Theory of Magnetic Relaxation in a Near-Ising System: DyES

A theory of magnetic relaxation in an Ising system is developed, and the results are compared with the experiments of Cooke, Edmonds, Finn, and Wolf on dysprosium ethyl sulfate (DyES), believed to be an Ising dipolar ferromagnet below 0.13°K. Small spin-spin perturbations are postulated to give rise to relaxation within the spin system without having to invoke spin-lattice coupling. The methods of Kubo and Tomita are used to express the relaxation rate in terms of time correlation functions. These can be evaluated far more easily in an Ising system than in a Heisenberg one, and what appear to be reliable estimates are made for the DyES lattice. The resulting relaxation rate is strongly dependent on the spontaneous magnetization, which is calculated from a phenomenological model similar to the one employed by Cooke et al. (nearest-neighbor Ising linear chain plus molecular field). Good agreement is then obtained with experiment for temperature dependence of the ferromagnetic relaxation time. Numerical agreement requires either a strain-induced $g_{\perp }$ of about 0.05 or a next-nearest-neighbor spin-spin interaction of about 2×${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. These are shown to be plausible numbers by investigating effects of rhombohedral lattice distortion and electric quadrupole-quadrupole interaction.