Single-domain particles suspended in a fluid: a longitudinal magnetic response in the case of “frozen” superparamagnetism

Abstract

The paper presents a theory of a longitudinal magnetic response of single-domain particles suspended in a liquid to which a constant magnetizing field and a harmonic field of arbitrary amplitude are applied. The study is performed for particles whose internal diffusion of the magnetic moment can be neglected. The dependence of the relaxation spectrum of such particles on the magnitude of the external magnetic field has been established. It is shown that in the linear approximation with respect to the perturbing field, their dynamic magnetic susceptibility can be represented as a sum of a countable set of Debye-type terms. In the case of a weak (the corresponding Zeeman energy is less than the thermal energy) or strong (the Zeeman energy exceeds the thermal energy by several times) magnetizing field, the longest-lived relaxation mode completely dominates, and the frequency dependence of the susceptibility can be described by a relatively simple expression. An increase in the amplitude of the alternating field leads to a growth of the fundamental Fourier harmonic of the magnetization. At the same time, in the absence of the bias field, the dynamic magnetic susceptibility of the particle decreases, and the maximum of its imaginary part shifts to the right – to the region of higher frequencies. However, if a constant field is applied to the particle and the corresponding Zeeman energy exceeds the thermal energy, then the effect is opposite: the dynamic magnetic susceptibility increases and the maximum of its imaginary part shifts to the left when amplitude of the exciting field goes up.