Forced coupled motion of the nanoparticle magnetic moment and the whole nanoparticle in a viscous fluid

We considered the coupled motion of the magnetic moment of a ferromagnetic uniaxial nanoparticle and its mechanical rotation about the center of mass. This particle is supposed to be placed into a viscous liquid and excited by an external alternating magnetic field. Two modes of motion were studied analytically in the noise-free approximation. Within the first mode, both the nanoparticle magnetic moment and easy axis perform small oscillations around the initial position. The oscillation amplitudes were obtained in the harmonic approximation. Just the magnetic moment demonstrates the resonant behaviour that causes the main features of the oscillation mode. Within the second mode, the nanoparticle magnetic moment and easy axis are rotated synchronously. In this case we obtained the system of algebraic equations, where the precession and lag angles of the magnetic moment and easy axis are the solutions of these equations. The results obtained allow to make an analysis of the mechanism of ferrofluids heating by alternating magnetic fields.