Spin-orbital physics in the optical conductivity of quarter-(3)

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

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entparities.WithincreasingTmagneticexcitationsareincludedinthethermodynamicaveragewithreducedef-fectivehopping,whosevalueisdictatedbytheDEmech-anismforcorrelatedegelectrons.Thusthereductionofthesecondorderterm2t2/ cforthesestatesresultsinaspectralshifttowardslowerωc.FurtherreductionofωciscausedbymeltingoforbitalandCOleadingtogaplessorbitalexcitations[18]andareductionof c.

IntheFMspinstateσ(ω)ischaracterizedbytwobroadpeaksandawell-developedchargegap[Fig.2(b)].Here,spin uctuationsaresmallandσ(ω)isdominatedbycharge-orbitonexcitations,i.e.,thepurechargeexcita-tioniswellseparatedfromtwofurtherpeakscorrespond-ingtotheadditionalexcitationofoneandtwoorbitons.Ontheotherhand,intheAF-CEspinorderedstatespin uctuationsaresubstantialandinter-sitechargetrans-ferisaccompaniedbymagnonandorbitonexcitationsleadingtoabroadenedspectrumabovethechargegapaswellastosubstantialin-gapabsorption.ThelatteriscompletelyabsentintheFMstateatlowtemperature.Togainadeeperinsightintothestructureofσ(ω)intheCEspin-orbitalphase,wehavecalculated[usingasimilar nite-temperatureprocedureasforσ(ω)]thedy-namicalspin,orbital,andspin-orbitalresponsefunctions:

Aq(ω)=

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