First-principles approach to lattice-mediated magnetoelectri

We present a first-principles scheme for the computation of the magnetoelectric response of magnetic insulators. The method focuses on the lattice-mediated part of the magnetic response to an electric field, which we argue can be expected to be the dominan

First-principlesapproachtolattice-mediatedmagnetoelectrice ects

Jorge´I niguez

InstitutdeCi`enciadeMaterialsdeBarcelona(ICMAB-CSIC),CampusUAB,08193Bellaterra(Spain)Wepresenta rst-principlesschemeforthecomputationofthemagnetoelectricresponseofmag-neticinsulators.Themethodfocusesonthelattice-mediatedpartofthemagneticresponsetoan

electric eld,whichwearguecanbeexpectedtobethedominantcontributioninmaterialsdis-playingastrongmagnetoelectriccoupling.WeapplyourmethodtoCr2O3,arelativelysimpleandexperimentallywellstudiedmagnetoelectriccompound.

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002 raM 6 ]ics-lrtm.tam-dnco[ 16v580.3080:viXraPACSnumbers:75.80.+q,71.15.Mb

Magnetoelectric(ME)materialsareinsulatorsthatal-lowcontroloftheirmagneticpropertiesbymeansofex-ternalelectric elds[1,2],thusattractinggreattechno-logicalinterest.CurrentresearchfocusesonobtainingcompoundswitharobustMEbehavioratambientcon-ditions.Thisisprovingamajorchallenge,asprogressishamperedbyonefundamentaldi culty:thescarcityofferromagneticinsulators(nottomentionferromagneticandferroelectricmultiferroics[3])withahighCurietem-perature.Anadditionalproblempertainstothemagni-tudeofthee ect:theMEresponseisusuallyverysmall,re ectingtheweaknessofthespin-orbitinteractionsthataretypicallyresponsibleforthecoupling.

Quantumcalculationsbasedone cientschemeslikeDensityFunctionalTheory(DFT)haveprovedveryuse-fulinstudiesofmagneticandferroelectricmaterials,andareexpectedtofacilitateprogressonmagnetoelectrics.Indeed,thereisagrowingnumberofDFTworkstack-lingthesearchfornewcompounds[4]andevenpropos-ingnewcouplingmechanisms[5,6].However,westilllacka rst-principlesschemetocomputetheMEcou-plingcoe cients,somethingthatiscriticaltoaidtheexperimentalwork.InthisLetterweintroduceonesuchabinitiomethodologyanddemonstrateitsutilitywithanapplicationtoCr2O3.

Lattice-mediatedMEresponse.–ComputingthefullMEresponseofamaterialwouldrequirequantumrela-tivisticsimulationswithsimultaneouslyappliedelectricandmagnetic elds.Whilepossibleinprinciple,suchcal-culationsconstituteagreatchallengeevenforthecaseofstatic elds,anditisconvenienttolookforsimpli ca-tionsoftheproblem.

Inthefollowingargumentswewillconsideranideal-izedone-dimensional(1D)crystaldisplayingalinearMEe ect,thegeneralizationbeingstraightforward.Atzeromagnetic eld,themagnetizationinducedbytheappli-cationofanelectric eldEisgivenby:

M(E)=M(E) MS=αE+O(E2),

(1)

whereαisthelinearMEcoe cientandwehavein-cludedaspontaneousmagnetizationMSforgeneral-ity.ThemagnitudeoftheMEresponseislimitedbythemagnetic(χm)anddielectric(χd)susceptibilitiesas

α2<χdχm[7],whichsuggeststhatstrongMEcouplingswilloccurinmaterialsdisplayinglargedielectricandmagneticresponses.Onmorephysicalgrounds,onecanarguethatlargeMEe ectswillbeassociatedtosigni -cantelectronichybridizationsororbitalrearrangementsinducedbyappliedelectric elds,asitisprocessesofthatnaturethatmayleadtoamagneticresponseviathespin-orbitcoupling.Itisthenworthnotingthat(1)sucharesponsetoanelectric eldistypicalofessentiallyallhighlypolarizablecompoundsusedinapplicationsand,mostimportantly,(2)suchstrongdielectricresponsesareneverapurelyelectronice ect;rather,theyaredrivenbythestructuralchangesinducedbytheapplied eld.OnecanthusconcludethatlargeMEe ectswillmostlikelybebasedonlattice-mediatedmechanisms.

Formally,thelattice-mediatedcontributiontothedi-electricsusceptibilityisde nedasχddd

latt=χ χelec,whereχdelecaccountsforthepurelyelectronice ectcor-respondingtoclampedatomicpositionsandlatticepa-rameters.TheMEcouplingcoe cientαcanalsobede-composedinthisway,andthediscussionabovesuggeststhatαlattwillbetheleadingcontributioninmaterialsdisplayingstrongMEe ects.Weshallthusfocusonitscomputation.

Methodology.–Thestructuralresponseofaninsulatortoasmallelectric eldcanbemodeledintermsoftheinfra-red(IR)modesofthematerial,whichareobtainedfromthediagonalizationoftheforce-constantmatrixattheΓpointoftheBrillouinzone(BZ).(Workingwithsmall eldsallowsustotruncateallthefollowingTaylorseriesatthelowestorderpossible.)Letusdenotebyuitheamplitudeofthei-thIRmode,withirunningfrom1toNIR,andbyCithecorrespondingeigenvalue.Takingtheui’sandtheapplied eldEasindependentvariables,wewritetheenergyofouridealized1Dcrystalarounditsequilibriumstateas

E({ui},E)=E0+

1

We present a first-principles scheme for the computation of the magnetoelectric response of magnetic insulators. The method focuses on the lattice-mediated part of the magnetic response to an electric field, which we argue can be expected to be the dominan

2

havedecomposedthelinearpartoftheinducedpolar-izationintoelectronic(χdelecE)andlatticecontributions,thelatterbeinggivenby

Platt=

1

Ci

E.(4)

Ontheotherhand,theassumptionthatourmodelcrys-taldisplaysalinearMEe ectimplies

M({ui},E)=αelecE+

1

0

NIRmd pp

i

i

i=1

0

NIRmd pp

i

i

i=1

We present a first-principles scheme for the computation of the magnetoelectric response of magnetic insulators. The method focuses on the lattice-mediated part of the magnetic response to an electric field, which we argue can be expected to be the dominan

FIG.1:Panela:PrimitivecellofCr2O3.Solidarrowsrepre-senttheAFMgroundstate.DashedarrowssketchtheatomicdisplacementswithintheabplaneassociatedtoatypicalEuIRmode,aswellastheinducedspinrotationsthatrenderanetmagneticmoment.Panelb:ComputedpolarizationandmagnetizationinducedbythecondensationoftheIRmodes.DashedandsolidlinescorrespondtoA2uandEumodes,re-spectively.NotethatthepolarizationsandmagnetizationsassociatedtotheEu(A2u)modesliewithintheabplane(alongthecdirection).Notealsothatthemagn …… 此处隐藏：8710字，全部文档内容请下载后查看。喜欢就下载吧 ……