Two--magnon scattering and the spin--phonon interaction beyond the adiabatic approximation

Abstract

We consider a model of Raman scattering for a two--dimensional $S=1/2$ Heisenberg Anti-Ferromagnet which includes a {\it dynamical} spin--phonon interaction. We observe a broadening of the line shape due to increased coupling with excited high--energy spin states. Our results are close to a model of random static exchange interactions, first introduced in this context by Haas {\it et al.} [J. Appl. Phys. {\bf 75}, 6340, (1994)], which, when extended to large numbers of spins, explains experiments in the parent insulating compounds of high-$T_c$ superconductors.