Thermal Agitation of Single Domain Particles

The direction of magnetization of fine single-domain particles is known to fluctuate because of thermal agitation. The relaxation time for these fluctuations is calculated here for the case of uniaxial anisotropy and zero magnetic field. It is found that the commonly used approximation for high-energy barrier is still a good approximation when the barrier is of the order of $\mathrm{kT}$. For lower barriers, the eigenvalue is expressed as a power series in the energy barrier in terms of $\mathrm{kT}$.