Viscoelastic ferrocolloid modelled as the Jeffreys fluid: dynamic magnetic susceptibility in the presence of a bias field

Orientational Brownian motion of a solid nanoparticle embedded in a viscoelastic medium modelled by the Jeffreys fluid is studied. The particle bears a magnetic moment and is subjected to a combination of a constant (bias) and a weak (probing) AC magnetic fields. First, the set of Langevin equations of the problem is presented and then on that basis a corresponding kinetic equation (KE) is derived. The solution of the KE that is linear with respect to the AC field amplitude is worked out. This solution is virtually exact since it is cast as a series that enables one to obtain the result with arbitrary accuracy. In that framework, a closed expression for the dynamic magnetic susceptibility of a statistical ensemble of magnetic particles in a viscoelastic environment is found, analyzed and compared to the previously existed approximate solution. It is shown that: (i) the dynamic elasticity of the medium has a substantial effect on the magnetic spectra; (ii) to correctly describe this effect, one has to retain a considerable number of terms in the series that presents the KE solution.