1s2p Resonant Inelastic X-ray Scattering Magnetic Circular Dichroism as a probe for the local and non-local orbitals in CrO 2

(1)

HAL Id: hal-01708748

https://hal.sorbonne-universite.fr/hal-01708748

Submitted on 14 Feb 2018

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire

HAL, est

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Distributed under a Creative Commons

Attribution| 4.0 International License

Sikora, James Ablett, Jean-Pascal Rueff, Blair Lebert, Philippe Sainctavit, Frank M.F. de Groot, Amélie Juhin

To cite this version:

Patric Zimmermann, Nadejda Bouldi, Myrtille O.J.Y. Hunault, Marcin Sikora, James Ablett, et al..

1s2p Resonant Inelastic X-ray Scattering Magnetic Circular Dichroism as a probe for the local and

non-local orbitals in CrO 2. Journal of Electron Spectroscopy and Related Phenomena, Elsevier, 2018,

222, pp.74 - 87. �10.1016/j.elspec.2017.08.004�. �hal-01708748�

(2)

ContentslistsavailableatScienceDirect

Journal of Electron Spectroscopy and Related Phenomena

j o u r n a l ho me p ag e :w w w . e l s e v i e r . c o m /l o c a t e / e l s p e c

1s2p Resonant Inelastic X-ray Scattering Magnetic Circular Dichroism as a probe for the local and non-local orbitals in CrO

2

PatricZimmermannâ,NadejdaBouldi^b,c,MyrtilleO.J.Y.Hunaultâ,MarcinSikoraê, JamesM.Ablett^b,Jean-PascalRueff^b,d,BlairLebert^b,c,PhilippeSainctavit^b,c, FrankM.F.deGrootâ,∗,AmélieJuhin^c

aDebyeInstituteofNanomaterialScience,UtrechtUniversity,3584CAUtrecht,TheNetherlands

bSynchrotronSOLEIL,L’OrmedesMerisiers,BP48Saint-Aubin,91192Gif-sur-Yvette,France

cInstitutdeMinéralogie,dePhysiquedesMatériauxetdeCosmochimie(IMPMC),SorbonneUniversités,UMRCNRS7590,UPMCUnivParis06,Muséum Nationald’HistoireNaturelle,IRDUMR206,4PlaceJussieu,F-75005Paris,France

dLaboratoiredeChimiePhysique-MatiéreetRayonnement,SorbonneUniversités,UPMCUnivParis06,CNRS,UMR7614,F-75005Paris,France

eAcademicCentreforMaterialsandNanotechnology,AGHUniversityofScienceandTechnology,30-059Kraków,Poland

a r t i c l e i n f o

Articlehistory:

Received12November2016

Receivedinrevisedform22August2017 Accepted25August2017

Availableonline14September2017

Keywords:

RIXS-MCD

Magneticcirculardichroism Non-local

4p3dhybridisation CrO2

Distortion

a b s t r a c t

Wehavedeterminedthemagneticgroundstateofthehalf-metalCrO2basedon1s2pResonantInelastic X-rayScatteringMagneticCircularDichroism(RIXS-MCD)experiments.Thetwo-dimensionalRIXS-MCD mapdisplaysthe1sX-rayabsorptionspectrumcombinedwiththe1s2pX-rayemissiondecay,where thereisalargeMCDcontrastintheﬁnalstateinvolvingthe2pcorehole.

OurmeasurementsshowthattheCrKpre-edgestructureisdominatedbydipolarcontributionsand thequadrupolepeakisinvisibleindirectKpre-edgeabsorption.UsingRIXS-MCD,werevealthatthe quadrupole1s3dpre-edgehasalargeMCDcontrast,whichappearsatlowerenergywithrespecttothe Kpre-edgemaximum.

WeusecrystalﬁeldmultipletcalculationstomodeltheexcitonicRIXS-MCDspectralshapeintetragonal (D4h)symmetry.TheRIXS-MCDisstronglysensitivetothegroundstatedistortionoftheCr⁴⁺sites.

ThecalculationsoftheRIXS-MCDmapssuggestthatthe3dspin–orbitinteractionisfullyquenched (3d=0meV)andthegroundstateelectronconﬁgurationmustcontaina³B2g(D4h)contribution,which isrequiredtoexplaintheappearanceoftheMagneticCircularDichroism(MCD)intheCrKpre-edge.

Thisisinapparentcontrastwiththecompressedtetragonaldistortion.

1. Introduction

ThedetectionoftheX-raymagneticcirculardichroism(XMCD) hasbecomeapowerfultoolfortheelement-speciﬁcstudyofthe magneticpropertiesofcomplexsystems.TheMCDof3dtransition metalionsisusuallystudiedatthespin–orbitsplitL2,3absorption edges(2p→3d)toallowthedeterminationofthespinandorbital magneticmomentsusingthesumrules[15,44].

TheL2,3-edgesof3dtransitionmetalsareinthesoftX-rayrange requiringvacuumconditions,implyingthattheyaredifﬁcultfor liquidorhigh-pressurecells.Thislimitsthenumberofpossible applicationsandthenatureofthesamples.TheenergyoftheK-

∗Correspondingauthors.

E-mailaddress:F.M.F.deGroot@uu.nl(F.M.F.deGroot).

edgeof3dtransitionmetalsliesinthehardX-rayrange,butthe directK-edgeMCDsignalisweakandtheabsenceofspin–orbit splittinga prioriprohibitsaquantitativeanalysisusingthespin sumrules.

Someoftheabovelimitationscanbeaddressedwiththenovel RIXS-MCDapproach,inwhichonecombinesXMCDandresonant inelasticX-rayscattering(RIXS)attheKpre-edgeof3dtransition metalsaccordingtothefollowingtwo-step-model(Fig.1).

The excitation step (X-ray AbsorptionSpectrum, XAS)is per- formedwithcircularpolarisedlight,beingeitherleft(lcp, )or rightcircularpolarised(rcp, ).Thedetectionofthesubsequent X-rayemissionspectrum(XES)caninprinciplealsobepolarisation https://doi.org/10.1016/j.elspec.2017.08.004

(3)

Fig.1. Atomictermschemeforthe1s2pRIXS-MCDphoton-inphoton-outprocess fora3d²electronconﬁguration.EinandEoutdenotetheenergiesoftheincoming andoutgoinglight,andETtheenergytransferredtothesystem.

dependent,however,forthisstudynopolarisationanalyserwas usedintheXESchannel.

RIXS measurements are established to study the electronic structure,whileRIXS-MCDadditionallyoffersmagneticinforma- tionwiththeadvantagethatitenhancesthecontrastofresonant features.Theﬁrst1s2pRIXS-MCDexperimentshaveshownthat theRIXS-MCD signalof iron in magnetite, can beof thesame orderof magnitudeasL_2,3-edge XMCD[27,44,51,52].The RIXS- MCDapproachcanthusbeconsideredasahighresolutionmagnetic spectroscopy,whilehardX-raysyieldbulksensitivity.

Chromium dioxide (CrO₂) is a half-metallic ferromagnet (T_Curie≈390K)whichmeansthatonespinchannelisconductive whiletheotheroneisinsulating;inotherwordstheelectronsin theoccupiedCr(3d)bandsinCrO2shownearly100%spinpolar- isation[35,40,53].Thismakesitapromisingcandidateforfuture applicationsintheﬁeldofspintronics[40],forexampleasasource for spin-polarised currents, magnetic tunnel junctions or other magneto-electronicdevicesthatrequirealargespinpolarisation [60].

Theferromagnetismisusuallyexplainedintermsofaspeciﬁc double-exchangemechanism[30,46]relatedtotheexistenceofthe combinationofastronglylocalisedstatejustbelowtheFermilevel andanotherdispersedbandathigherenergy.AsSchlottmannstates Hund’srule couples thespin ofthe localised electronwith that of theitinerantelectronsandthehoppingbecomescorrelated[46].This impliesastrongcorrelationbetweenthespinsofthelocalisedand non-localisedelectrons[46].Themetallicityisduetothedispersed bandsthat hybridisewiththeO(2p)bandsand crosstheFermi level.Thismechanismandtheimportanceoflocalandnon-local correlationsisasubjectofactiveresearch[29].

Inspiteofthelargenumberofstudies,theelectronicstructure thatinducesbothferromagnetismandmetallicityinCrO₂remains tobeunderstoodandtheoriginofthehalf-metallicferromagnetism ishighlynontrivial[54].

ItisexpectedthatRIXS-MCDprobesspeciﬁcallythelocalmag- neticcontributionyieldingvaluableinformationonthecomplex electronicstructurethatleadstometallicferromagnetisminCrO₂. InRIXS-MCD,transitionsinvolvinglocaliseddstatesareexpected togiveanenhancedintensitywithrespecttoconventionalXMCD, whilethoseinvolvingdelocalisedstatesarenot[52].

RIXS measurements are established to study the electronic structure,whileRIXS-MCDadditionallyoffersmagneticinforma- tionwiththeadvantagethatlocalfeaturesappearonresonance withenhancedcontrast.The bulksensitivity of1s2p RIXS-MCD addressesthecommonproblemofareducedsurface(Cr⁴⁺→Cr³⁺) insurfacesensitivemeasurementsinthesoft X-rayrange,asin L_2,3-edgeXMCD[2,8,17,18,22,23,28,40]orL-edgeRIXS[32].

Fig.2.Schemeoftheexperimentalsetupwiththesampleinorangebetweenthe twopolesoftheelectromagnet.Thecircularlypolarisedincidentbeaminblue,mag- neticﬁeldinredandthedetectedX-rayemissioningreen.Thedetector,anavalanche photodiode(APD),isnotshownforclarity.

2. Technicaldetails

2.1. Experimentalsetupandmeasurements

Themeasuredsampleis acommercially availablecrystalline CrO₂ powder (Magtrieve^TM)witha density of =4.85g/cm³ at 25^◦Candagrainsizeof44␮m(mesh325)[50].Thepowderwas milledbyhandwithmortarandpestleandthenpressedintoapill.

The measurements were performed at ambient conditions (T≈25^◦C, p≈1bar) at theGALAXIES inelastic-scattering beam- line at the SOLEIL synchrotron radiation facility [45]. The synchrotron radiation was monochromatised using a Si(111) nitrogen-cooledﬁxed-exitdouble-crystalmonochromator(DCM) withE/E≈1.4×10⁻⁴,followed bya Pd-coatedsphericalcolli- matingmirror. TheX-rays werethen focused toa spot-sizeof 30␮m(vertical)by 90␮m(horizontal)full widthathalf maxi- mum(FWHM)atthesamplepositionbya3:1focusingtoroidal Pd-coatedmirror.AverticalRowlandcirclegeometrywasimple- mentedusinga Ge(422)spherical-bentanalysercrystal(R=1m) whichwasusedtoenergy-selectandfocustheemittedX-raysonto asiliconavalanchephotodiodedetector.

The overall resolution was found to be FWHM≈0.74eV or E/E≈7700bymeasuringthequasi-elasticlineat5.4keV,cor- responding to the energy of the Cr K˛ ﬂuorescence line. A diamondquarter-waveplatein(111)-orientationwithathickness ofd=500␮m,locatedimmediatelyaftertheDCM,wasusedinorder toselectbetweenleft( )andrightcircularpolarised( )light.An electromagnetcreatedamagneticﬂuxdensityBofupto|B|≈0.7T onthesample.

Thesetupwasalignedinlongitudinalgeometry[31]withk||B||z asshowninFig.2.Theanglesofthesampleandtheanalyserwith respecttotheincidentbeamwere=45^◦and=90^◦respectively.

Eachmeasurementwasperformedwithalternatingpolarisation (lcp↔rcp)foreachdatapoint.Allspectrawereacquiredasinci- dentenergyscanswiththespectrometerﬁxedtodetectagiven emissionenergy Eout.Forthespectrain Fig.7 theemittedpho- tonscorrespondingtotheCrK˛1emissionatEout=5415.3eVwere detected.FortheRIXSmapsthedetectedemissionenergieswere variedaccordinglybetweenEout=5406eVandEout=5423eV.After completionofaspectrumthedirectionofthemagneticﬁeldwas reversedandthemeasurementrepeated.Thisyieldstwoinverse spectrawhichareaddedtominimisenoiseandreducesystematic errors.

Thetwo-dimensionalRIXSmapsaredisplayedeitherinanemit- tedenergyviewwiththeintensityI(E_in,Eout),orinanenergytransfer viewwiththeintensityI(E_in,ET).TheincidentenergyE_inisinboth

(4)

casesthehorizontalxaxis,andtheyaxisis eithertheemitted photonenergyEoutortheenergytransferET=Ein−Eout.Theinci- dentenergyE_inoftheexperimentalspectrawascalibratedagainst aCrO₂reference[38].TheenergiesoftheemittedphotonsEoutand energytransferETwerecalibratedwithliteraturevaluesfromthe X-rayDataBooklet(http://xdb.lbl.gov/).Theintensitiesofallspec- traarenormalisedwithrespecttothesummaximumandgivenin arbitraryunits(a.u.).

2.2. Calculationsofthedensitiesofstates

The density of states (DOS) has been calculated using density-functional theory (DFT) as implemented in Quantum- Espresso[16],i.e.usingaplane-wavebasisset,pseudo-potentials and periodic boundary conditions. We used Troullier–Martins [61]norm-conservingpseudo-potentialsand theformulation of Perdew–Burke–Ernzerhof[41] (GGA) fortheexchange and cor- relation density functional. The electric dipole and quadrupole contributionstotheabsorptioncross-sectionarecalculatedwith Xspectra[19,56].

Tointerprettheexperimentalspectra,a1scoreholeisadded inthecalculation.It is described withina staticapproximation byincludingacore-holeinthepseudo-potentialoftheabsorbing Cratom.TheHubbardUcorrection,whoserelevanceinthecase ofCrO₂isdiscussedinRefs.[6,30,36,58],wasnotincludedinthe calculation.

Thelattice parameters and thedimensionless internal coor- dinate deﬁning the positions of the atoms were set to their experimentalvalues (a=b=4.421 ˚A,c=2.916 ˚A[18,35],u=0.303 [33]).Theself-consistentchargedensitycalculationwasperformed usingacentered6×6×9k-pointsgridfortheconventionalcellthat containsoneCratomand twoOatoms.Thenon-self-consistent calculation is performed with a 12×12×18 k-point grid and theprojected densityof statesareobtainedbyprojectingwave functionsontoorthogonalisedatomicwavefunctions.A2×2×3 supercellisusedtominimiseinteractionsbetweenneighbouring core-holesuponapplicationofperiodicboundaryconditionsand thek-pointgridisreducedaccordingly.

2.3. Crystal-ﬁeldmultipletcalculations

Thequadrupolecontributiontothepre-edgestructurecannot be accurately reproduced with the present DFT-based calcula- tionsduetothestrong3d3dcorrelationeffectsthatdeterminethe pre-edgespectralshapeandalsotheX-rayemissionmatrixele- ments.Instead,acrystal-ﬁeldmultiplet (CFM)calculationofthe 1s²3d²→1s¹3d³ quadrupole transitionwithsubsequentdipole decay1s¹3d³→1s²2p⁵3d³isapplied.

Themultipletcalculationsarebasedontheabsorptionandemis- sionmatricescreatedwiththeCTM4XAS program[55].It takes intoaccountallthe3d-3d,1s-3d and2p-3delectronicCoulomb interactions,aswellasthespin–orbitcouplingoneveryopen shelloftheabsorbingatomandtreatsthegeometricalenvironment througha crystal-ﬁeldpotential. Allcalculations areperformed usingtheC₄pointgroupsymmetrytotakeintoaccountthepres- enceofamagneticﬁeld(B||k).TheRIXSprocessismodelledwiththe Kramers–Heisenbergrelation[44]usingadditionalscriptswritten forthispurpose.

TheatomicSlatercoefﬁcientsfor the3d3dCoulombinterac- tionF_ddarescaledto65%oftheHartree–Fockvaluesandthe2p3d CoulombF_pdandtheexchangeinteractions(G_pd,G_sd)arescaledto 52%.ThisreductionoftheSlaterintegralsisaresultoftheexpan- sionofthewavefunctionduetochargetransfereffectsandthe actualvaluesusedareanempiricalresultastheyshowthebest resultspresentedhere.Theatomicvaluesforthespin–orbitinterac-

Fig.3.Energysplittingsofthemulti-electronicstate³F⁺forCr⁴⁺(3d²configuration inhigh-spinS=1),foreachsymmetryforO3→Oh→D4h→D2h(localexchangeis included,butnospin–orbitormagneticfieldistakenintoaccount).Theorderof theenergylevelsshownaboveisnotfixed.Itcanbealteredindependencyonthe specificcrystal-fieldparameterschosen.

tionareinthegroundstate_3d=41meV,intheintermediatestate _3d=54meVandintheﬁnalstate_2p=5.668eVand_3d=53meV.

ForCrO₂,therearesomereportedvaluesforthecrystal-field parameter10Dq(Ikeno:2.28eV[25],Lewis:2.5eV[33]),butwe arenotawareofanyreportsforthetetragonaldistortionparam- etersDsandDt.Basedonthemagnitudeofthespatialdistortion weestimatethetwodistortionparameters,DsandDt,tobeofthe orderoftensofmillielectronvolt(meV).Thecrystal-fieldparame- ters(Dq,Ds,Dt)havebeenvariedacrossasignificantsectionofthe parameterspace.Onlyafewrepresentativemapshavebeencho- sentoillustratethegeneralappearanceforagivengroundstate.

Thedisplayedcalculationsrefertothecrystal-fieldsplittingparam- eter10Dq=2.347eVandthedistortionparametersDs=−0.036eV, Dt=−0.007eVfor³EgandDt=−0.2eVforthe³B2gcase.Themolecu- larfieldMreflectingtheinteratomicexchangeinteractionsissetto M=30meV,beingestimatedwiththeCurietemperatureTc≈390K.

ThefollowingLorentzianbroadeningsareappliedfortheinter- mediatestate(IS)L_IS=1.2eVandtheﬁnalstate(FS)L_FS=0.6eV.

HereL_FSisanintermediatevaluebetweenthetwonaturalbroad- eningsforthe2p_3/2and2p_1/2ﬁnalstates,correspondingtotheK˛1

andK˛2emissionrespectively.Asdiscussedelsewhere[11,14]the lifetimebroadeningofthe2p_1/2 shell(K˛₂ line,L₂ edge)canbe uptoﬁvetimeslargerwithrespecttothe2p_3/2shell(K˛1line,L3

edge).Theexperimental(Gaussian)broadeningGIS=0.7eVisset totheexperimentallyacquiredFWHMofthequasi-elasticscatter- ingpeak.Fortheemission,aresolutionofG_FS=0.4eVisused.All broadeningsaregivenasfullwidthathalfmaximum.

Finally,theenergycalibrationforthetheoreticalmapsisnot absolute.Thecalculatedspectrawereshiftedinbothdirectionsfor thebestagreementwiththeexperimentalMCD.

3. Theory

3.1. Crystal-ﬁeldmultiplettheory

TheCrO₂crystalhasarutilestructureandbelongstothespace- groupP4₂/mnm(136)[35,53].Withthemetalionastheinversion center(inversionsymmetry)localpd-mixingisforbidden,butmix- ingbetweendifferentsitesispossible.TheCr⁴⁺ionsoccupythe six-foldoxygen-coordinatedsiteswithWyckoffposition2acorre- spondingtoD_2hpointgroupsymmetry[1,18,35,40,53,59,60].Inthe groundstate,Cr⁴⁺inCrO₂hasahighspin(S=1)3d²electroncon- ﬁguration[8],whichcorrespondstothemulti-electronicground state³F⁺insphericalsymmetry(O3)asderivedwithHund’srules.

Thesplittingoftheatomicmulti-electronicstatebythecrystal- ﬁeld,throughthesuccessivebranchingsO₃→O_h→D_4h→D_2his illustratedinFig.3.