Nonlinear response of a dilute ferrofluid to an alternating magnetic field

Abstract

The response of dilute monodisperse ferrofluid to alternating magnetic field is studied theoretically. Brownian rotational relaxation of magnetic nanoparticles is taken into account. Susceptibilities of magnetization harmonics are calculated in a wide range of field amplitudes and frequencies via three common approaches: the Fokker-Planck equation for the one-particle orientation distribution function, the Martsenyuk-Raikher-Shliomis effective field method and the Langevin dynamics simulation which is based on direct numerical integration of particles’ stochastic equations of motion. A comparison of these approaches revealed that all of them are able to describe accurately the behavior of the fundamental magnetization harmonic in a broad range of field parameters. But in the case of high-order harmonics, shortcomings of Langevin dynamics and the effective field method manifest themselves. Due to strong random fluctuations of the system magnetization, Langevin dynamics fails to produce reliable results in the weak-field limit, i.e. when the characteristic magnetic energy scale is lower than the system thermal energy. The Martsenyuk-Raikher-Shliomis equation gives a large systematic error for high-order harmonics if the field period is comparable with (or smaller than) the Brownian relaxation time.