Ab initio electronic structure calculation of corr

arXiv:cond-mat/0309304v1[cond-mat.str-el]12Sep2003Abinitioelectronicstructurecalculationofcorrelatedsystems:EMTO-DMFTapproachL.Chioncel1,L.Vitos2,3,I.A.Abrikosov4,J.Koll´ar2,M.I.Katsnelson1,4,5,andA.I.Lichtenstein11UniversityofNijmegen,NL-6525EDNijmegen,TheNetherlands2ResearchInstituteforSolidStatePhysicsandOptics,P.O.Box49,H-1525Budapest,Hungary3AppliedMaterialsPhysics,DepartmentofMaterialsScienceandEngineering,RoyalInstituteofTechnology,SE-10044Stockholm,Sweden4UppsalaUniversity,P.O.Box530,S-75121Uppsala,Sweden5InstituteofMetalPhysics,620219,Ekaterinburg,Russia(10March2003)AbstractWeproposeaself-consistentmethodforelectronicstructurecalcula-tionsofcorrelatedsystemsthatcombinesthelocaldensityapproximation(LSDA)andthedynamicalmeanfieldtheory(DMFT).TheLSDApartisbasedontheexactmuffin-tinorbitals(EMTO)approach,meanwhiletheDMFTusesaperturbationschemethatincludestheT-matrixwithfluc-tuationexchange(FLEX)approximation.ThecurrentLSDA+DMFTimplementationfulfillsbothself-energyandchargeself-consistencyre-quirements.Wepresentresultsontheelectronicstructurecalculationsforbulk3dtransitionmetals(Cr,FeandNi)andforFe/Crmagneticmultilayers.Thelatterdemonstratestheimportanceofthecorrelationeffectsforthepropertiesofmagneticheterostructures.TypesetusingREVTEX1I.INTRODUCTIONIntheabinitiodescriptionoftheelectronicpropertiesofmaterialsthemostwidelyusedmethodsarebasedonthedensityfunctionaltheory(DFT)[1]implementedwithinthelocalspindensityapproximation(LSDA)[2,3]totheexchangeandcorrelationen-ergy.Groundstatepropertiesofthemostofmetals,semiconductors,ioniccompounds,etc.,arequantitativelywelldescribedbytheDFT-LSDAapproach.Attemptstoap-plythesefirstprinciplesmethodstostronglycorrelatedsystems,however,encounteredmanyfundamentaldifficulties[4–6].Evenforelementaltransitionmetals,suchasMn,Fe,orNi,theimpactofthecorrelationeffectsontheelectronicstructureturnsouttobeessential[7].Therefore,oneofthemostchallengingproblemsinthephysicsoftransitionmetals,theiralloysandcompoundsistodevelopsimpleandefficientelec-tronicstructuremethodsthatgobeyondtheLSDAbyincludingimportantmany-bodyeffects.IthasprovedafruitfulapproachtocombinethesimpleHubbardmodelwiththeLSDAtechnique,providingaDFTscheme”beyondLSDA”[4–7].Unfortunately,thesimplestrealizationofsuchanapproach,theLSDA+Uscheme[4],cannotdescribethemany-bodyeffectsbeyondtheHartree-Fockapproximation.Theseeffectsareconnectedwiththefrequencydependenceoftheelectronself-energy.Inordertoincludedynam-icaleffectstheLSDA+Uschemewascombinedwiththedynamicalmeanfieldtheory(DMFT)[5,6].TheDMFTmapslatticemodelsontoquantumimpuritymodelssubjecttoaself-consistentconditioninsuchawaythatmany-bodyproblemforcrystalsplitsintoone-bodyimpurityproblemforthecrystalandmany-bodyproblemforaneffectiveatom.Infact,theDMFT,duetonumericalandanalyticaltechniquesdevelopedtosolvetheeffectiveimpurityproblem[8],isaveryefficientandextensivelyusedapprox-imationforenergydependentself-energyΣ(ω).TheemergedLSDA+DMFTmethodcanbeusedforcalculatingalargenumberofsystemswithdifferentstrengthoftheelectroniccorrelations[7,9,10].TounderlinetheimportanceofcompleteLSDA+DMFTself-consistencywementionthatthefirstsuccessfulattempttocombinetheDMFTwithLSDAchargeself-consistencygaveanimportantinsightintoalong-standingproblemofphasediagramandlocalizationinf-electronsystems[11].Toincorporatethedynamicalmeanfieldapproachinthebandstructurecalcula-tionweadopttheexactmuffin-tinorbitals(EMTO)densityfunctionalmethod.TheEMTOtheorycanbeconsideredasascreenedKorringa-Kohn-Rostoker(KKR)muffin-tinmethod,wherelargeoverlappingpotentialspheresareusedforaccuraterepresen-tationoftheLSDAone-electronpotential.AcomprehensivedescriptionoftheEMTOtheoryanditsimplementationwithintheLSDAmaybefoundinRefs.[12]and[13,14],respectively.Thepaperisorganizedasfollows:SectionIIpresentsageneralformulationofthecombinedmultiplescatteringanddynamicalmeanfieldapproach.ThecalculationschemefromSectionIIIillustratesthemultiplescatteringsolutionoftheLSDAprob-lemviatheEMTOmethodandthemany-bodysolutionoftheDMFTproblemviatheT-matrixFLEXapproach.First-principlesresultsobtainedfromEMTO-DMFTcalculationsarediscussedinSectionIV.ThepaperissummarizedinSectionV.2II.FORMULATIONOFTHEPROBLEMThedensityfunctionaltheoryreformulatestheNelectronproblemintooneelectronproblembyconsideringanon-interactingsystem,whereeachelectronfeelsaneffectivepotentialvσeff(r)createdbytherestoftheelectronsandexternalfields.Thus,withintheDFTthesolutionoftheoriginalinhomogeneoussystemisconstructedfromtheone-electronKohn-Shamequations[2]h−∇2+vσeff(r)iΨσ(ǫ,r)=ǫΨσ(ǫ,r),(1)whereσstandsforspin.Themany-bodypartoftheeffectivepotentialμσxc(r)isanunknownfunctionalofthespindensitiesnσ(r)=Pǫ|Ψσ(ǫ,r)|2.Themostcommonlyadoptedapproachforμσxc(r)isthelocalspindensityapproximation(LSDA),wheretheeffectofinteractionsbetweenelectronsistakenintoaccountbysubstitutinglocallytherealsystembytheuniformelectrongaswiththedensityequaltotheactualdensityatpointr.InthispaperwewillnotdistinguishbetweendifferentspecificformsoftheLSDA.Inordertoincludethemany-bodycorrelationeffectsbeyondtheLSDAwesubstitutetheKohn-Shamequati