We report the experimental results and propose a theory of resonant two-magnon Raman scattering from antiferromagnetic insulators. On the experimental side, we present the first measurements on YBa2Cu3O6.1 at T = 4 K, and find the resonant frequency at higher photon energies than previously believed. On the theoretical side, we argue that the conventional Loudon-Fleury theory does not work in the resonant regime, in which the energy of the incident photon is close to the gap between the conduction and valence bands, and identify the most relevant contribution to Raman intensity. We find good agreement between the theoretical prediction for the power-law behavior of the strength of the two-magnon scattering and the data. We argue that this agreement is evidence for the existence of coherent quasiparticle states in these materials.
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occursa t slightlyh igherf requencietsh an beenr eportedp re- viously [S]:t he resonancefr equencyis greatert han 3.1 eV To understandt he experimentarle sults,w e developa di- agrammatica pproacht o Raman scatteringv alid in both nonresonanta nd resonantr egimesW. e considert he one- band Hubbard modela nd uset hel argeU spin densityw ave (SDW) formalism[ 8]t o describet he electronics tatea t half- filling, the excitationsa roundi t, and thei nteractionb etween fermions and spin wavesw hich in the SDW formalisma re the collectivem odeso f fermions.T he resonantp art of the scatteringm atrixe lementM R is obtainedf rom thet erml in- ear in the vectorp otentiali n the 2nd order of perturbation theory . In this process,a photon with energy wi and momentumw hich can be safely set equal to zero, creates a virtual particle-holes tateo f the fermionic systemw hich can emit or absorbt wo spin-wavesw ith momentak and -k beforec ollapsingi nto an outgoingp hoton with the energy co/. In the situationw henthe photon frequenciesa rem uch smaller than the Mott-Hubbard gap 2A N U, we rewv- eredd iagramaticallyth eLoudon-Fleury theory.H oweverin The 3/2 power of the denominatori n (1) is due to triple the resonantr egion, when the incoming photon frequency resonancew, hile the small factor in the numeratorc omes is close to the gap value, we found that the most singular from the vanishing of the numeratori n Raman intensity contribution to the Raman vertexc omesf rom the diagram (and opticala bsorption)r ight at the top of the band (i.e. at which does not contributet o the Loudon-Fleury theory, k = 0). In practice,t he differenceb etweenW Y and co?” but for which there exists a region of wi and off where can be neglected,a nd eqn (1) yields inverse square-root all threeo f the energyd enominatorsv anish simultaneously. singularityi n i& which implies a linear singularityi n the This phenomenonis known as a triple resonance[6 ,7].V ia Raman intensity,R N j&l2 N IWi - W;al-‘. a combination of analytical and numericalt echniquesw, e In Fig 2 we fit the low-temperaturdea ta on the peak in- found that for relevantw i the triple resonancein the Ra-tensityi n YRa2CusO6i at T = 4 K by eqn (1). We seet hat man vertexo ccurso nly in a narrow rangeo f the final pho- the fit to the theoreticadl ependenceis quite good. The in-ton energiesW I. The region of triple resonancesis shaded verseli neard ependencset artsf rom wi N 2.5e V and extends in Fig. 1. In this region,t he Raman vertex,& , diverges in nearlyu p to the resonancefr equencyw p iz 3.1 eV The ef- the absenceo f quasiparticled amping. fectso f fermionicd ampinga rep robablyr elevanto nly in the It is easyt o checkt hat the triple resonancec ondition is immediatev icinity of the resonanceW. e considert his agree-rigorouslys atisfiedo nly for thed iagramw hichd oesn ot con-ment as a partial verificationo f the large U SDW picture tain final-statem agnon-magnoni nteractionsO. n the other for the carriers,w hich, despitem uch theoreticawl ork, has hand, for S = l/2, the dominant contribution to the con- not beenw ell-establisheedx perimentallyin thesem aterials. ventional two-magnonp eak at N 35 comesf rom the di-Acknowledgements-isIt our pleasure to thank everyone with agramsw ith multiple magnon-magnonin teractions[ 2]. In whom we discussed this paper. DE was supported by the TCS at this situation the Raman spectrumR (w) can be consid-the University of Houston. G.B. and M.K. were supported by the ereda s containingt wo independent peaks:o ne is due to the NSF under DMR 91-20000 through the STCS at the University triple resonancein the Raman vertexi n the shadedr egion of Illinois. in Fig. 1, and the other,a t transferredfr equencyo f about 3J, is due to the magnon-magnons catteringS. upposew e now iix CIJ at the two-magnonp eak frequency_ 3J, and considert he variation of the peak amplitudea s a function of the incident photon frequencyW i. Obviously,t his am- plitude will by itself havea maximumw hen the two peaks in R(w) merge, ie, when the w = const line intersectsth e region of triple resonancesF.r om Fig. 1 we seet hat the in- tersectiono ccurs at wiU = 2A + 7.9J which is very close to Co;” = 2A + 8J, wheret he particlea nd hole are excited near the tops of their respectiveb ands.W e calculatedt he Raman vertexi n the vicinity of the intersectiona nd found that it diverges( in the absenceo f damping)a s