Approach to a Limiting Cycle in Thermally Relaxing Media

The thermally activated dynamics of an uniaxial superparamagnetic particle are studied here from the point of view of approach towards a steady state minor hysteresis loop representing a limiting cycle. The particle is initially at an arbitrary state, and is driven by a sufficiently small external applied ac magnetic field till the limiting minor hysteresis loop is reached with a desired precision. The number of periods required to reach the limiting cycle is found to satisfy an Arrhenius-type law, with an exponential dependence on the inverse ambient temperature. We tentatively associate this result with energy dissipation, its origin, however, remains quite unclear.