Temperature dependence of hysteresis in thin film cobalt grains

We introduce the stochastic Langevin-Gilbert equation and describe a simple numerical integration scheme for a pointwise solution converging to the Stratonovich interpretation. Reversal of the magnetisation vector is illustrated at various temperatures. We then develop a Galerkin finite element discretisation of the problem. The zero-field relaxation of an isolated thin film cobalt grain at ambient temperature is examined. Despite thermal agitations which are uncorrelated in space or time the magnetisation configuration is observed to pass smoothly between low-energy states. Finally, hystersis simulations are performed; frustration of the magnetisation configuration is shown to cause a reduction in calculated coercivity values at ambient temperature as compared with athermal simulations