Nonlinear response of a dipolar system with rotational diffusion to a rotating field

The rotational diffusion equation for a dipole in the presence of a rotating field is solved by expansion of the orientational distribution function in terms of spherical harmonics. For the stationary solution, the distribution function rotates bodily in angular space. The magnitude of the average dipole moment and the lag angle are studied as functions of field strength and frequency. A comparison is made with the nonlinear response calculated from approximate macroscopic relaxation equations, proposed by Shliomis [Zh. Eksp. Teor. Fiz. 61, 2611 (1972) [Sov. Phys. JETP 34, 1291 (1972)]] and by Martsenyuk et al. [Zh. Eksp. Teor. Fiz. 65, 834 (1973) [Sov. Phys. JETP 38, 413 (1974)]]. Shliomis found that for sufficiently high field, the lag angle and the absorption are multivalued functions of frequency. This is not the case for the exact solution of the rotational diffusion equation presented here. The response of a macroscopic system of interacting dipoles is calculated in a mean-field approximation for a spherical sample.