Critical Spin Relaxation in Anisotropic Ferromagnets

The decay times of the spin correlation functions have been calculated for uniaxial anisotropic ferromagnets which order in the plane perpendicular to the axis. The self-consistent theory when applied to the hydrodynamic region just above the critical temperature leads to coupled nonlinear integral equations, which have been solved numerically. In addition to obtaining a temperature dependence in agreement with the dynamic scaling laws, our calculation yields absolute values of the decay times that are one or two orders of magnitude larger than in the conventional theory, which predicts a temperature dependence inversely proportional to the susceptibility. The dynamic scaling-law behavior is followed over a temperature range of about $0.1\frac{(T_y-T_z)}{T_y}$, where $T_y$ and $T_z$ are the perpendicular and parallel paramagnetic Curie temperatures, respectively. We have also made a comparison with experimental values of the decay rates in terbium. The agreement, while not precise, is an order of magnitude better than with the conventional theory.