Square root relaxation: two possible mechanisms

Magnetic relaxation in large spin molecular paramagnets is often found to behave as δM(t) ∼ √ t 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 δM(t) is initially proportional to t, then to √ t and finally to exp(−t/τ ). This behaviour may be mostly expected in dilute systems. pacs 05.30.-d, 05.40.Fb, 75.50.Xx Synthetic molecular nanomagnets[1] provide reproducible microscopic systems with a large magnetic moment which may have macroscopic properties. The most widely studied materials are, in the usual terminology, Mn12ac (with a relaxation time of 2 months for the magnetization at 2 K) and Fe8, whose faster relaxation allows easier experiments. Magnetic relaxation of these materials at low temperature is a challenging problem. The material is initially magnetized by a strong magnetic field H in the easy magnetization direction z. At t = 0, the external field is suddenly given the value Hext, also in the z direction. One measures the magnetization Mz(t) = Mz(0) + δMz(t). At low enough temperature, the following behaviour is observed for short times in Fe8 [2, 3] and Mn12 [4, 5]. δMz(t) = δMz(∞)A √ t (1) where A is a positive constant. This square root behaviour is in contrast with usual relaxation which is exponential, and therefore linear for short times, δMz(t) = δMz(0)A t. The square root behaviour (1) was predicted theoretically by Prokofiev & Stamp [6] for the demagnetization of a saturated sample. The molecule of