M Sandratskii and P Bruno MaxPlanck Institut f ur Mikrostrukturphysik Weinberg 2 D06120 Halle Germany lsandrmpihallede brunompihallede Abstract We report the densityfunctionaltheory calculations of the exchange interactions and Curie temperature for ID: 23767
Download Pdf The PPT/PDF document "Part II Diluted Magnetic Semiconductors ..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
First-PrinciplesStudyoftheMagnetismofDMS115istheroleoftheCoulombcorrelationsofthe3delectrons.Theso-calledLDA+Umethodintroducesexplicitlytheon-siteCoulombinteraction(Hub-)andleadstoabetterdescriptionofmanysystemswithstrongCoulombcorrelations[].However,thesuperiorityoftheLDA+Umethodisnotuniversal.Fornumeroussystemswith3datomstheLDAgivesbetteragreementwithexperiment.Inthepaper,wereportbothLDAandLDA+UcalculationsforanumberofDMS.TheinuenceofHubbardonvariouselectronpropertiesofthesystemsisanalyzed.Wherepossibletheresultsofbothcalculationsarecom-paredwithexperimenttoestablishwhichoftwoapproachesprovidesbetterdescriptionoftheDMSstudied.2CalculationalTechniqueThecalculationalschemeisdiscussedin[]towhichthereaderisreferredformoredetails.TheschemeisbasedonDFTcalculationsforsupercellsofsemiconductorcrystalswithonecationatomreplacedbyaMnatom.ThesizeofthesupercelldeterminestheMnconcentration.Mostofthecalculationsareperformedforthezinc-blendecrystalstructureofthesemiconductormatrix.Tocalculatetheinteratomicexchangeinteractionsweusethefrozen-magnontechniqueandmaptheresultsofcalculationofthetotalenergyofthehelicalmagneticcongurations=(cos()sin)sin)(1)ontoaclassicalHeisenbergHamiltonianeffisanexchangeinteractionbetweentwoMnsites(i,j)andistheunitvectorpointinginthedirectionofthemagneticmomentatsitearethelatticevectors,isthewavevectorofthehelix,polaranglegivesthedeviationofthemomentsfromtheAdeviationoftheatomicmomentsfromtheparalleldirectionscausesachangeoftheatomicexchange-correlationpotentials[]whichleadstoaperturbationoftheelectronstates.Thevalueoftheperturbationofagivenstatedependsonotherstatesofthesystem,bothoccupiedandempty,sincethesestatesenterthesecularmatrixoftheproblem.WithintheHeisenbergmodel()theenergyoffrozen-magnoncongura-tionscanberepresentedintheform)(3) First-PrinciplesStudyoftheMagnetismofDMS117Theeigenvaluesofthematrix()havetheform )(8) 4(HH+)21 2 (HH+ 4 2)1 andareillustratedinFig. -0.4-0.200.20.4 01234energy (abit. units) magnon q Fig.1.Theenergybands(thicksolidline)ofthespiralstructurewith=2,and=45).Thelatticeparameterisassumedtobeunity.Thethinsolidlinesshowthebandsofaferromagneticconguration.ThebrokenlinesgivetheferromagneticbandsshiftedinthereciprocalspaceaccordingtothegivenForcompletelylledbandsthetotalenergy ((k)++(k)]= )(9)doesnotdependonmagneticconguration.[isthevolumeoftheBril-louinzone(BZ)].Thismeansthatthekineticexchangetakenintoaccountby()doesnotcontributeintoeectiveintersiteexchangeinteractioninthecaseofcompletelylledbands.Foralmostemptyandalmostlledbandstheminimumofthetotalen-ergyalwayscorrespondstotheferromagneticconguration.Foradetailedproofofthisstatementthereaderisreferredto[].Figureillustratesthatundertheinuenceofthefrozenmagnonthebandsbecomenarrower:Theminimalelectronenergyoftheferromagnetislowerthantheminimalelec-tronenergyofthespiralandthemaximalelectronenergyoftheferromagnetishigherthanthemaximalenergyofthespiral.Incombinationwith()thisissucienttoprovethatsmallnumberofelectronsorsmallnumberofholesleadtotheferromagneticgroundstate. 118L.M.SandratskiiandP.BrunoThuswithinthemodelofasinglespin-degeneratedbandinafrozen-magnonexchangeeldthepresenceofholesmakestheferromagneticstruc-turefavorable.Inthefollowingsectionsweshowthattheimportanceoftheholesforestablishingferromagneticorderispreservedinthefull scaleDFT4Resultsfor(GaMn)As,(GaCr)As,(GaFe)AsNextweconsidercalculationsforthreeIII-VDMS:(GaMn)As,(GaMn)Asand(GaFe)As.FigurepresentstheDOSofthesystemsfortheimpurityconcentrationof3.125%.ForcomparisontheGaAsDOSisshown.Inthecaseof(GaMn)AsthereplacementofoneGaatominthesupercellofGaAsbyaMnatomdoesnotchangethenumberofspin-downstatesinthevalenceband.Inthespin-upchanelthereare,however,veadditionalenergybandswhicharerelatedtotheMn3dstates.Sincethereareveextraenergybandsandonlyfourextravalenceelectrons(theatomiccongurationsofGaandMnare4sand3d)thevalencebandisnotlledandthereappearunoccupied(hole)statesatthetopofthevalenceband.ThereisexactlyoneholeperMnatom.In(GaCr)As,theCr3dstatesassumeahigherenergypositionrelativetothesemiconductor-matrixstatesthantheMn3dstatesin(GaMn)As.Asaresult,thespin-upimpuritybandisseparatedfromthevalencebandandliesinthesemiconductinggapofGaAs.Thisimpuritybandcontainsthreeenergybands.SinceCrhasoneelectronlessthanMn,onlyonethirdoftheimpuritybandisoccupied:theoccupiedpartcontainsoneelectronperCratomandthereisplaceforfurthertwoelectrons. -0.4-0.20 -20020DOS(states/Ry) -0.4-0.20 -0.4-0.20 -0.4-0.20 1e/Cr GaAs (GaFe)As Fig.2.Thespin-resolvedDOSfor(GaMn)As,(GaCr)As,(GaFe)As.Forcompar-isontheDOSofGaAsisshown.TheconcentrationofMnis3.125%.Upperpartofthegraphshowsspin-upDOS.TheinsertszoomtheimportantenergyregionsabouttheFermilevel.In(GaMn)AsthereisoneholeperMnatom.In(GaCr)AsthereisoneelectronperCratomintheimpurityband 120L.M.SandratskiiandP.Bruno -101 -400-2000200400Curie Temperature (K) -101 -101 3.125%6.25%(GaFe)As3.125%6.25%12.5%6.25%3.125% Fig.4.TheCurietemperatureasafunctionoftheelectronnumber.isthenum-beroftheexcesselectrons(ormissingelectronsfornegativevalues)permagneticimpurityatom.Thenominalelectronnumbercorrespondsto=0.Inallcasesofcompletelylledelectronbands(kinksonthecurves)theprevailingexchangeinteractionsareantiferromagnetic 00.10.2 -1000100200300500Curie Temperature (K) n=-0.4n=0.0n=0.2n=0.4n=0.6n=0.8*experiment Fig.5.TheCurietemperatureof(GaMn)AsasafunctionofMnconcentrationfordierentnumbersofholes.Theexperimentalvaluesaretakenfrom[InFig.weshowtheCurietemperatureasafunctionofMnconcentrationfordierentnumbersofholesperMnatom.Forthecaseof6(thatis0.4holeperMnatom)thecalculatedCurietemperaturesareclosetotheexperimentalvalues.In(GaCr)Asthesituationisdierent.BecauseofadecreasednumberofvalenceelectronstheimpuritybandcanaccepttwofurtherelectronsperCratomandisfarfromthefulloccupation.Asaresultthedonordefectsdonot First-PrinciplesStudyoftheMagnetismofDMS123 DelocalizationPolarizationOrdering Fig.8.Bothdelocalizationoftheholesandtheexchangeinteractionhole-impurityarecrucialforestablishingferromagneticorder.Theupperlineshowsschematicallytheholeslocalizedabouttheimpurityatoms.Theholesarestronglyspin-polarizedbutdonotmediatetheexchangeinteractionbetweenimpurities.Inthesecondline,theholesarenotdisturbedbytheimpuritiesandarecompletelydelocalized.They,however,arenotspin-polarizedbytheimpuritiesandalsocannotmediatetheexchangeinteraction.Thethirdlinepresentsanintermediatesituation:Theholestatesaredisturbedbytheimpurities.Theyare,however,notcompletelylocalizedabouttheimpurity.Combinationofthedelocalizationandspin-polarizationallowstomediateexchangeinteractionbetweenMnatomswhichappearsasaconsequenceoftheinteractionofthesestateswithMn3delectrons.In(istheaverageatomicspinmomentsofthemagneticistheimpurityconcentration.However,theapplicabilityofthemean-eldapproachisnotself-evidentandneedstobeinvestigated.TheanalysisoftheexperimentaldatashowsthatforII-VIDMSthevalueiswellestablished[].ForIII-Vsystemsthesituationisdierent.Forinstance,theexperimentalestimationsofmadefor(GaMn)Asonthebasisofdierentexperimentaltechniquesvarystronglyfromlargevaluesof3eV[]and5eV[]toamuchsmallervalueof2eV[].(Negativecorrespondstoantiparalleldirectionsofthespinsofthedandpstates.)InFig.wepresentthecalculatedexchangesplittingatthetopofthevalencebandin(ZnMn)Se.ForlowMnconcentrationsthissystemisparamagneticuptoverylowtemperatures.Itshows,however,agiantZeemansplittinginexternalmagneticeld.ThegiantZeemansplittingrevealsstrongp dexchangeinteraction.TwoDFTapproachesareused:LDAandLDA+U(Fig.).TheLDA+Uexchangesplittingsarewelldescribedbythemean-eldformula()thatassumesproportionalitybetweenthesplittingandtheMnconcentration.Thecoecientproportionalitygivesthevalueof3eVinverygoodagreementwithexperiment.Ontheotherhand,theLDAresultsde-viatestronglyfromthemean-eldbehavior.TheLDAcalculationsdoesnotgivetheproportionalitybetweensplittingandconcentration.Correspond-ingly,theratiobetweenthesplittingandtheconcentrationvarieswiththe First-PrinciplesStudyoftheMagnetismofDMS125bandtheaccountforHubbardresultsinastrongdecreaseoftheMn3dcontributioninthisenergyregion.Thefailureofthemean-eldtreatmenttodescribetheLDAsplittingsisdirectlyrelatedtothestrongadmixtureoftheMn3dstates.SincetheatomicMnmomentin(ZnMn)SedoesnotdependsubstantiallyontheMnconcentrationtheexchangesplittingoftheMn3dstatescannotbedescribedwithinamean-eldapproximation.Summarizingweformulatesomeconclusions:First,inthecaseofsub-stantialadmixtureoftheimpurity3dstatestothestatesatthetopofthevalencebandthemean-eldapproachtothecharacterizationofthep dinter-actiondoesnotapply.Second,inthecaseof(ZnMn)SetheapplicationoftheLDA+UschemeleadstotheshiftoftheMn3dspin-upstatesfromthetopofthevalencebandtolowerenergiesmakingthemean-eldapproximationapplicable.Third,for(ZnMn)SetheLDA+UgivesbetteroverallagreementwithexperimentthanLDA[7ComparativeStudyof(GaMn)Asand(GaMn)NInthissectionwecomparethemagnetismoftwoprototypesystems,(GaMn)Asand(GaMn)N,focusingagainonthepropertiesoftheholes.Tocircumventthedicultyoftheestimationoftheparameterwewillchar-acterizethestrengthofthep dinteractionbythevalueoftheadmixtureofthe3dstatestothehole.Thisquantityisdiculttomeasurebutitiseasilyaccessibletheoretically.Thissectionisbasedonthepaper[InFigs.,wepresenttheDOSof(GaMn)Asand(GaMn)Nfor5%.ThemainfeaturesoftheDOSdiscussedbelowarevalidalsoforotherMnconcentrations.Wefoundthat(GaMn)Asand(GaMn)NdierstronglyinbothLDAandLDA+Ucalculations.InLDA,thespin-upimpuritybandof(GaMn)Asmergeswiththevalenceband.Ontheotherhand,in(GaMn)Ntheimpuritybandliesinthesemiconductinggap.(Weperformedcalculationsforbothzinc-blendeandwurzitecrystalstructuresof(GaMn)N.Themainpartoftheresultsisqualitativelysimilarforbothcrystalstructures.)Forbothsys-temstheLDAcalculationsgivelargeMn3dcontributionintoimpuritybandIntheLDA+Ucalculations,theimpuritybandof(GaMn)Asdisappearsfromtheenergyregionatthetopofthevalenceband.Incontrast,(GaMn)Nstillpossessesimpuritybandwhichliesnowclosertothevalenceband.TheMn3dcontributiontotheimpuritybanddecreasescomparedwiththeLDA-DOSbutisstilllarge(Fig.Nowweturntothediscussionofthepropertiesoftheholes.WeagainpresenttheresultsforoneMnconcentration.FromFig.andTableseethatforthecalculationsperformedwithinthesamecalculationalschemetheholesin(GaMn)NaremuchstrongerlocalizedabouttheMnatomthan 128L.M.SandratskiiandP.Bruno -2 -101 0 -1012 (GaMn)N 3.125% Fig.14.asafunctionoftheelectronnumberfor=0correspondstothenominalelectronnumber(oneholeperMnatom)thecontributionoftheAndersonssuperexchange.Bothcontributionsplayanimportantrole(Fig.).ThusthenalvalueoftheCurietemperaturecanbeinterpretedasaresultofthecompetitionbetweenantiferromagneticsuperexchangethroughthelledbandsandferromagnetickineticexchangemediatedbytheholes.ItisremarkablethatHubbardproducesoppositetrendsinthevariationofTin(GaMn)Asand(GaMn)N(Fig.).Takingthenominalnumberofelectrons(=0)wegetastrongdecreaseoftheCurietemperaturein(GaMn)Asandasubstantialincreasein(GaMn)N.Thereforein(GaMn)Asthestrongdropofthep dinteractionprevailsoverthedelocalizationoftheholes.Ontheotherhand,in(GaMn)Ntheincreaseddelocalizationoftheholesprevailsoverdecreasedp dinteraction.ThecomparisonoftheroleoffordierentMnconcentrations(Fig.showsthatin(GaMn)NthesametrendtoincreasingCurietemperatureisobtainedforthewholeintervalofconcentrationsstudied.In(GaMn)As 600 C, LDA 00.10.2 0600K( erutarepmet eiruC C, L+U (GaMn)As Fig.15.asafunctionoftheMnconcentrationfornominalelectronnumber