Spin-orbital physics in the optical conductivity of quarter-(4)

Using finite-temperature diagonalization we investigate the optical conductivity $\sigma(\omega)$ and spin-orbital dynamics in the CE phase of half-doped manganites. We find $\sigma(\omega)$ characterized by a broad spectrum with pronounced optical gap due

=

jxGS=t-+α++__tβ-+β

+

+

__t’β-

2

+

...

+

...

FIG.5:AFMsegmentshowingthedominanttermsintheAF-CEgroundstatewithCO(α,β 1)inthelimitJH→∞(left).Whenapplyingthecurrentoperatorjx(right),onlythe rsttermwouldcontributeintheFMcase.Thesecondterm～βinjx|GS (describinganorbitalexcitation)is niteduetoquantum uctuationsinanAFenvironment.Heretandt′(t>t′)standfortwoe ectivehoppingsbetweencornerandbridgesites,whilefull(empty)symbolsstandforthesitesoccupied(unoccupied)byanegelectronwithtotalspin(arrows)S=1(S=1/2),and|0 ≡|S=1,Sz=0 .

standsforaboundstate[23,24]whileatω 1.5tastrongmaximumisfoundhavingacharacterofananti-boundstate.Thisindicatesthattheorbitalexcitations,althoughmuchmorerobustthanthespinones,playanactiverolealsoatalower-energyscale.Athigherenergiesω 1.5t,however,Cq(ω)andTq(ω)structurefactorsstronglydi er.

Asalientfeatureofσ(ω)isthein-gapabsorption(ω< c)intheAF-CEphase,Fig.2(a),andtheabsenceofsuchabsorptionfortheFM-CEcaseinFig.2(b)atlowtemperature(T 0.1t).Wearguethatthestructureatω tisanorbiton-likecollectiveexcitationwhichbe-comesinfrared-activewhenparityisbrokenbyAFcorre-lations.ThisisillustratedschematicallyinFig.5.IntheCOphasethegroundstate(GS)isdominatedbycon g-urationswithoccupiedbridgesitesbuthybridizedwithstatesreachedbyinter-sitehopping(～t)orchangedbycorespinsuperexchange(～JAF).AswedealwithdorbitalsthehoppingmatrixhasevenparityleadingtoevenGSasfaraschargedistributionisconcerned.Con-sequently,theGSchangedbythecurrentoperatorisoddwithrespecttochargeand(neglectingcorespins)onlyprocessesacrosstheopticalgapareallowed( rstlineofjxselection|GS inrulesFig.5).noInlongerthepresencestrictlyofhold,AF uctuationsasspin-exchangetheseleadstoanadmixtureofspinandspin-orbitalexcitations(secondandthirdlineofjxcancelbysymmetry.

|GS inFig.5)whichdonotThisorbiton-magnonmechanismforthein-gapab-sorptionissupportedbythefactthattheintensityofthestructureinσ(ω)atω t[seeinsetinFig.2(a)]increases(abovethebackgroundofotherexcitations)withdecreasingtemperatureinthespin-orderedcase(T 0.1t).Themomentumconservationpresentinop-ticalprocessescanbeful lledcombiningTwithq=(±π/2,±π/2)whichareq andSz

dominant qex-citationsintherespectivedynamicalstructurefactors[seeFig.3(a)andFig.4(a)].Thedecreaseofthestaticstructurefactor

4

Sq= ∞

∞dωSq(ω)atq=(±π/2,±π/2)withtempera-tureisapparentlycorrelatedwiththesuppressionofthein-gapabsorptioninσ(ω).

Insummary,opticalconductivityandspin-orbitaldy-namicshavebeeninvestigatedintheCEphaseofcharge-orderedmanganitesatquarter lling.Twocontributionsinourtheorydeterminethechargegap:(i)elasticforcesand(ii)Coulombinteraction.Thisisimportanttoex-plaintherecentlydiscoveredpico-secondswitchingofop-ticalspectra,whichcanbeunderstoodbytheinstanta-neousreductionoftheCoulombcontributionduetothesuppressionofCObytheultra-shortpulse,aswellasthefastrecoveryafterthepulse.WehaveshownthatthecooperativeJTcouplingbetweenfurtherMnneigh-bors,stabilizingtheCE-typecorrelationsinourmodel,canexplainsemi-quantitativelytheopticaldataanditstemperaturedependenceinhalf-dopedmanganites.Spinandorbitalexcitationsleadtocollectivemodesactiveinopticalexperiments,andareresponsibleforcharacteris-ticdi erencesbetweenAF-andFMCEphases.WewouldliketothankA.M.Ole´sforfruitfuldis-cussions.J.B.acknowledgesthesupportoftheMPIf¨urFestk¨orperforschung,StuttgartandbythePolishStateCommitteeofScienti cResearch(KBN)ofPoland,ProjectNo.1P03B06826.

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