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 $〈\omega 〉$ over the full temperature range ($0\le T\le \infty$) 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 $〈\omega 〉$ are estimated using the molecular-field formalism, but modified to include the effects of short-range fluctuations. Exact expressions for the second moment $〈{\omega }^2〉$ 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 $〈\omega 〉$ decreases with increasing $T$ and shows critical-type behavior near the Néel temperature $T_N$; in the paramagnetic state the agreement between experiment and theory is very good, especially at $T_N$ where the observed $〈\omega 〉=17\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ is to be compared with the theoretical value of 15 ${\mathrm{cm}}^{-1\mathrm{}}$. The observed high-temperature $〈{\omega }^2〉$ are also in reasonable accord with theory. Detailed comparison is made between theory and experiment for $〈\omega 〉$ 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.