Structural (B1 to B8) Phase Transition in MnO unde

arXiv:cond-mat/0608101v2[cond-mat.str-el]13Dec2006Structural(B1→B8)PhaseTransitioninMnOunderPressure:ComparisonofAll-electronandPseudopotentialApproachesJindˇrichKolorenˇc∗andLubosMitasDepartmentofPhysics,NorthCarolinaStateUniversity,Raleigh,NorthCarolina27695,USA(Dated:February6,2008)WeemploythedensityfunctionaltheorytostudyastructuraltransitionofMnOfromB1(rock-salt)toB8(NiAs)structuresthatwasobservedexperimentallyatpressuresaround100GPa.Weutilizeall-electrondescriptionaswellasnorm-conservingpseudopotentialsanddemonstratethatthesetwoapproachescansignificantlydifferinquantitativepredictions.Weexplicitlyshowthatevensmall-corepseudopotentialsexhibittransferabilityinaccuraciesforquantitiessensitivetotheenergydifferencesbetweenhigh-andlow-spinpolarizationsofvalenceelectrons.PACSnumbers:72.80.Ga,71.15.-m,71.20.-b,64.30.+tI.INTRODUCTIONTransitionmetaloxideshavereceivedaconsiderableattentionofcondensedmatterphysicistsinthepastsev-eraldecades.Oneofthereasonsforsuchanelevatedinterestisthatthestandardbandtheorymethods,suchasthedensityfunctionaltheory(DFT)representedbythelocaldensityapproximation(LDA)orbyitssemi-localgeneralization(GGA),donotsatisfactorilydescribethesematerials.Forexample,theLDA/GGApredictsincorrectequilibriumcrystalstructureforFeO.1,2InthecaseofequilibriumpropertiesofMnO,theseapproxima-tionsperformreasonablywellaswasshownbyseveralgroups.3,4Thesourceofdeficienciesofsimplebandtheo-riesisagreedtobeunderestimationofcorrelationsamong3delectrons.ImprovedaccountforthesecorrelationsisneededtoadequatelycaptureMottinsulatingmechanismandthecompetingchargetransfereffects.Severalmethodshavebeendevisedtoresolvetheissueofstronglycorrelatedelectrons,suchasGW,LDA+U,self-interactioncorrection(SIC)orhybridexchange-correlationfunctionalsthatcombinelocalexchangefromLDAorGGAwithnon-localFockexchange.Perfor-manceofseveraloftheseapproacheshasrecentlybeenthoroughlycomparedinRef.5,usingthepressure-inducedhigh-spintolow-spintransition6inMnOasabenchmarktest.Itturnedoutthatalthoughthecur-rentcomputationaltechniquesworkwellforsomeas-pectoftheelectronicstructure(suchastheequilibriumvolumeorthecharacterofthegroundstateatambientpressure),theyarenotquitedependableifoneconsidershigh-pressurepropertiesofthismaterial.Oneofthegoalsofthispaperistoprovideadditionalbenchmarksfortheelectronicstructureofmanganeseoxideathighpressure,expandingthusthetestsetofRef.5.Ourmainmessagedoesnotdirectlyrelatetothe3delectronsbuttoarathersurprisingfindingthatthedeepcorestatesandthetypeofmethodusedfortheirdescriptioncansignificantlyinfluencecertainpropertiesgenerallyconsideredtoberelatedtothevalenceelec-tronsonly.AnexampleofsuchaquantityisthecriticalpressurePcforthepressure-inducedtransitionfromB1(rocksalt)toB8(NiAs)structurethathasbeenreportedrecently.7,8ThistransitionisaccompaniedbyacollapseofthelocalmagneticmomentsofMnatoms8aswellaswithelectronictransitiontoametallicstate.9Anotherkeymotivationforthisstudyofcore-valenceinteractionsincrystallineMnOisourinterestinappli-cationsofquantumMonteCarlo(QMC)techniquestotransitionmetaloxidesandothermaterialscontainingstronglycorrelatedelectrons.Theaccuraterepresenta-tionofphysicalionsbynorm-conservingpseudopoten-tialsisessentialforobtainingmeaningfulandpredictivequantumMonteCarloresultsanditisthereforecrucialtoassesstheaccuracyandlimitsofsuchpseudopoten-tialHamiltonians.Ideally,onewouldcompareresultsofpseudopotentialQMCwithall-electronQMC.Unfor-tunately,sucharouteisprohibitivelycomputationallyexpensiveatpresent.WehavethereforedecidedtocarryoutacarefulstudywithintheDFT,Hartree-Fock(HF)approximationandcombinationofthesemethods,sincetheaccuracyofone-particleorbitalsisimportantinQMCasmentionedbelowandexplainedelsewhere.10,11Similarproblemswereinvestigatedinseveraldensity-functionalstudies(e.g.,Refs.12,13,14,15)andprovidedimportantsignalsthatthechoiceofthemethodsandtreatmentofpseudopotentialscanaffectthefinalresults.Ourstudyprovidesnewinsightsinseveralimportantandcomplementarydirections.First,weemployDirac-Fockpseudopotentials,whichnominallyshouldnotre-quireanyadditionalcorrections(suchastheDFTnon-linearcorecorrectionascommentedlateron).Therea-sonforthischoiceisthatthesepseudopotentialsweredesignedtobeaccurateforcorrelatedwavefunctioncal-culationsand,infact,severaltestshavebeencarriedoutwithinbothpost-Hartree-Fock(configurationinter-action)andquantumMonteCarlomethodswithquitesatisfactoryresults.10,11Second,wewantedtoquantifythepseudopotentialvs.all-electrondifferenceswithintheDFT,HFandhybridfunctionalssinceourprevious10(andcurrentpreliminary)calculationsshowthatthehy-bridfunctionalsprovidethemostoptimalone-particleorbitals,whichminimizethefixed-nodeerrorinthequan-tumMonteCarlomethod.Theuseoftwoindepen-dentcodesandbasissetsprovidesasolidcomputational2frameworkforaccuratebenchmarkingoftheseissues.Inaddition,studyofhigh-pressurephaseaddsanotherim-portanttest,sincethedramaticchangesinelectronicstructureprobethepseudopotentialsintheregime,forwhichtheirreliabilitycannotbetakenforgranted.II.AMBIENTPRESSUREBeforeweproceedwithinvestigationoft