Nuclear Spin-Wave Relaxation and Narrowing of NMR Lines in Ferro- and Antiferromagnets

It is shown that if a well-defined nuclear spin-wave spectrum exists in a ferro- or antiferromagnet, the NMR linewidth is considerably narrower than would be calculated from the second moment $〈\Delta {\omega }^2〉$ due to the Suhl-Nakamura interaction. We argue that if the frequency pulling ${\omega }_c$ is large compared to ${〈\Delta {\omega }^2〉}^{\frac{1}{2}}$, only a small band of nearly degenerate modes can interact; so the situation is analogous to standard transition-probability calculations. This explains why the observed NMR linewidth in RbMn${\mathrm{F}}_3$ is an order of magnitude smaller than ${〈\Delta {\omega }^2〉}^{\frac{1}{2}}$. Nuclear spin-wave relaxation rates are calculated for RbMn${\mathrm{F}}_3$. For zero wave vector the rate is 1.5 × ${10}^3$ ${\sec }^{-1\mathrm{}}$ at 4.2°K in a field of 3000 Oe. This figure is much less than the NMR width, but is in close agreement with parallel-pumping data. It is suggested that the NMR width may be due largely to random inhomogeneities.