Nonlinear response of dipolar systems to superimposed ac and dc bias fields

Abstract

The main purpose of this thesis is to study the nonlinear ac stationary response of dipolar systems to superimposed ac and dc bias fields via the rotational Brownian motion model. In this way we investigate (i) the nonlinear dielectric and Kerr effect ac stationary responses of noninteracting permanent electric dipoles and the analogous nonlinear magnetic relaxation of noninteracting magnetic dipoles in ferrofluids, (ii) the nonlinear dielectric and dynamic Kerr effect of a system of permanent dipoles in a uniaxial mean field potential, and (iii) the frequency-dependent dc component of the magnetization of noninteracting magnetic nanoparticles possessing simple uniaxial anisotropy. A new effective matrix method of calculation of the nonlinear ac stationary responses of dipolar systems for arbitrary dc field strength via perturbation theory in the ac field is developed for a uniaxial mean field potential. Furthermore, accurate analytic equations for nonlinear dynamic susceptibilities, allowing one to qualitatively understand the main features of the nonlinear ac stationary response of dipolar systems, are also derived using the two-mode approximation. Two distinct dispersion regions appear in the dc components of the polarization and birefringence of electric dipoles and the dc component of the magnetization for magnetic dipoles at low- and mid-frequencies, corresponding to slow overbarrier and fast intrawell relaxation modes, respectively. Such frequency-dependent behaviour allows one to estimate the longest relaxation time via the half-width of the low-frequency spectra of the dynamic susceptibility. In the nonaxially symmetric case, a third high-frequency resonant dispersion in the dc component of the magnetization appears, accompanied by parametric resonance behaviour due to excitation of transverse resonance modes with characteristic frequencies close to the precession frequency. It is also shown how the results obtained can be generalized to anomalous relaxation via the fractional rotational diffusion equation. Possible experimental verifications of theoretical predictions in polar dielectrics and ferrofluids, are discussed.