Resonant x-ray scattering spectra from multipole orderings N

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumpti

NpO2/ver.3

Resonantx-rayscatteringspectrafrommultipoleorderings:

NpM4,5edgesinNpO2

TatsuyaNagao

FacultyofEngineering,GunmaUniversity,Kiryu,Gunma376-8515,Japan

Jun-ichiIgarashi

arXiv:cond-mat/0506467v1 [cond-mat.str-el] 18 Jun 2005

FacultyofScience,IbarakiUniversity,Mito,Ibaraki310-8512,Japan

(Dated:February2,2008)

Westudyresonantx-rayscattering(RXS)atNpM4,5edgesinthetriple-kmultipoleorderingphaseinNpO2,onthebasisofalocalizedelectronmodel.WederiveanexpressionforRXSamplitudestocharacterizethespectraundertheassumptionthatarotationalinvarianceispreservedintheintermediatestateofscatteringprocess.Thisassumptionisjusti edbythefactthatenergiesofthecrystalelectric eldandtheintersiteinteractionissmallerthantheenergyofmultipletstructures.Thisexpressionisfoundusefultocalculateenergypro leswithtakingaccountoftheintra-Coulombandspin-orbitinteractions.AssumingtheΓ8-quartetgroundstate,weconstructthetriple-kgroundstate,andanalyzetheRXSspectra.Theenergypro lesarecalculatedingoodagreementwiththeexperiment,providingasoundbasistopreviousphenomenologicalanalyses.

PACSnumbers:78.70.Ck,75.25.+z,75.10.-b,78.20.Bh

I.INTRODUCTION

Resonantx-rayscattering(RXS)techniquehasat-tractedmuchattentiontostudyspinandorbitalprop-ertiesof3dtransition-metalcompounds.RXSattheK-edgeisdescribedbyasecond-orderopticalprocessthatanincidentx-rayexcitesa1scoreelectrontounoccupied4pstatesandthenthe4pelectronisrecombinedwiththecoreholewithemittingx-rayinthedipoleprocess(E1).Itbecamewidelyknownaftertheobservationofintensi-tiesonorbital-orderingsuperlatticespotsatMnK-edgeinLaMnO3.1Attheearlierstage,thespectrawerein-terpretedasadirectobservationoforbitalHowever,subsequenttheoreticalstudiesbasedonbandstructurecalculationsrevealedthatthespectraareadi-rectre ectionoflatticedistortion,3,4,5sincethe4pstateintheintermediatestateisin uencednotbytheorbitalorderingof3delectronsbutbylatticedistortionthroughthehybridizationwiththe2pstateatneighboringoxygensites.

Di erentfromtransition-metalcompounds,M4,5edgesareavailableforforbiddenre ectionBraggspotsinac-tinidecompounds.6,7,8TheRXSspectraaremoredi-rectlyre ectingmultipoleorderingsof5fstates,sincetheE1processinvolvesatransitionfromthe3d-coreto5fstates.Eachactinideatomusuallycarrieslocalmulti-polemoments,whichcanorderatlowtemperaturesduetointersiteinteractionssuchasexchangeinteractions.Forsuchlocalizedelectronsystems,RXSamplitudesaregivenbysummingupcontributionsateachsite.Thecrystalelectric eld(CEF)andtheintersiteinteractioncanbesafelyneglectedintheintermediatestate,becausetheyaremuchsmallerthantheintra-atomicCoulombinteraction.Therefore,itmaybereasonabletoassumethattheintermediatestatepreservestherotationalin-variance.Undertheassumption,wederiveanexpressionfortheRXSamplitudeintheE1processtocharacter-

izethespectra.AlthoughtheexpressionisessentiallythesameastheformulabyHannonetal.,9thepresentformisusefultocalculateenergypro http://doc.guandang.netingthisexpressionto-getherwithamicroscopicmodel,wecalculatetheRXSspectrainthetriple-kmultipoleorderingphaseinNpO2.NpO2undergoesasecond-orderphasetransitionbelowT0=25.5SinceNpionsareKramersionsinthe(5f)3con guration,amagneticgroundstateisnaturallyexpected.However,neitherM¨ossbauerspectroscopy12,13norneutrondi raction14,15coulddetectanyevidenceofthesizablemagneticmoment.Actually,theformerexperimentgaveanestimateoftheupperlimitofthemagnitudeofthemagneticmoment～0.01µB,whichwastoosmalltoexplainthee ectiveparamagneticmo-ment～2.95µBAnothercomplicationisthatamuonspinrelaxation(µSR)experimenthassuggestedthelow-temperaturephaseofbreakingtime-reversalsymmetry.17Anaturalwaytoreconcilewiththeaboveobservationsistointroducethehigher-rankmultipoleorderingratherthanthedipolemoment.Actually,SantiniandAmorettiproposedaoctupoleorderingofΓ2(xyz)symmetry.18,19However,thisphasecanberuledoutbecauseitgivesrisetonoRXSintensity.Recently,Paix aoetal.havereportedthatalongitudinaltriple-koctupoleorderingaccountswellfortheirRXSexperiment.20Thereasonforanticipatingtriple-korderingsisthatitexcludesacrystaldistortionorashiftofoxygenpositions,whichisconsistentwiththeexperiment.Experimentaldataobtainedfromthe17ONMRspectrum,whichindicatetheexistenceoftwoinequivalentoxygensites,supporttheoccurrenceofthetriple-koctupoleorderingphase.21Sometheoreticalworksalsohavelentsupporttorealiza-tionofthistypeofthephase.22,23

AssumingtheΓ8-quartetgroundstate,weexplicitlyconstructatriple-koctupoleorderingstate.Thisstateisfoundtosimultaneouslycarrya nitequadrupolemo-

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumpti

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ment,whichgeneratestheRXSintensity.SincetheRXSamplitudesarecharacterizedbythreeterms,thescalar,dipole,andquadrupoleones,itisnotnecessarytoas-sumetheexistenceofthehexadecapolemomentinsteadofthequadrupolemoment.Wecalculatetheenergypro- leswithtakingfullaccountofmultipletstructuresintheintermediatestate.Weobtainspikes-likecurvesatNpM4edgesforsmallervaluesofthecore-levelwidthΓasare ectionofmultipletstructures.TheyarefoundtomergeintoasinglepeakwithΓ>1eV.Theenergypro- lewithΓ～2eVseemstoagreewiththeexperiment.Theazimuthal-angledependenceoftheRXSspectraisobtainedinagreementwiththepreviousanalysis.20,24Thepresentanalysisprovidesasoundbasistotheprevi-ousphenomenologicalanalysis.

Thepresentpaperisorganizedasfollows.InSec.II,wepresentanexpressionfortheRXSamplitude,whichisusefultocalculatetheenergypro les.InSec.III,weanalyzetheRXSspectrainthetriple-koctupoleorderingofNpO2onthebasisofalo …… 此处隐藏：24440字，全部文档内容请下载后查看。喜欢就下载吧 ……