Lévy field distributions and anomalous spin relaxation in disordered magnetic systems

We investigate the precession of a spin in d-dimensional random assemblies of superparamagnetic clusters that change the orientation of their magnetic moment by thermally activated transitions. By considering generalised magnetic fields decreasing as r−μ with distance r (μ=3 for dipolar fields), we calculate local field distributions and show that they follow a Lévy type law in the generic case μ>d/2. The Lévy statistics of the field fluctuations leads to anomalous relaxations of an initially polarised ensemble of spins that is characterised by stretched exponentials and power laws with exponents depending on μ and d.