CaFeO3 and La0.33Sr0.67FeO3

PHYSICALREVIEWB71,245110?2005?

RamanscatteringinCaFeO3andLa0.33Sr0.67FeO3acrossthecharge-disproportionation

phasetransition

ShankarGhosh,1N.Kamaraju,1M.Seto,2A.Fujimori,3Y.Takeda,4S.Ishiwata,5S.Kawasaki,5M.Azuma,5

M.Takano,5andA.K.Sood1,*

DepartmentofPhysics,IndianInstituteofScience,Bangalore560012,IndiaResearchReactorInstitute,KyotoUniversity,Kumatori-cho,Osaka590-0494,Japan

3

DepartmentofPhysicsandDepartmentofComplexityScienceandEngineering,UniversityofTokyo,Bunkyo-ku,

Tokyo113-0033,Japan

4DepartmentofChemistry,MieUniversity,Tsu514-8507,Japan5

InstituteofChemicalResearch,KyotoUniversity,Uji,Kyoto611-0011,Japan

?Received14February2005;published22June2005?

2

1

Temperature-dependentmicro-RamanstudiesoforthorhombicCaFeO3andrhombohedralLa0.33Sr0.67FeO3werecarriedoutwithanaimtostudytheroleofalatticeintheformationofthecharge-disproportionedstate?Fe4+→Fe5++Fe3+?belowthetransitiontemperature?Tco?of290and200K,respectively.Shell-modellattice-dynamicalcalculationswereperformedforCaFeO3toassigntheRamanmodesanddeterminetheirvibrationalpattern.Thetemperaturedependenceofthepeakpositionsandthepeakwidthsofvariousmodesforbothsystemsshowdistinctchangesacrosstheirrespectivetransitiontemperatures.InCaFeO3,thesymmetric-stretchingmodeat707cm?1splitsintotwomodes,707cm?1and684cm?1,correspondingtothebreathing-typedistortionoftheFeO6octahedra.Incomparison,thespectralfeatureat704cm?1inLa0.33Sr0.67FeO3,whichhasbeenassignedtotheRaman-forbiddensymmetric-stretchingmode,disappearsbelowTco.Theseobservationsindicatethepresenceof?niteJahn-TellerdistortionsoftheFeO6octahedrainCaFeO3intheentiretemperaturerange,whereasthesedistortionsarepresentonlyaboveTcoinLa0.33Sr0.67FeO3.Twomodesat307cm?1and380cm?1inLa0.33Sr0.67FeO3approacheachotheratTco,indicatingareductionofrhombo-hedraldistortionsbelowTco.DOI:10.1103/PhysRevB.71.245110

PACSnumber?s?:71.27.?a,71.30.?h

I.INTRODUCTION

Inrecentyears,stronglyelectroncorrelatedthree-dimensional?3D?transition-metaloxideshaverevealedarichvarietyofinterestingphysicalphenomena,suchasthemetal-insulatortransitionandorderingofcharge,spin,andorbitaldegreesoffreedom.1Inthisclass,ironpervoskitescontainingironinFe4+?d4?,namelyCaFeO3?CFO?andLa0.33Sr0.67FeO3?LSFO?,areinterestingsystemsinwhichtoexploretheroleofelectron-latticeinteractionsvis-à-vistheelectroncorrelationsinunderstandingthecharge-order?CO?transitionassociatedwithchargedisproportion.Inthesesys-tems,theproposedelectroniccon?gurationoftheFeO6oc-tahedronisnotFe4+?O6?12?,butisclosetoFe3+?O6?11?,

??L?standsforaholeinthewhichisexpressedasFe3+L

oxygen2porbitals?.SincethegroundstateofFeinthese

??ratherthanFe4+?3d4?,systemsispredominantlyFe3+?3d5L

theJahn-Teller?JT?distortionsinthesesystemsarenotexpectedtobelarge.2ThetransitionofCFOfromanorthorhombicmetal?T?Tco?toacharge-orderedmono-clinicsemiconductor3atTco=290Kisassociatedwithchargedisproportion2Fe3++L?→Fe3+?largeoctahedra?

?2?smalloctahedra??nominallywrittenas2Fe4++Fe3+L

→Fe3++Fe5+?.Astemperatureisloweredfurther,thereisanothertransitionfromtheparamagneticinsulatortoanan-tiferromagneticinsulatoratTN=115K.Ontheotherhand,LSFOwithaformalvalueofFe3.67showsacharge-ordering

?2/3→2Fe3++Fe3+L?2.transition4atTco=200K,i.e.,2Fe3+L

Thelow-temperature?T?Tco?phaseexhibitschargedispro-1098-0121/2005/71?24?/245110?7?/$23.00

portionwithFe3+:Fe5+?2:1inthe?111?direction.5Theoc-tahedraldistortionresultingfromtheorderingofFe3+andFe5+statesisreferredtoasafreezingofabreathingphononmode.Thecharge-disproportionedstatesinbothsystemshavebeenwellestablishedexperimentallyusingMössbauerspectroscopy.16–18

RecentphotoemissionandunrestrictedHartree-Fockband-structurecalculations4havesuggesteddifferentroutestochargedisproportioninCFOandLSFO.Ithasbeenar-guedthatbothbreathingandtiltingdistortionsofFeO6arenecessarytoinducechargedisproportioninCFO,whereasonlyelectroncorrelationsholdthekeytochargedispropor-tioninLSFO.Neutron-diffractionexperiments6inLSFOshowedthatFe-Obondlengthsremainalmostthesameinthetemperaturerange300–50K,whereastheFe-O-Febondangledecreasesslightlyfrom174°to171°.However,morerecentneutron-scatteringexperiments7showthattheFe-Obondlengthdecreasesslightlyfrom1.939Åat300Kto1.936Åat15K,whiletheFe-O-Febondangledecreasesfrom173.29°to172.89°.

Recentnuclearresonantscatteringmeasurements8ofCFOandLSFOshowedthatthephonondensityofstates?DOS?forbothsystemschangesinthespectralregionof300–500cm?1acrosstheirrespectiveTco’s.However,thechangesintheDOSwerefoundtobemorepronouncedforCFOascomparedtoLSFO.TheobjectiveofthepresentworkistoaddresstheroleofalatticeintheCOtransitioninthesesystemsusingRamanspectroscopy,whichhasbeenusedveryeffectivelyinrecentstudiesofmagnetite9and

©2005TheAmericanPhysicalSociety

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GHOSHetal.PHYSICALREVIEWB71,245110?2005?

manganites10–14acrossthemetal-insulatorandcharge-orderingtransitions.

II.EXPERIENTIALDETAILS

PolycrystallinesamplesofCFOandLSFOwerepreparedbysolid-statereactionsandasubsequenttreatmentunderhigh-pressureoxygen,asdescribedearlier.15Thephasetran-sitionsasdescribedabovewerecharacterizedbyelectricalmeasurementsandMössbauerspectroscopy.16Confocalmicro-RamanstudiesonthesepolycrystallineCFOandLSFOsampleswerecarriedoutinbackscatteringgeometryusingaDILOR-XYinstrumentequippedwithaliquid-nitrogen-cooledCCDdetector.Ramanspectrawererecordedusing514.5nmradiationofanargon-ionlaserwithapowerof5mWusinga50?longworkingdistanceobjective.Atemperaturerangeof330–4.2Kwascoveredusingacontinuous-?owheliumcryostatfromM/sOxford,UK.Thepolycrystallinesamplesusedconsistedofirregularlyshapedopticallyisotropicgrains.Itwas,therefore,possibletoobtainonlytwotypesofpolarizationspectra:HH?Ei?Es?andHV?Ei?Es?polarizationsoftheincident?i?andscattered?s?electric?elds?E?.

III.RESULTSANDDISCUSSIONSA.Ramanspectraatroomtemperature

FIG.1.Roomtemperature,i.e.,300KRamanspectraof?a?CFOand?b?LSFO.ThedottedlinesareLorentzian?tstothedata.TheCFOspectrumcanberesolvedintoeightmodeswhiletheLSFOspectrumcanberesolvedintosevenmodes.Thecorrespond-ingmodesarelabeledinthe?gure.

CFOisanorthorhombiccrystalhavingaGdFeO3struc-tureatroomtemperaturebelongingtothespacegroupPnma.Ithasfourformulaunitsperunitcell.TheCaionsoccupythe4c?x,1/4,z?site,theplanaroxygen?O1??x,y,z?ionsoccupythe8dsite,theapicaloxygen?O2?ionsoccupythe4c?x,1/4,z?site,whiletheFeionsoccupythe4b?0,0,1/2?site.Accordingly,ithas24zone-centerRaman-activemodesgivenbyirreduciblerepresentationsas7Ag+7B1g+5B2g+5B3g.12Inallthesemodes,Feionsdonotmove.Sixteenofthe24Raman-activemodesinvolvevibra-tionsoftheFeO6octahedra,whiletheremainingeightmodesinvolvemotionofCaions.19Incomparison,LSFOhasarhombohedralstructureandbelongstothespacegroupR¯3cwithtwoformulaunitsperunitcell.TheLa/Srionsoccupythe2a?1/4,1/4,1/4?,theOions6e?x,?x+1/2,1/4?,andtheFeions2b?0,0,0?sites.The27opticalmodesareclas-si?edasA1g?R?+4Eg?R?+3A2u?IR?+5Eu?IR?+2A1u+3A2g.12Ofthe?veRaman-activemodes,four?3Eg+1Ag?involvevibrationsassociatedwiththeFeO6octahedrawhilethere-mainingEgmodeinvolvesvibrationofLa/Srions.11,20

Figure1showsRamanspectraofCFO?panel?a??andLSFO?panel?b??atroomtemperature.ItcanbeseenthattheobservedRamanspectra?shownby?lledcircles?canbe?ttedtoasumofn-Lorentzians?shownbysolidlines,n=8forCFOandn=7forLSFO?.Theindi-vidualcomponentsareshownbydottedlines.TheeightmodesofCFO,labeledasW1¯W8,are149cm?1?W1?,

218cm?1?W3?,305cm?1?W4?,197cm?1?W2?,

844cm?1?W6?,898cm?1?W7?,and707cm?1?W5?,

?1

922cm?W8?.TheRamanspectrumofLSFOshowssevenbandslabeledasM1¯M7:251cm?1?M1?,

307cm?1?M2?,380cm?1?M3?,704cm?1?M4?,843cm?1?M5?,897cm?1?M6?,and920cm?1?M7?.WenotethatbothCFO?orthorhombic?andLSFO?rhombohedral?haveverysimilarRamanspectra.SuchasimilarityhasalsobeenseeninthecaseoforthorhombicandrhombohedralmanganiteswhenJahn-Tellerdistortions11aresmall.ThisisbecausethebendingandthetiltmodesoftheMnO6octahe-draareverysimilarinbothstructures?seeFigs.4?a?and6?b?ofRef.11?.Beforeweshowthetemperaturedependenceofthemodes,wewillpresentthelattice-dynamicalcalculationstoassigntheobservedRamanbands.

B.Lattice-dynamicalcalculationsandmodeassignments

Thelattice-dynamicscalculations?LDC?forthephononsofCFOattheBrillouin-zonecenterwerecarriedoutusingtheshellmodel.21Thelong-rangeinteractionsbetweeneachpairofionsweretakentobeofCoulombicform,whiletheshort-rangeinteractionsbetweentheshellsweretakentobeofBorn-Mayer-Buckinghanform,

Vkk??rij?=Akk?exp??rij/Rkk???Ckk?/r6ij,

whererijisthedistancebetweenthetwoionsiandjof

specieskandk?,respectively.TheparametersAkk?,Rkk?,andCkk?aregiveninTableI.Intheshellmodel,eachionofchargeZ?e?isrepresentedbyamasslessshellofchargeY?e?andacoreofcharge?Z?Y??e?.TheshellsareelasticallyboundtothecoreswithaforceconstantKwhosevaluesaregiveninTableI.TheparametersusedforCFOarethesameasforCaMnO3,19exceptforthevalueoftheshellcharge?Y?e??forFeandO:Y?Fe?=2.5ascomparedtoY?Mn?=2.3;Y?O?=?2.1inCFO;andY?O?=?3.0inCaMnO3.ThesechangesinthevalueofYwereguidedtoreproducetheex-perimentallyobservedsymmetricstretchvibrationfrequency?W5mode?.ThereducedvalueofY?O?inCFOislikelyduetothelocalizationoftheholeontheoxygeninthesesys-tems.Assignmentofthesymmetryforanormalmodevibra-tionwasdeterminedbynotingthateachnormalmodetrans-formsasrequiredbythecharactersoftherepresentationtowhichitbelongs.Thecharacter???ofaneigenvector,EV,

of

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TABLEI.Parametersoftheshellmodeldescribedinthetext.Z,theioniccharge;Y,shellcharge;K,core-shellforceconstant.Akk?

,Rkk?,andCkk?areparametersoftheBorn-Mayer-Buckinghanpotential.ionCaOFe

Z?e?1.91?1.913.82

Y?e?3.5?2.12.5

K?Nm?1?18821037121881

ionicpairCa-OO-OFe-O

Akk??eV?84022764900

Rkk??Å?0.3670.1490310.374532

Ckk??eVÅ6?020.370

amodeunderaparticularsymmetryoperationisobtainedby?=EV·ES,whereESisthesymmetry-transformedEV.WehaverepeatedourcalculationsforCaMnO3withtheparam-etersasinRef.19,andtheresultsforsymmetryassignments?showninFig.3ofRef.19?agreeexactlywithours,thusputtingcon?denceinourcalculationsforthecaseofCFO.TheeigenvectoranalysisoftheopticalmodesofCFOgives24Raman-activemodes.Thefrequenciesofthe?vemodes?W1¯W5?observedinourexperimentsareveryclosetothecalculatedRamanmodes,thushelpingustoassignthevibra-tionalpatternsofthesemodes,asgiveninTableIandshowninFig.2.Thelow-frequencyW1?149cm?1?modeisassoci-atedwiththeAgin-phaseyrotation?seenat160cm?1inCaMnO3?,theW2?197cm?1?modeisassociatedwiththeB1gout-of-phaseyrotation?seenat179cm?1inCaMnO3?,andtheW3?218cm?1?modeisassociatedwiththeAgout-of-phasexrotation?seenat184cm?1inCaMnO3?.TheW4?305cm?1?modeisclosetothecalculatedB1gmodeat301cm?1associatedwithin-phasexrotationaswellastotheB2g?302cm?1?modeinvolvingthemixedmotionofCaandOions.ItisalsoseenthatLSFOhasaRamanbandat307cm?1?M2?.SincethevibrationalpatternofW4andM2modesisexpectedtobesimilar,theymaynotinvolveionsofverydifferentmasses?i.e.,Cavis-à-visLaandSr?.22ThusweassociatetheW4modewiththeB1gin-phasexrotationoftheadjacentFeO6octahedra,similartotheB1gassignmentofthe?320cm?1modeintherare-earthorthoferritesRFeO3?R=Y,Tb,Ho,Er,andTm?.23TheW5?707cm?1?modeisassociatedwiththeB2gsymmetricstretchingoftheFeO6octahedra.Thecorrespondingmodeisseenat611cm?1inLaMnO3?predictedbyLDCtobeat669cm?1?.24Forisos-

tructuralorthorhombicCaMnO3,theLDCpredictstheoccur-renceofthismodeat749cm?1.However,inCaMnO3thismodeisexperimentallynotobserved.19ThereasonforthishasbeenattributedtothelackofJTdistortioninCaMnO3.ThusthepresenceoftheW5modeintheRamanspectraimpliesthatsomeamountofJT-typedistortionispresentatroomtemperatureinCFO,indicatingtheexistenceofaJT

?,state.TheFe4+ionicstatealongwiththenon-JT,Fe3+L

LDCofCFOdonotyieldanyphononmodesabove730cm?1andhenceweexpectthehigh-frequencymodesW6?844cm?1?,W7?898cm?1?,andW8?922cm?1?tobeduetothetwo-phononRaman-scatteringprocess,probablyin-volvingtheW5phononalongwithotherlow-frequencymodes.Forexample,theone-phonondensityofstatesofCFOatroomtemperature8showsprominentbandsat?137cm?1and?190cm?1.TheW6modecanbeacombi-nationof?707cm?1and?137cm?1phonons;W7canbe707cm?1and191cm?1andW8?707cm?1and218cm?1modes.

TheassignmentoftheRamanmodesobservedinLSFOwasguidedbytheexperimentallyobservedRamanmodesandtheLDCperformedbyAbrashevetal.20fortherhom-bohedralr-LaMnO3.TheM1?251cm?1?modeisassignedtotheA1grotationalmodeofFeO6octahedra.20Itcorrespondstotheobservedmodeat236cm?1?249cm?1inLDC?inr-LaMnO3.TheothermodesM2,M3,M4arenotclosetoanyoftheotherfourRaman-activemodescalculatedinr-LaMnO3.20Thesefourmodesforr-LaMnO3arecalculatedtobeat42,163,468,and646cm?1.20However,thefrequen-ciesofM2andM3areclosetothecalculatedIR-activemodesinr-LaMnO3.Further,thetemperaturedependencesofM2andM3arecloselycorrelatedwitheachother?tobediscussedlater?.HencewesuggestthattheM2andM3modesareIR-activeA2uandEubendingmodesoftheFeO6octahedra.20Thesemodesarecalculatedtobeat310cm?1?A2u?TO??and357cm?1?Eu?TO??inr-LaMnO3.20HereTOstandsforthetransverse-opticalmode.Thecorrespondinglongitudinal-optical?LO?modescalculated

areat465cm?1?A2u?LO??andforr-LaMnO3

?1

488cm?Eu?LO??,whosesignaturesarenotfoundinLSFO.TheM4?704cm?1?featureisassociatedwiththesymmetry-forbiddensymmetric-stretchingmodeofFeO6,similartotheW5modeseeninCFO.TheM5?843cm?1?,M6?897cm?1?,andM7?920cm?1?modesoccuralmostatthesamefrequen-ciesasW6,W7,andW8,respectively,andhenceareas-signedtotwo-phononRamanscattering.

C.TemperaturedependenceofmodesinCaFeO3

FIG.2.VibrationalpatternoftheRamanactivemodesassignedtoW1,W2,W3,W4,andW5forCFO.

RamanspectraofCFOatfewselectedtemperaturesareshownforvariousspectralranges:?i?100–350cm?1inFig.

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http://wendang.chazidian.comparisonbetweentheexperimentsandLDCcalculation.

Exptcm?1149?W1?218?W3?

Calc.cm?1171209280316347522540190301375537670168247302385519579708297340518536727

Assignment

AgAgAgAgAgAgAgB1gB1gB1gB1gB1gB2gB2gB2gB2gB2gB2gB2gB3gB3gB3gB3gB3g

VibrationalPatternIn-phaseyrotationOut-of-phasexrotationMovementofCaionsMovementofCaionsMovementofCaionsOut-of-phasebendingIn-phasestretchingOut-of-phaseyrotationIn-phasexrotation

MixedmotionofCaandOions

Out-of-phasestretchingOut-of-phasestretchingOut-of-phasezrotation

MotionofCa

MixedmotionofCaandOionsMixedmotionofCaandOions

Out-of-phasebendingIn-phasebendingIn-phasestretchingMotionofCaIn-phasezrotationOut-of-phasebendingOut-of-phasestretchingOut-of-phasestretching

197?W2?305?W4?

707?W5?

3,?ii?550–800cm?1inFig.4?a?,and?iii?750–1000cm?1inFig.5?a?.ItcanbenotedfromFig.3thattheW2modeisabsentinthespectrabelow175K.Thefrequenciesandthefullwidthathalfmaximum?FWHM?ofthemodesW1¯W4showtheusualtemperaturedependence:thefre-quenciesincreaseby?5cm?1andtheFWHMdecreasesby?5cm?1astemperatureislowered?notshown?.Thetem-peraturebehavioroftheRamanbandW5?centeredabout707cm?1?asshowninFig.4?a?isinteresting.AboveTco,themodeappearsatthesamefrequencyinboththeHHandHVpolarizations.BelowTco,inHHpolarizationtheasymmetricRamanlineshapecanbe?ttedtotwomodes:themainstrongmodeat?707cm?1andaveryweakmodeat684cm?1;inHVpolarization,thestructureisreversed.Wesuggestthattheminorcomponentisduetopolarizationleak-age.Inotherwords,belowTcothefrequencyofthemainmodeis?707cm?1inHHpolarizationand?684cm?1inHVpolarization.ThetemperaturedependenceofthepeakpositionsisshowninFig.4?b?.Interestingly,aboveTcothemodefrequencyincreaseswithincreasingtemperature,whichcannotbeunderstoodintermsofanharmonicinterac-tions.ThefrequencyofthemodeinHHpolarizationin-creasesslightlyasthetemperatureislowered.Theactivatingdistortionrequiredfortheobservationofthesymmetric-stretchingmodeinRamanscatteringcausesthedeformationoftheFeO6octahedrasothatthesquareformedbythepla-

FIG.3.RamanspectraofCFOforafewselectedtemperatures?shownbythesideofthespectrum?inthespectralwindow100–350cm?1.ThedottedlinesshowLorentzian?tstothedata,whichareresolvedintofourpeaks,i.e.,W1,W2,W3,andW4.

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FIG.4.?a?TheHHandHVpolarizedspectraoftheW5modeofCFOatafewtemperatures.ThesolidlinesareLorentzian?tstothedata.?b?ThevariationofW5modeasafunctionoftemperature.Themodesplitsintoahigh-frequency?HH-polarized?andalow-frequencymode?HV-polarized?belowTco?290K?

.

naroxygenatomstransformstoarhombus.19BelowTco,thechargedisproportionationcausesthearrangementofFe3+?largeoctahedra?andFe5+?smalloctahedra?inarock-salt-typeorderingofFe3+andFe5+ionssuchthateachlargeoctahedraissurroundedbysixsmalloctahedrainthelow-temperaturemonoclinic?P1121/a?phaseofCFO.3ThiscausesthedistancebetweenFeandthetwononequivalentplanaroxygens?O2,O3?tobedifferent.3Fe5+-O2=1.870Å,Fe5+-O3=1.894Å,Fe3+-O2=1.971Å,andFe3+-O3=1.974Å.Thisdistortionwouldresultintheobservationofthesymmetric-stretchmodebelowTco.Ithasbeenexperi-mentallyobservedthatthestretchingmodefrequencyhasa?d?1.5?dependence,11wheredistheFe-Odistance.Thusthesplittingofthe707cm?1in-phasestretchingmodebelowTco

FIG.6.RamanspectraofLSFOforafewselectedtemperatures?shownbythesideofthespectrum?inthespectralwindow175–450cm?1.ThedottedlinesshowLorentzian?tstothedata,whichwereresolvedintothreepeaks,i.e.,M1,M2,andM3.?b?Variationofpeakpositionsand?c?FWHMwithloweringoftemperature.

canbeattributedtotheoccurrenceoftwoaverageFe-Odistancesassociatedwiththeformationofthesmallandlargeoctahedrainthecharge-disproportionedstate.Theav-erageFeuOdistanceforthesmalloctahedrais1.872Åandforthelargeoctahedra1.974Åat15Kincomparisontothe1.922Åatroomtemperature.3Since??/?=?1.5?d/d,the707cm?1modewillsplitintotwomodesat734cm?1and680cm?1,whichareclosetotheobservedvaluesseeninFig.4.However,thepolarizationdependenceoftheW5isnotunderstood.

ThepeakpositionsofW6,W7,andW8remainalmostconstantwiththeloweringoftemperature?notshown?.Fig-ures5?a?and5?b?showthetemperaturevariationoftheFWHMforthesemodes.TheFWHM’sofW6andW7donotchangemuchwithtemperature.However,thetemperaturedependenceoftheFWHMoftheW8modeisanomalous:itincreasessigni?cantlybelowTco.Wedonothaveaquanti-tativeunderstandingofthisresult.ItislikelythatbelowTco,newmodescanbecomeRaman-activeduetoloweringofthecrystalsymmetry.3TheincreaseintheFWHMcanbeduetoinhomogeneousbroadeningarisingfromtheappearanceofnewmodesbelowTco.

D.TemperaturedependenceofmodesinLSFO

FIG.5.RamanspectraofCFOforafewselectedtemperatures?shownbythesideofthespectrum?inthespectralwindow650–1000cm?1.ThedottedlinesshowLorentzian?tstothedata,whichwereresolvedintothreepeaks,i.e.,W6,W7,andW8.?b?ThevariationoftheFWHMswithloweringof

temperature.

RamanspectraofLSFOatfewselectedtemperaturesareshownforvariousspectralranges:?i?175–450cm?1inFig.6?a?and?ii?650–1000cm?1inFig.7?a?.Therearenospec-tralfeaturesbetween450and650cm?1.ThetemperaturedependenceofthefrequenciesandtheFWHMforthethreemodesM1,M2,andM3areshowninFigs.6?b?and6?c?,respectively.ItcanbeseenthatfortheM1mode,the

peak

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