Frequency moments for two-spin light scattering in antiferromagnets

Abstract

The low-order frequency moments for two-spin light scattering in antiferromagnets are calculated in terms of static multispin correlations and compared with experimental data in Mn${\mathrm{F}}_{2}$, Ni${\mathrm{F}}_{2}$, and RbMn${\mathrm{F}}_{3}$. Expressions for the integrated scattering intensity $A$ (the zeroth moment) and the first moment $〈\ensuremath{\omega}〉$ over the full temperature range ($0\ensuremath{\le}T\ensuremath{\le}\ensuremath{\infty}$) are obtained. These can be evaluated exactly in the limits of infinite temperature and of zero temperature, within the spin-wave formalism. For intermediate temperatures, suitable approximations are made. In the paramagnetic phase, the multispin correlations are decoupled into products of two-spin correlations which are evaluated using recently published results for pair correlations in Heisenberg ferromagnets. In the ordered state, $A$ and $〈\ensuremath{\omega}〉$ are estimated using the molecular-field formalism, but modified to include the effects of short-range fluctuations. Exact expressions for the second moment $〈{\ensuremath{\omega}}^{2}〉$ in the infinite-temperature limit are also derived. In Mn${\mathrm{F}}_{2}$ the intensity increases with increasing $T$, in qualitative agreement with theory, although an anomalous, unexplained increase is observed in the paramagnetic state. The first moment $〈\ensuremath{\omega}〉$ decreases with increasing $T$ and shows critical-type behavior near the N\'eel temperature ${T}_{N}$; in the paramagnetic state the agreement between experiment and theory is very good, especially at ${T}_{N}$ where the observed $〈\ensuremath{\omega}〉=17$ ${\mathrm{cm}}^{\ensuremath{-}1}$ is to be compared with the theoretical value of 15 ${\mathrm{cm}}^{\ensuremath{-}1}$. The observed high-temperature $〈{\ensuremath{\omega}}^{2}〉$ are also in reasonable accord with theory. Detailed comparison is made between theory and experiment for $〈\ensuremath{\omega}〉$ in the zero temperature limit in Mn${\mathrm{F}}_{2}$, Ni${\mathrm{F}}_{2}$, and RbMn${\mathrm{F}}_{3}$. The implications of these results for studies of the dynamics of short-range spin correlations and for a determination of the spin-system parameters are discussed.