Spin-cluster theory in magnetic materials and applications to spin glasses

Exact calculations are presented for the real and imaginary magnetic susceptibilities chi '( omega , T) and chi "( omega , T) and for the time dependence of the thermoremanent magnetisation in magnetic materials using a spin-cluster model. The interactions between clusters are neglected, which is appropriate for magnetic rocks and assemblies of fine-particle suspensions, and is an approximation in spin glasses at high enough frequencies. The distribution used for the cluster size and relaxation times is a Poissonian. The derived analytic forms for chi ' and chi " yield their temperature peaks as a function of frequency. These and the calculated remanent magnetisation compare favourably with the theoretical results obtained from statistical mechanical models using analytical and computational techniques, and with some experimental measurements on spin glasses.