Square root relaxation: two possible mechanisms

Magnetic relaxation in large spin molecular paramagnets is often found to behave as the square root of time at short times t. This behaviour was explained by Prokofiev & Stamp as arising from dipole interactions between molecular spins. However, as observed by Miyashita & Saito, the same behaviour can arise from a different mechanism which, in the present work, is related to hyperfine interactions. The Miyashita-Saito scheme is found to be possible at short times if the nuclear longitudinal spin relaxation is very slow. In the case of moderately slow nuclear spin relaxation, the electronic magnetization variation is initially proportional to t, then to the square root of t and finally to decay exponentially. This behaviour may be mostly expected in dilute systems.