Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy

We study the linear response of a system of single-domain ferromagnetic particles with cubic magnetic anisotropy to a weak external a.c. magnetic field. By averaging the Gilbert equation with a fluctuating field for the magnetization of an individual particle we derive a system of recurrence equations for the spectra of equilibrium correlation functions describing the longitudinal relaxation of the system. We find the solution of this system by using matrix continued fractions. We also evaluate the longitudinal relaxation time and the spectrum of the complex-valued magnetic susceptibility. Finally, we show that the nature of susceptibility dispersion is determined by the anisotropy and dissipation parameters.