Probing spin correlations with phonons in the strongly frust

The spin-lattice coupling plays an important role in strongly frustrated magnets. In ZnCr$_2$O$_4$, an excellent realization of the Heisenberg antiferromagnet on the ``pyrochlore'' network, a lattice distortion relieves the geometrical frustration through

ProbingspincorrelationswithphononsinthestronglyfrustratedmagnetZnCr2O4

A.B.Sushkov,1O.Tchernyshyov,2W.Ratcli II,3S.W.Cheong,3andH.D.Drew1

MaterialsResearchScienceandEngineeringCenter,UniversityofMaryland,CollegePark,Maryland20742

2

DepartmentofPhysicsandAstronomy,TheJohnsHopkinsUniversity,Baltimore,Maryland212183

DepartmentofPhysicsandAstronomy,RutgersUniversity,Piscataway,NewJersey08854

(Dated:February2,2008)Thespin-latticecouplingplaysanimportantroleinstronglyfrustratedmagnets.InZnCr2O4,anexcellentrealizationoftheHeisenbergantiferromagnetonthe“pyrochlore”network,alatticedistortionrelievesthegeometricalfrustrationthroughaspin-Peierls-likephasetransitionatTc=12.5K.Conversely,spincorrelationsstronglyin uencetheelasticpropertiesofafrustratedmagnet.Byusinginfraredspectroscopyandpublisheddataonmagneticspeci cheat,wedemonstratethatthefrequencyofanopticalphonontripletinZnCr2O4tracksthenearest-neighborspincorrelationsaboveTc.ThesplittingofthephonontripletbelowTcprovidesawaytomeasureofthespin-Peierlsorderparameter.

PACSnumbers:75.50.Ee,78.30.Hv,75.30.Et,75.10.Hk

1

arXiv:cond-mat/0411213v2 [cond-mat.str-el] 14 Dec 2004

Geometricallyfrustratedmagnetscanresistmagneticorderingandremaininastronglycorrelatedparamag-neticstatewellbelowtheCurie-WeisstemperatureΘCW[1,2,3].ParticularlystrongfrustrationisfoundintheHeisenbergantiferromagnetonthe“pyrochlorelattice”,whereinmagneticsitesformalatticeofcorner-sharingtetrahedra.ThedynamicsofthemagnetisdeterminedbythespinHamiltonian

Si·Sj,(1)H=J

ij

(a)(b)

withtheinteractionrestrictedtonearest-neighborbonds

ij .Theoreticalinvestigationsindicatethatclassicalspinsonthislatticemaynotorderdowntozerotem-peratureCubicspinelZnCr2O4o ersagoodreal-izationofthismodel.Observationofmagneticorderatlowtemperatureshasbeenexplainedintermsofaspin-drivenJahn-Tellere ectthatisreminiscentofthespin-Peierlsinstabilityinspinchains.Thecouplingbetweenspinandlatticedegreesoffreedomthusplaysamajorroleinrelievingthegeometricalfrustration.

TheBsitesofZnCr2O4areoccupiedbymagneticionsCr3+withspinS=3/2[Fig.Acrystal eldofanearlycubicsymmetrysplitsthe ve3dorbitalsofCr3+intoat2gtripletandanegdoublet.ByHund’srules,thethreeelectronsofCr3+havealignedspins(S=3/2)andoccupyallofthethreet2gstates.Thelackoforbitalde-generacyprecludestheordinaryJahn-Tellere ectcom-montospinelsandensuresaverysmallspinanisotropy[7].Theshapeofthet2gorbitals,pointingtowardstheneighboringCr3+ions,makesdirectexchangethepri-marymechanismformagneticinteractions11].Asaresult,interactionsbeyondnearestneighborsareneg-ligiblysmall,whilethenearest-neighborinteractionsarehighlysensitivetothemotionofCr3+ionscreatingastrongspin-phononcoupling.

ThemagneticsusceptibilityofZnCr2O4followsthe

FIG.1:(a)One(outof ve)ofthesymmetrycoordinatesoftheF1umodewhichmodulatesCr–Crexchange,arrowsshowdisplacements;(b)spinorderingexpectedforatetragonallydistortedtetrahedroninZnCr2O4,arrowsindicatespins.

Curie-WeisslawathightemperatureswithΘCW=390K,whichgivesthenearest-neighborexchangecou-plingJ=4.5meVAsthetemperatureisloweredbelowΘCW,themagnetgraduallyentersaparamagneticstatewithstrongcorrelationsbetweenspinsbutnomag-neticorder:thespinsliquidbuttheirmotionsarehighlycoordinated[12].AtTc=12.5Kthemag-netundergoesa rst-ordertransitionintoaphasewithantiferromagneticorderandastructuraldistortion[7].Accordingtothetheory[8,9,13],thephasetransitionisdrivenbylocaldistortionsofthetetrahedrathathavetheEsymmetryinthelanguageofthetetrahedralpointgroupTd.ThisisconsistentwiththeobservationofatetragonaldistortionbelowTc[7].

Inthisworkwedemonstratethatlatticevibrationscanprovidequantitativeinformationaboutspincorrelations.WehavemeasuredthefrequenciesofIR-activephononsandfound,belowthemagnetoelasticphasetransition,alargesplittingofaphononmodeinvolvingmagneticions.

The spin-lattice coupling plays an important role in strongly frustrated magnets. In ZnCr$_2$O$_4$, an excellent realization of the Heisenberg antiferromagnet on the ``pyrochlore'' network, a lattice distortion relieves the geometrical frustration through

y

tivitcelfeR200300400500600700800

Wave number (cm)

FIG.2:(Coloronline)Topcurve:RLT—re ectivity

spectrumofZnCr2O4singlecrystalinthelow-temperaturephase;bottomcurve:2(RLT RHT);inset:RLTandRHT(line+symbols)inanarrowrange.

Fromthemagnitudeofthesplittingwehaveinferredtheabsolutevalueofthespin-Peierlsorderparameter Si·Sj Sk·Sl ,where ij and kl arenearest-neighborbonds[13].

Experimentaldetails.PowdersofZnCr2O4werepre-paredinairusingthestandardsolidstatereactionmethod.SmallsinglecrystalsofZnCr2O4weregrownusingthesepowdersusingchemicaltransportmethodinquartztubessealedwithCl2gasasatransportagent.Thecrystalswereofregularhabitwiththe 111 faceclearlyvisible.Theworkingsurfaceofoursampleistiltedslightly(～3.5 )fromthe 111 planeasdeterminedbyX-rays.Re ectivitymeasurementswereperformedusingaFourier-transformspectrometerinthefrequencyrangefrom100to5000cm 1.Thetemperaturedependencefrom6to300Kwasmeasuredusingliquidheliuminacontinuous owcryostat(sampleinvacuum)withopticalaccesswindows.

Theroomtemperaturephononspectrumofcubicspinelsiswellstudied.Ourmeasurementsatroomtem-peratureagreewithpreviouslypublisheddataforsin-glecrystalsofZnCr2O4[14].Asexpectedonsymmetrygrounds,thespectrumconsistsoffourphonontripletsoftheF1usymmetry(pointgroupOh,spacegroupFd¯3m).Figure2showsthere ectivityspectrumRLTforthelow-temperature(LT)phaseaveragedoverthetemperaturerangefrom9to11K.Italsoshowsamagni eddi er-enceofthespectra2(RLT RHT),whereRHTisthere- ectivityspectrumaveragedbetween13and14K.Themostprominent …… 此处隐藏：12376字，全部文档内容请下载后查看。喜欢就下载吧 ……