Spin-fluctuation light scattering at high temperature

Two-spin-fluctuation light scattering in a Heisenberg paramagnet is treated theoretically in the limit of infinite temperature and the results for the intensity I(ω) as a function of frequency shift ω are compared directly with room-temperature data on RbMnF₃. The method of computing the four-spin correlation functions which appear in I(ω) is to use a type of randomphase approximation which reduces the problem to calculating the spectral density 〈OqO_-q〉ω at frequency ω, where ${O}q={{{→}}{S}}q·{}{{{→}}{S}}_{{-}q}{-}〈{{{→}}{S}}q·{}{{{→}}{S}}_{{-}q}〉$ and $q$ is the wave vector. This treatment is shown, for an infinite system, to be equivalent to the standard decoupling approximation of replacing the four-spin function by products of pairs of two-spin functions. Our formulation is advantageous for computational purposes, though, since the decoupling procedure requires the calculation of (〈→Sq·→S_-q〉²)_ω, whereas theories only exist for 〈→Sq·→S_-q〉_ω. A convolution integral would then be required to complete the solution if the decoupling were used. Here we approximate 〈OqO_-q〉_ω directly by the method of a Gaussian generalized diffusivity and avoid the convolution altogether. The resulting I(ω) gives good agreement with experiment using the accepted low-temperature value of the exchange constant J in RbMnF₃ and no adjustable parameters. The nature of the photon-spin coupling is such as to discriminate against long-wave-length q→0 modes, and thus there is no anomaly in I(ω) for ω→0, as can occur for diffusive modes and strong weighting of the interaction at $q=0$.