Dynamic susceptibilities of an assembly of dipolar particles in an elastic environment

Theoretical model to describe magnetodynamics of a ferrogel, i.e., an assembly of ferromagnetic nanoparticles embedded in a gel, is proposed. The reorientations of the particles are determined by the influence of the elastic matrix and the rotational Brownian motion. Due to the interplay between these two factors, the main parameter characterizing the static magnetic susceptibility of the system is the ratio of the elastic modulus of the matrix times particle volume to the thermal energy. It is shown that the main components of the dynamic magnetic-susceptibility tensor are determined by the combinations of the reference rates of several processes inherent to the system, namely, the elastic restoration of the particle orientation, Brownian rotary diffusion, and viscous relaxation of the particle angular momentum. In the framework of the model, absorption of the energy of an alternating external field by a ferrogel is studied. With allowance for the ever present interaction of elastic and Brownian forces, the effective relaxation times for the longitudinal and transverse components of the ferrogel magnetization are evaluated.