Micromagnetic Theory of Phase Transitions in Inhomogeneous Ferromagnets IV. Dynamics of the Spin System

A time‐dependent molecular field theory (Landau‐Ginzburg theory) with correlations in space and time is proposed to calculate the dynamical properties of a spin system near the ferromagnetic phase transition. This theory moreover is a mean field theory, but it takes into account the effect of the thermal and spatial spin fluctuations implicitly when calculating the molecular field. The critical slowing down of the relaxation of the magnetization near the transition temperature, Tc, is enhanced in comparison to the result of the conventional molecular field theory as an effect of the finite lifetime of the spin clusters, even in spatially homogeneous materials. A further enhancement of the critical slowing down is obtained for the case of amorphous ferromagnets with spatial fluctuations of the exchange integral due to the finite size of the spin clusters for temperatures T > Tc. The relation between this dynamic theory and the static spatially correlated molecular field theory recently proposed for the calculation of the static paramagnetic susceptibility for amorphous ferromagnets is discussed in full detail.