Dynamics of two interacting dipoles

We study the deterministic spin dynamic of two interacting magnetic moments with anisotropy and dipolar interaction under the presence of an applied magnetic field, by using the Landau-Lifshitz equation with and without a damping term. Due to different kinds of interactions, different time scales appear: a long time scale associated with the dipolar interaction and a short time scale associated with the Zeeman interaction. We found that the total magnetization is not conserved; furthermore, for the non-dissipative case it is a fluctuating function of time, with a strong dependence on the strength of the dipolar term. In the dissipative case there is a transient time before the total magnetization reaches its constant value. We examine this critical time as a function of the distance between the magnetic moments and the phenomenological damping coefficient, and found that it strongly depends on these control parameters.