Inertial rotational diffusion and magnetic relaxation of the spin system in a strong magnetic field

Analytical expressions for the longitudinal and transverse correlation functions pertaining to inertial magnetic relaxation are obtained by expanding the deterministic magnetization trajectories into a Fourier series and averaging the result over all possible initial conditions applying the stationary Boltzmann distribution function. The longitudinal and transverse components of the magnetic susceptibility tensor are calculated for a system of noninteracting macrospins in a strong uniform external field using Bloch's phenomenological approach, which postulates the exponential evolution of the spin system towards equilibrium, and the Lorentz model of rotational diffusion of the magnetization vector. It is shown that the strength of the external field and the magnitude of the inertia parameters noticeably affect the shape of the susceptibility in the THz (nutation resonance) spectrum region. It is also demonstrated that the simple analytical Lorentz-type expression describes the main features of the complex susceptibility in the ferromagnetic resonance and nutation resonance regions.