Spin-Wave Damping in a Heisenberg Antiferromagnet

Neutron scattering measurements are reported on the linewidth $\Gamma$ of spin waves in the simple cubic antiferromagnet RbMn${\mathrm{F}}_3$ at relatively low temperatures $T$ and spin-wave energies $E_q$. The results are well fitted by $\Gamma =AE_q^{}{}_{}{}^{\alpha }{T}^{\beta }$, where $\alpha =2.13\mathrm{}\pm 0.18$, consistent with the scaling law prediction $\alpha =2\mathrm{}$ of Halperin and Hohenberg, and $\beta =3.29\mathrm{}\pm 0.39$, in agreement with the prediction $\beta =3\mathrm{}$ of two regimes considered by Harris, Kumar, Halperin, and Hohenberg, although the magnitude $A$ is not in agreement with theory.