Uniaxial pressure dependencies of the phase transitions in GdMnO$_3$

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arXiv:cond-mat/0605515v1 [cond-mat.str-el] 22 May 20060(2008)1–0UniaxialpressuredependenciesofthephasetransitionsinGdMnO3

J.Baiera,D.Meiera,K.Berggolda,J.Hembergerb,A.Balbashovc,J.A.Mydosha,T.Lorenza,∗

aII.PhysikalischesInstitut,Universit¨atzuK¨oln,Z¨ulpicherStr.77,50937K¨oln,Germany

bExperimentalphysikV,Institutf¨urPhysik,UniversityofAugsburg,86135Augsburg,Germany

cMoscowPowerEngineeringInstitute,105835Moscow,Russia

GdMnO3isoneofthemultiferroicrare-earthmangan-itesRMnO3withR=Gd,Tb,andDywheremagneticandferroelectricordercoexist.[1]WhileforR=TbandDythemultiferroicbehaviorisalreadypresentinzeromag-neticfield,[2]afinitemagneticfieldalongthebaxisisnec-essarytoinducemultiferroicityinGdMnO3.Recently,wehavedeterminedtheH-Tphasediagramfordifferentfieldorientationsbymeasurementsoftheuniaxialthermalex-pansionandmagnetostrictionalongthea,b,andcaxisofGdMnO3.[3]AsshowninFig.1,thereisatransitionfromtheparamagnetic(PM)toanincommensuratean-tiferromagneticphase(ICAFM)aroundTN≃42K.Forfieldsabove≃2T,theICAFMtransformsintoacantedA-typeantiferromagnet(cAFM)aroundTc≃20K,andatransitiontoaferroelectric(FE)phaseoccursaroundTFE≃12K.Thenotations’ICAFM’and’cAFM’shouldbetreatedwithsomecaution,becausethemagneticstructureofGdMnO3hasnotyetbeendeterminedunambiguously.Withincreasingfield-strength,TNshowsaweak,andTcamoderate,increasewhileTFEpassesthroughabroadmaximumaround7T.ThePM-to-ICAFMtransitionisofsecondorder,whiletheothertwotransitionsareoffirst-orderwithverystronghysteresis,whichismostpronouncedinthelow-fieldregion.[3]Thethermalexpansionmeasure-mentsdonotonlyallowtodetectthetransitiontempera-turesTc.Togetherwithspecificheatdata,itisalsopossibletodeterminetheirdependenceonuniaxialpressurepivia

∂pi=Vm∆Li/Li∂pi

=VmTc

∆αiJ.Baieretal./0(2008)1–02102030-505

FEcAFMbaxiscaxisα(10-5/K)Temperature(K)H=2T||baaxisICAFM102030

0.04

0.05ICAFMFEε=(b−a)/(a+b)Temperature(K)cAFMFig.2.Left:ThermalexpansionofGdMnO3alongthea,b,andcaxismeasuredinamagneticfieldof2Tparalleltob.Right:Orthorhombicdistortioncalculatedviaintegrationofαaandαb(seetext).

Fig.2displaysαiofthea,b,andcaxes.Inallthreecasesamagneticfieldof2Thasbeenappliedalongthebaxis.Wehavechosenthisconfiguration,becauseonlyforfieldsabove≃2TalongbcanallthreetransitionsbeobservedinGdMnO3.Itwouldbeevenbettertousealargerfield.However,thecantedmomentofthecAFMphaseisparal-leltoc,andthetorque−→M×−→Htendstorotatethesampleinfieldsappliedalongaorb.AlongallthreeaxesαishowsverylargeanomaliesattheICAFM-to-cAFMandatthecAFM-to-FEtransition.Theanomaliesforthedifferentioccuratslightlydifferenttemperatures.Wesuspectthatthesedifferencesarisefromamisorientationofthesamplewithrespecttothefielddirection.Inthetransversecon-figurations,partofthemisorientationisduetotheabove-mentionedtorque,sincethesampleisnotcompletelyfixedduringthemeasurement.Thisproblemwouldhamperaquantitativedeterminationofthepressuredependencies.Inthefollowingwewill,however,restrictourselvestoaqualitativediscussion,sinceuptonowspecific-heatdataareonlyavailableformagneticfieldsappliedalongc.[4]BecauseanyorderingdecreasesS,theanomalies∆Sand∆chavepositivesigns.Thus,thesignsof∂Tc/∂piarede-terminedbythesignsof∆Lior∆αi.AschematicoverviewoftheexpectedchangesofTN,TcandTFEunderuniax-ialpressurealonga,b,andcisgiveninFig.3.Forthepressure-dependenciesofTNweusedourpreviousdata.[3]Thesecanbecomparedtotheincreasingstructuraldistor-tionoftheGdFeO3typeasafunctionofdecreasingionicradiusofR=La,...DyintheseriesRMnO3.[1,5]Start-ingfromacubicperovskite,theGdFeO3distortioncanbedescribedbyarotationoftheMnO6octahedraaroundthecaxisandatiltaroundthebaxis.Asaconsequence,thecaxiscontinuouslydecreasesandtheorthorhombicdistor-tionε=(b−a)/(b+a)increaseswithdecreasingradiusofR.FromR=La,...,Eu,TNofthecAFMorderingde-creasescontinuously,whileTNoftheICAFMorderslightlyincreasesfromGdtoTbanddecreasesagainfromTbtoDy.Inasimplifiedmodel[5],thedecreasingTNuntilEuarisesfromacontinuousdecreaseoftheferromagneticnearest-neighborexchangeJFMNNintheabplane,becauseofthede-creasingMn-O-Mnbondangle.Inaddition,theantiferro-magneticnext-nearest-neighborexchangeJAFMNNNbecomesanisotropic.ThecompetitionofJFMNNandJAFMNNNcausesthe

p||bICAFMcAFMPMFEp||aTCTNICAFMcAFMPMTFEFEp||cICAFMcAFM

PM

FEFig.3.DependenciesofthetransitiontemperaturesofGdMnO3onuniaxialpressurealongthea,b,andcaxis(seetext).

ICAFMorderforR=Gd,...,Dy,andcertaintypesofhelicalmagneticordermayinducealsoaFEordering.[6]AteachtransitionofGdMnO3,pacausestheoppositeef-fectaspb.Thisanti-correlationjustreflectsthebehaviorofε.Usingtheroom-temperaturelatticeconstants,wehavealsocalculatedε(T)byintegrationofαaandαb.AsshowninFig.2,theICAFM-to-cAFM(cAFM-to-FE)transitioncausesanabruptdecrease(increase)ofε.Withintheabove-mentionedmodelweinterprettheuni-axialpressuredependenciesasfollows:Pressurealongain-creasesεanddecreasesJFMNN.Asaconsequence,TNandTc