Role of Brownian motion and N\'{e}el relaxations in Mossbauer spectra of magnetic liquids

The absorption cross section of M\"{o}ssbauer radiation in magnetic liquids is calculated, taking into consideration both translational and rotational Brownian motion of magnetic nanoparticles. Stochastic reversals of their magnetization are also regarded in the absence of external magnetic field. The role of Brownian motion in ferrofluids is considered in the framework of the diffusion theory, while for the magnetorheological fluids with large nanoparticles it is done in the framework of the Langevin's approach. For rotation we derived the equation analogous to Langevin's equation and gave the corresponding correlation function. In both cases the equations for rotation are solved in the approximation of small rotations during lifetime of the excited state of M\"{o}ssbauer nuclei. The influence of magnetization relaxations is studied with the aid of the Blume-Tjon model.