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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.

A phenomenological model is proposed to describe the plasticity of soft magnetic elastomer composites under an external field. Along with high-elasticity, internal dry friction is introduced whose origin is attributed to the dipole-dipole interaction of the embedded particles. Numerical estimates of the model parameters are obtained from comparison with the measurements performed on iron carbonyl dispersions in soft silicon-rubber matrices.

An investigation is made of the dependence of the width of a line emitted by a single-mode semiconductor laser on the intensity of this line. The line width is calculated allowing for the saturation effect. It is shown that saturation results in an additional broadening of the laser line. In a weak field, when the saturation parameter η is small, the product of the line width and the number of photons increases proportionally to the line intensity. In a strong field (η1), this product becomes constant but its value is considerably greater than the value in a weak field.