Solid StateCommunications,Vol. 24,pp.829—831,1977. PergamonPress Printedin GreatBritain

TWO-MAGNON RAMAN SCATTERING IN THE TWO-DIMENSIONAL ANTIFERROMAGNET K2FeF4

M.P.H. Thurlings,A. van derPol and H.W. deWijn

FysischLaboratorium,Rijksuniversiteit,Utrecht,The Netherlands

(Received2 July 1977by A.R. Miedema)

Two-magnonRamanscatteringin theplanarquadraticantiferromagnetK2FeF4 is investigated.Thetemperaturedependenceof the energyshiftis in goodagreementwith second-orderGreen-functiontheory,as is thelinewidthat low temperature.Numerical results,includingrenormalization,arethe HeisenbergexchangeJ/kB = —14.5±0.7K andthe anisotropy~.(T=O)=gpBHA/4jJ~s=o,I8±o.o5,butwithJ[1+~(r=o)]/k~=r— 17.06±0.10K,

THE COMPOUNDK2FeF4is a newexampleof two- thereforeexpectsafairly strong single-ionarusotropy,atdimensional(2D) quadraticlayerantiferromagnetism. leaststrongerthan in the caseof K2NiF4, of the generalThe magneticpropertieshavenotbeenstudiedpre- spinHamiltonianform D[S~— ~S(S+ 1)]. As saidbefore,viously,but, asexpected,appearto be similar to those thespinsorderin the(x,y) planesothatD >0. Theof the isomorphRb2FeF4,whichhasbeeninvestigated directionof the orderedspinswithin the planewill thenby MOssbauer[1] andneutron-scattering[2] techniques. bedeterminedby themuchweakerfourth-orderani-themagneticmomentsin K2FeF4orderbelowTN sotropyterm.TheHamiltoniancanthusbewritten as60K with the axisof magnetizationin the(x,y) plane[3]. K2FeF4thereforepresentsan interestingcontrastto ,j ~ s~Sm —gpBH~(S~’—S~) (1)K2MnF4 andK2NiF4, whichare 2D antiferromagnets o,m)with uniaxial ratherthanbasal-planeanisotropy.In thiscommunicationwe reporttwo-magnonRamanscattering wherein thesemi-classicalapproachHA = D(2S— l)/gp~as a functionof temperaturewith the objectiveto obtain is ananisotropyfield alongthex axis,andthe indices1quantitativeinformationon the magneticinteractions, andm run over the “up” and “down” sublattices,respect-theanisotropy,andthemagnondamping. ively. Anisotropyof the exchangeparameterJ, which

The specimenusedwasa singlecrystalwith dimen- will existbecauseof orbital contributions,hasbeensions3 x 3 x 6mm

3grownby a horizontalzonemelting ignoredin theHamiltonian,sinceitsprecisestrengthistechnique.Thecrystallographicstructureis tetragonal, unknownandits effectsarelargely incorporatedin anidenticalto K

2MnF4 andK2NiF4, with latticeparameters effectiveanisotropyHA.a = 4.14A andc = 12.98A at 300K [4]. In theRaman- At low temperatures(T< 4.2K) theexperimentalscatteringexperimentsthe primarylight, providedby ~ peakpositionis 184.2±0.5cm~”.Applying first-orderargon laseroperatingat 4880A, wasincident alongthe Green-functiontheorywith anOguchi-renormalized[5]z axisandpolarizedalongthex axis. Thex-polarized spin-waveHamiltonianderivedfrom equation(1) andacomponentof the light scatteredat 90°wasanalyzedby Ft-symmetryscatteringoperator,ina wayanalogoustouseof a doublemonochromatoranddetectedby photon- thatusedfor the2D uniaxialantiferromagnets[6], we findcountingtechniques.The two-magnonRamanspectrum from the T = OK positionJ[ 1 + ~(0)] /k~= — 17.06±is observedto consistof a broadasymmetricalline, 0.10K.Thisparticularcombinationof Jand~(0) maywhich with increasingtemperaturebroadensandshifts readilybeinferredfrom theJ and~(0) dependenceoftowardslowerenergies. thedispersionrelationnearthe zoneboundary,andex-

Thepeakpositionof the two-magnonline ispre- pressesa strongcorrelationof thesequantitiesasderived

sentedin Fig.1, andisseento dropby 10%overa from thelow temperaturedata.To arriveat separaterangeof 40K. In calculatingthe peakposition,we valuesforJ and~(0) it is howevermandatoryto includenotice thata preciseanalysisof thecrystal-fieldeffects thetemperaturedependenceof thepeakposition.on Fe

2+ in,K2FeF4cannotyetbedevelopedbecauseof In calculatingthe temperaturedependenceof the

lack of spectroscopicdata.However,it generallyappears peakposition(Fig. 1),wehavetakenthetemperaturevan-that thegroundstateof theFe

2” ion at a tetragonalsite ationof theanisotropy~(T)/~(0), which hasnotbeenis closelydescribedby aneffectivespinS = 2 with sig- measuredin K

2FeF4,from theisomorphRb2FeF4(TN =

nificant orbital contributionsto themoment.One 563 ±0.2K [2]) by scalingsuchasto havevanishing

829

830 RAMAN SCATTERING IN THE ANTIFERROMAGNETK2FeF4 Vol. 24,No. 12

I I I I

185— - 40- -

0

0

0o

- 30- -

E

~0~0

165 I I I I I I I I

0 10 20 30 40 50 0 10 20 30 40 50TEMPERATURE (K) TEMPERATURE (K)

Fig. 1. Peakpositionof the two-magnonRaman- Fig. 2. Full width at halfheight of the two-magnonscatteringline vs temperature.The full curve represents Raman-scatteringline vs temperature.The full curveisthe adjustedresultof Green-functiontheory. theresultof Green-functiontheorywith the parameters

deducedfrom Fig. 1.

anisotropyat TN. In Rb2FeF4,in turn, ~T) is takento treatmentof the relevantsummationsover theBrilouinvarywith thesquare[7] of the sublatticemagnetization, zonein theexpressionfor theone-magnondamping.which hasbeenmeasuredby Mössbauertechniques[1] - Theseare treatedby useof a 2D versionof a zone-Then,adjustingof the resultsof Green-functiontheory boundaryapproximation[9], which is notlikely to beincludingrenormalizationleadsto the solid curvein Fig. effectivewhen,becauseof therelatively largeamsotropy,1, correspondingtoI/k8 = — 14.5 ±0.7K and themagnon-energydistribution is ratherflat. Conse-~(0) = 0.18±0.05. Here,as alreadynoticed,theerrors quently,thecalculatedline mustbeconsideredto beain land ~(O)are stronglycorrelated,i.e.land i~(0)are lower limit only.restrictedto thosecombinationsthat satisfy thepre- In conclusion,Ramanscatteringhasprovidedinfor-scriptionJ[l + ~(O)]/k8 = — 17.06 ±0.10K. More mationon the magneticinteractionaswell asthe one-detailedinspectionof the calculationsshowsthat the magnondampingin K2FeF4.Thelatterquantityis notshift of thepeakpositionis in aboutequalpartsdue to correctlydescribedby an approximativesecond-orderthetemperature-dependentrenormalizationandthe Green-functiontheory.Theexchangeparameteris aboutdropof z~(T).It is finally notedthat the effect of 10%largerthanthevalue of 13K deducedfor Rb2FeF4renormalizationwasto reduceJ by 3.7%. [2] , a factor thatis commonlyfound betweencorre-

As Fig. 2 shows,thereisa remarkableincreaseof spondi.ngRb andK compounds.A pointof interestisthe linewidthwith temperature.The full curvein Fig. 2 thatK2FeF4is a planar2D antiferromagnet,in contrastrepresentsthe resultsof theGreen-functioncalculation to themorestudiedK2MnF4, whichis uniaxial2D. Fromto secondorder,with thevaluesfor land ~(T) obtained ~(0) and!obtainedherefor K2FeF4and~(0) = 0.0039aboveinserted.It is quitegratifying that the linewidth at and!= —8.40Kin K2MnF4 [9], onemay estimatethelow temperaturesis correctlypredicted,themoreso concentrationx at whichthespinsin the mixed corn-sincethereare no adjustableparametersinvolved. How- poundK2Mn1_~Fe~F4will flop from alongthec axis toever,the increaseof thelinewidthwith temperature, theplane.At this point theMn andFe anisotropywhich Green-functiontheorywasableto predictsuccess- energiessupposedlycancel,yieldingspin flop atfully in uniaxial 2D systems[6] ,is notsatisfactorily x = 1.8 ±0.5%,in excellentaccordancewith the findings.accountedfor. An explanationcould beinadequate of Bevaarteta!. [10].

Vol. 24,No. 12 RAMAN SCATTERING IN THE ANTIFERROMAGNETK2FeF4 831

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