Computational approaches to thermally activated fast relaxation

The formalism allowing the simulation of thermally activated magnetisation reversal based on the Langevin equation is described. Intrinsically, thermal effects are introduced by the inclusion of a random field in the deterministic (Landau-Lifshitz) equation, whose statistical properties are determined by the fluctuation-dissipation theorem. Using this approach for a single spin, breakdown of the exponential relaxation law for short timescales is demonstrated. Application of the Langevin equation approach to a chain of interacting spins leads to a magnetic response in the form of correlated magnetisation fluctuations (spin waves). An alternative formalism is finally given which takes explicit account of the magnetisation fluctuations. This leads naturally to the prediction of spin wave spectra