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 $I\left(\omega \right)$ as a function of frequency shift $\omega$ are compared directly with room-temperature data on RbMn${\mathrm{F}}_3$. The method of computing the four-spin correlation functions which appear in $I\left(\omega \right)$ is to use a type of randomphase approximation which reduces the problem to calculating the spectral density $〈{\mathcal{O}}_q{\mathcal{O}}_{-q}〉\omega$ at frequency $\omega$, where ${\mathcal{O}}_q={\overrightarrow{\mathrm{S}}}_q·{\overrightarrow{\mathrm{S}}}_{-q}-〈{\overrightarrow{\mathrm{S}}}_q·{\overrightarrow{\mathrm{S}}}_{-q}〉$ 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 ${\left({〈{\overrightarrow{\mathrm{S}}}_q·{\overrightarrow{\mathrm{S}}}_{-q}〉}^2\right)}_{\omega }$, whereas theories only exist for ${〈{\overrightarrow{\mathrm{S}}}_q·{\overrightarrow{\mathrm{S}}}_{-q}〉}_{\omega }$. A convolution integral would then be required to complete the solution if the decoupling were used. Here we approximate ${〈{\mathcal{O}}_q{\mathcal{O}}_{-q}〉}_{\omega }$ directly by the method of a Gaussian generalized diffusivity and avoid the convolution altogether. The resulting $I\left(\omega \right)$ gives good agreement with experiment using the accepted low-temperature value of the exchange constant $J$ in RbMn${\mathrm{F}}_3$ and no adjustable parameters. The nature of the photon-spin coupling is such as to discriminate against long-wave-length $q\to 0$ modes, and thus there is no anomaly in $I\left(\omega \right)$ for $\omega \to 0$, as can occur for diffusive modes and strong weighting of the interaction at $q=0\mathrm{}$.