation effects a more featureless XAS spectrum witha shoulder peak intensity comparable to experiments is FIG. 7: Fe-pnictide L -edge XAS spectra obtained from smallcluster diagonalization for a fixed J ( e g ) = 0 . U . A strong Coulomb repulsion tends to suppress the XASshoulder peak intensity. The dashed line sketches the energyseparation of the dominant peak and its shoulder . The insetis a plot for the peak-shoulder energy separation versus theon-site repulsion U , from which a naive upper bound of U ∼ obtained. A naive upper bound for the on-site repulsion FIG. 8: Fe-pnictide L -edge XAS spectra obtained from smallcluster diagonalization for a fixed U = 8 . J ( e g ). The XAS shoulder peak is split into atwo-peak structure by a larger J , indicated by the black ar-rows. is therefore drawn by looking at the XAS shoulder peakstructure, as well as its energy separation from the domi-nant peak. According to the calculation, we estimate theCoulomb interactions to be U ∼ J ( e g ) = 0 . . This resultsuggests that it is more appropriate to treat Fe-pnictidesas weakly-correlated systems.A limitation of the cluster approach is that while it in-cludes interaction between the 3d electrons explicitly, thestates obtained from the cluster diagonalization do notinclude the atomic multiplet structures associated withthe spin-orbit coupling of the Fe 2p core-hole. To testhow this multiplet structure affects the resultant spec-tra, we have also computed XAS profiles including theatomic multiplets, at the expense of removing the pnic-tide atoms from the cluster. B. Multiplet Calculation
X-ray absorption spectra are calculated using Fermi’sgolden-rule, with a finite lifetime for the core-hole. Thus,the x-ray absorption intensity may be written explicitlyin terms of a sum over states | ψ i i as I ( ω ) = X i |h ψ i | ˆ d | ψ i| Γ /π ( ω + E − E i ) + Γ . (5)We considered the specific case of XAS experimentson BaFe As . During the optical transitions, the states | ψ i , | ψ i i and | ψ f i belong respectively to the configura-tions 2 p d , 2 p d and (2 p d ) ⋆ . For each of theseconfigurations, we have to consider electron-electron in-teractions, spin-orbit and crystal-field on an equal footingwhile the radial wave-functions are determined by solv-ing the Dirac equation. This leads to a splitting of theshells into multiplet levels . To be specific, the crystal-field is expressed as an electronic potential of externalpoint-charge ions interacting with the considered Fe-ion.
700 710 720 730Photon Energy (eV)
XAS ( a r b . un i t s ) BaFe As FIG. 9: X-ray absorption spectrum: Iron L-edge multipletcalculation for BaFe As . From there we can evaluate the associated XAS spectrawithin the dipole approximation.The obtained XAS spectrum of Fig.9 shows goodagreement with the experimental data and mostly ex-hibits the L -L splitting coming from the spin-orbitsplitting of the 2 p core-levels. However, the presentcalculation does not involve charge fluctuations, the ex-plicit inclusion of these would give rise to satellite peaksin a RIXS spectrum and the inclusion of the ligandswould give rise to the formation of bands where electron-electron scattering would occur.In the limit of a strongly correlated regime the initialand final states cannot be described by a single-site ap-proach, hence the XAS spectra would exhibit additionalpeaks that cannot be captured by the present multipletpicture. The experimental data do not exhibit such asignature: besides the spin-orbit splitting the XAS spec-trum is rather featureless and the additional shoulderscan be explained by the effects of the crystal-field on theatomic-multiplet. These facts combine to suggest thatBaFe As is rather not a strongly correlated material. C. DFT-based FEFF Calculation
For weakly correlated materials XAS and XES spec-tra can reliably be computed using ab initio methods.Such calculations, however, have a considerable degree ofcomplexity because in XAS/XES a core-hole is present inthe final/initial state. The computer code
FEFF is well-known for treating the core-hole potential with a highlevel of accuracy. Here we have used FEFF to calculatethe XAS near the L and L iron edges, the angular-momentum projected density of states (LDOS), and theXES spectra for the L edge.Our calculations begin by overlapping relativis-tic Dirac-Fock atomic potentials via the Mattheissprescription . This prescription fixes a “Norman”radius about each atomic site which contains Z i elec- FIG. 10: The Fe L edge XES signal (a) calculated using FEFF for the four different metallic iron-containing materialsconsidered in the experimental section. The Fe L , edge XAS(b) calculated using FEFF for the four different iron-containingmaterials considered in the experimental section. trons, where Z i is the atomic number of the atom at site i . The overlapped Mattheiss potentials are then usedas the starting point of a self-consistent (SCF) potentialcalculation which uses the ground-state von Barth-Hedinexchange-correlation potential on all iterations. Giventhe SCF potential, the relativistic radial wave-functionsand phase shifts associated with each atomic scatteringsite can be calculated. The single-electron Green’s func-tion for the entire system may then be written using a ba-sis of these radial wavefunctions and spherical harmonicswith system (cluster) dependent coefficients that are cal-culated within multiple scattering theory. Finally, theXAS can be calculated from Eq. (5), using the Green’sfunction to implicitly sum over states: µ ∼ − Im h ψ | ˆ d † ˆ G ( E c + ~ ω ) ˆ d | ψ i , (6)where d is the single-electron dipole operator, G is thephotoelectron Green’s function, and the state | ψ i is thecore state of interest which, in this work, is either the L or L edge of iron. The energy of the absorbed photonis ~ ω , and the ∼ symbol means that we have neglectedto write a number of constant prefactors as well as abroadened step function limiting the XAS spectrum to ω > | E c | + µ , where µ is the Fermi level. The XES canbe calculated from a similar formula, but is limited by thecomplementary step function to the absorption case. Thepresence of the core-hole on the absorbing atom, as wellas the effect of the Hedin-Lundqvist self-energy (in the“plasmon pole” approximation), are also included inthe FEFF calculations. The LDOS for each type of atomis calculated by integrating the spacially- and energy-dependent density about each atom within the Normansphere. This allows for an unambiguous definition of theLDOS for each type of atom.In the panel b) of Fig. 10 we show our
FEFF calcu-lations of the iron L , edge XAS for the four metallic FIG. 11: The local angular-momentum projected densitiesof states for each of the metallic materials considered in theexperimental section. Only the largest angular-momentumcontributions from each type of atom are shown; the p-DOSis shown for As, O, and P; the d-DOS is shown for Ba, La,Sm, and Fe. We note that the Fe DOS shown is that of theabsorbing atom with the core hole. iron-containing materials considered in the experimen-tal section. In the panel a) of Fig. 10 we show ourXES calculations at the iron L edge. These XES cal-culations may be compared to the RIXS data for highfixed incoming energy and detected photon energies be-low | E L | + µ . Similarly to our interpretation of the XASas reflecting the unoccupied dDOS, the near edge XESmay be simply interpreted as a reflection of the occupieddDOS which is dominated by the Fe contribution nearthe Fermi level. The similarity of the pnictide spectra tothat of ordinary Fe metal underscores the importance ofmetalicity in these materials. The calculated spectra inboth the pnictides and iron metal mimic the DFT den-sity of states as expected in a weakly-correlated picture;the XAS (which involves an initial p-state) is determinedin the near edge region largely by the unoccupied dDOS.The dDOS, in turn, is dominated near the Fermi levelby the contribution from iron for all the materials con-sidered, as shown in Fig. 11. Other features of both theXAS and the XES can be matched to the peaks in thedDOS shown in Fig. 11. For completeness we also showthe pDOS of As, O, and P, in Fig. 11, but we note thatit is not directly related to the XAS or XES spectra.The fact that in FEFF the features of the XAS and theXES spectra can be matched to the peaks in the Fe 3ddensities of states suggests that the core-hole is relativelyunimportant and its potential weak. We can test thisconclusion by computing the same spectra with a methodthat disregards the potential of the 2p core-hole, but re-tains the correct band-structure dipole matrix elements.For this we used the plane-wave based DFT computerprogram
WIEN2k . The resulting XES and XAS spec-tra for three types of iron based materials are shown inFig. 12. The L - L splitting and relative intensity cannotbe determined with this method and are therefore intro-duced by hand. The computed XAS and XES spectra ofthe pnictides agree well with both our FEFF calculationsand the experiments. We observed that in both
FEFF and
FIG. 12: The iron L , edge XAS and XES, calculated using WIEN2k , for three different iron containing materials.
WIEN2k calculations, the effect of oxygen doping and alsothe effect of replacement of one rare earth with another israther small since the XAS is determined largely by thelocal environment of the absorber which is dominated byiron. We also note that the theoretical spectra presentedhere are polarization averaged; we have investigated po-larization dependence in our
FEFF calculations but findno significant differences between polarized and averagedspectra in the pnictides.
IV. SUMMARY
In the young field of iron-pnictide superconductorsthere are currently several open issues. For instance, itis not well understood why the observed ordered mag-netic moment is so small. Also the role of local Coulombinteractions is not well characterized, as is the degree ofAs hybridization with Fe orbitals near the Fermi level.The tendency towards the formation of large iron mo-ments due to local Hund’s rule exchange and a possibleemerging role for orbital degrees of freedom are other dis-puted issues . These disputes stand in the wayof a consensus on the minimal model needed to describethe physics and ultimately the pairing mechanism in Fe-pnictide superconductors. In this context we have inves-tigated five iron containing materials including 122 and1111 Fe-pnictides with a combination of XAS and RIXStechniques. The first general observation is that the ex-perimental data for the Fe pnictides is qualitatively simi-lar to other metallic Fe materials and significantly differ-ent from large gap Fe-based insulators such as hematite α -Fe O .The three main theoretical approaches that we haveused to analyze the data incorporate electronic correla-tion effects due to electron-electron interactions to dif-ferent degrees. If the pnictides were very localized onewould expect that the essential features of XAS and RIXSspectra can readily be captured in a small FeAs cluster.Our exact diagonalization computation of the absorption spectra for such a cluster in the localized, strong couplinglimit (large Hubbard U ) clearly shows the appearance ofa high energy peak well separated from the main ab-sorption line at the L edge. In the experimental datathis peak is absent – or rather appears as a shoulder ofthe main XAS line. From a comparison of the energyposition of this shoulder in the data and the cluster sim-ulation we extract an upper limit of the Hubbard U of2 eV –substantially smaller than the Fe 3 d bandwidth.Hund’s rule J is about 0.8 eV. Coulomb correlations arethus much weaker then in the cuprates. This result isconfirmed by our multiplet calculation, which is a localapproach that has the advantage of including the spin-orbit and Coulomb interactions related to the core-hole.The calculated L - L edge energy splittings and intensityratios agree with the experimental data.The inference that the Hubbard U is small and the 3 d electrons weakly correlated, suggests a comparison of thespectroscopic data with the results of single-particle, abinitio calculations. Such approaches are complicated bythe fact that a core-hole is present in the final state ofXAS and the intermediate state of RIXS. The Coulombinteraction of the core-hole with the valence electrons canin principle be strong and such an electronic correlationeffect has a profound influence on XAS and RIXS spec-tra. The density-functional based FEFF code treats theeffects of the core-hole potential with a high level of ac-curacy. The spectra computed with
FEFF confirm thepresence of the XAS shoulder and agree with the experi-mental XAS and RIXS data very well. We have used thisagreement to further filter out the core-hole induced cor-relations. When calculating the spectra with plane-wavebased
WIEN2k code –which includes the proper dipoletransition matrix elements, but lacks the final state XAScore-hole potential– we observe that the simulated spec-tra basically do not change. We conclude that in theFe pnictides not only the Hubbard U but also the core-hole potential is therefore heavily screened. The elec-tronic correlations that the core-hole induces are thusweak and consequently the spectra can safely be inter-preted in terms of single-particle densities of states andthe appropriate dipole transition matrix elements. Thepresent spectroscopic data and its theoretical descriptionthus emphasize the role of strong covalency and Fe met-alicity in the Fe pnictides. Acknowledgments
The authors would like to acknowledge important dis-cussions with J. Zaanen, I. Mazin, D. Reznik, J. J. Rehr,A. Baron, S. Johnston, Y.-D. Chuang, W. A. Harri-son, S. Kumar and M. Golden. This work is supportedby the Office of Science of the U.S. Department of En-ergy (DOE) under Contract No. DE-AC02-76SF00515,and DE-FG02-08ER4650 (CMSN). This research used re-sources of the National Energy Research Scientific Com-puting Center, which is supported by DOE under Con-0tract No. DE-AC02-05CH11231. This work is supportedby the “Stichting voor Fundamenteel Onderzoek der Ma-terie (FOM)”. The Advanced Light Source (ALS) is sup-ported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy underContract No. DE-AC02-05CH11231. P. O. would like toacknowledge the support from CONTACyT, Mexico. L. Boeri, O. V. Golgov, and A. A. Golubov, Phys. Rev.Lett. , 026403 (2008). D. Reznik, K. Lokshin, D. C. Mitchell, D. Parshall,W. Dmowski, D. Lamago, R. Heid, K.-P-Bohnen, A. S.Sefat, M. A. McGuire, et al., arXiv:0810.4941 (2008). C. J. Zhang, H. Oyanagi, Z. H. Sun, Y. Kamihara, andH. Hosono, Phys. Rev. B , 214513 (2008). S. A. Kivelson and H. Yao, Nature Materials , 927 (2008). H. Zhai, F. Wang, and D.-H. Lee, arXiv:0810.2320 (2008). K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kon-tani, and H. Aoki, Phys. Rev. Lett. , 087004 (2008). S. Graser, T. A. Maier, P. J. Hirschfeld, and D. J.Scalapino, arXiv:0812.0343 (2008). I. Mazin, M. D. Johannes, L. Boeri, K. Koepernik, andD. J. Singh, Phys. Rev. B , 085104 (2008). G. Giovannetti, S. Kumar, and J. van den Brink, Phys. B , 3653 (2008). K. Haule, J. H. Shim, and G. Kotliar, Phys. Rev. Lett. , 226402 (2008). L. Craco, M. S. Laad, S. Leoni, and H. Rosner, Phys. Rev.B , 134511 (2008). V. Vildosola, L. Pourovskii, R. Arita, S. Biermann, andA. Georges, Phys. Rev. B , 064518 (2008). V. I. Anisimov, D. M. Korotin, S. V. Streltsov, A. V.Kozhevnikov, J. Kunes, A. O. Shorikov, and M. A. Ko-rotin, arXiv:0807.0547 (2008). A. Shorikov, M. Korotin, S. Streltsov, D. Korotin,V. Anisimov, and S. Skornyakov, arXiv:0804.3283 (2008). V. I. Anisimov, D. M. Korotin, M. A. Korotin, A. V.Kozhevnikov, J. Kunes, A. O. Shorikov, S. Skornyakov,and S. V. Streltsov, arXiv:0810.2629 (2008). D. H. Lu, M. Yi, S.-K. Mo, A. S. Erickson, J. Analytis,J.-H. Chu, D. J. Singh, Z. Hussain, T. H. Geballe, I. R.Fisher, et al., Nature , 81 (2008). F. de Groot and A. Kotani,
Core Level Spectroscopy ofSolids (CRC Press, 2008). T. Kroll, S. Bonhommeau, T. Kachel, H. A. Duerr,J. Werner, G. Behr, A. Koitzsch, R. Huebel, S. Leger,R. Schoenfelder, et al., arXiv:0806.2625 (2008). E. Z. Kurmaev, R. G. Wilks, A. Moewes, N. A. Skorikov,Y. A. Izyumov, L. D. Finkelstein, R. H. Li, and X. H.Chen, Phys. Rev. B , 220503R (2008). E. Kurmaev, J. McLeod, A. Buling, N. Skorikov,A. Moewes, M. Neumann, M. Korotin, Y. Izyumov, N. Ni,and P. Canfield, arXiv:09021141 (2009). A. L. Ankudinov, B. Ravel, J. J. Rehr, and S. D. Conrad-son, Phys. Rev. B , 7565 (1998). Z. A. Ren, W. Lu, J. Yang, W. Yi, X. L. Shen, Z. C. Li,G. C. Che, X. L. Dong, L. L. Sun, F. Zhou, et al., Chin.Phys. Lett. , 2215 (2008). Z. A. Ren, J. Yang, W. Lu, W. Yi, X. L. Shen, Z. C.Li, G. C. Che, X. L. Dong, L. L. Sun, F. Zhou, et al.,EuroPhys. Lett. , 57002 (2008). N. Ni, S. L. Budko, A. Kreyssig, S. Nandi, G. E. Rustan,A. I. Goldman, S. Gupta, J. D. Corbett, A. Kracher, and P. C. Canfield, Phys. Rev. B , 014507 (2008). G. F. Chen, Z. Li, J. Dong, G. Li, W. Z. Hu, X. D.Zhang, X. H. Song, P. Zheng, N. L. Wang, and J. L. Luo,arXiv:0806.2648 (2008). J. G. Analytis, R. D. McDonald, J.-H. Chu, S. C. Riggs,A. F. Bangura, C. Kucharczyk, M. Johannes, and I. R.Fisher, arXiv:0902.1172 (2009). J. J. Jia, T. A. Callcott, J. Yurkas, A. W. Ellis, F. J.Himpsel, M. G. Samant, J. Stohr, D. L. Ederer, J. A.Carlisle, E. A. Hudson, et al., Rev. Sci. Instrum. , 1394(1995). B. T. Thole and G. van der Laan, Phys. Rev. B , 3158(1988). F. M. F. de Groot, J. C. Fuggle, B. T. Thole, and G. A.Sawatzky, Phys. Rev. B , 5459 (1990). G. van der Laan and I. W. Kirkman, J. Phys. Condens.Matter , 4189 (1992). K. Haule and G. Kotliar, arXiv:0805.0722 (2008). A. Moewes, S. Stadler, R. P. Winarski, D. L. Ederer, M. M.Grush, and T. A. Calcot, Phys. Rev. B , 15951 (1998). C. T. Chen, Y. U. Idzerda, H. J. Lin, N. V. Smith,G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette,Phys. Rev. Lett. , 152 (1995). R. Nakajima, J. Stohr, and Y. U. Idzerda, Phys. Rev. B , 6421 (1999). X. Gao, D. Qi, S. C. Tan, A. T. S. Wee, X. Yu, and H. O.Moser, J. Electron Spec. Rel. Phenom. , 199 (2006). L. C. Duda, J. Nordgren, G. Drager, S. Bocharov, andT. Kirchner, J. Electron Spec. Rel. Phenom. , 257(2000). L. A. Marusak, R. Messier, and W. B. White, J. Phys.Chem. Solids , 981 (1980). F. Vernay, B. Moritz, I. Elfimov, J. Geck, D. Hawthorn,T. P. Devereaux., and G. A. Sawatzky, Phys. Rev. B ,104519 (2008). M. B. J. Meinders, H. Eskes, and G. A. Sawatzky, Phys.Rev. B , 3916 (1993). A. Kotani and S. Shin, Rev. Mod. Phys. , 203 (2001). W. A. Harrison,
Elementary Electronic Structure (WorldScientific, 2004). E. Dagotto, T. Hotta, and A. Moreo, Physics Reports ,1 (2001). D. van der Marel and G. A. Sawatzky, Phys. Rev. B ,10674 (1988). L. Mattheiss, Phys. Rev. , A1399 (1964). A. L. Ankudinov and J. J. Rehr, Phys. Rev. B , R1712(1997). U. von Barth and L. Hedin, J. Phys. C , 1629 (1972). J. J. Rehr and R. C. Albers, Phys. Rev. B , 8139 (1990). L. Hedin and S. Lundqvist, Solid State Phys. , 1 (1969). B. I. Lundqvist, Phys. Kondens. Mater. , 192 (1967). J. M. de Leon, J. J. Rehr, S. I. Zabinsky, and R. C. Albers,Phys. Rev. B , 4146 (1991). P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, andJ. Luitz,
WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karl-heinz Schwarz, Techn. Universitt Wien, Austria, 2001),iSBN 3-9501031-1-2. M. D. Johannes and I. Mazin, arXiv:0904.3857 (2009). F. Kr¨uger, S. Kumar, J. Zaanen, and J. van den Brink, Phys. Rev. B , 054504 (2009). L. Hozoi and P. Fulde, Physical Review Letters ,136405 (2009).55