Deterministic Inertial Dynamics Of The Magnetization Of Nanoscale Ferromagnets

Analytic solutions for the longitudinal and transverse components of the magnetization of a single-domain ferromagnetic nanoparticle with the simplest possible form of uniaxial magnetocrystalline anisotropy and Zeeman energy are obtained in terms of the appropriate Jacobi elliptic functions and elliptic integrals via the undamped limit of the inertial Landau-Lifshitz-Gilbert (ILLG) equation. Moreover, the nutation frequency is also determined in terms of the inverse period of a Jacobi elliptic function. All the results originate by starting from the analogy of the ILLG equation to a symmetric top with an electric dipole lying along its axis of symmetry as used to model inertial, i.e., high-frequency, effects in the Debye theory of dielectric relaxation of assemblies of noninteracting polar molecules, an analogy which allows one to simultaneously obtain closed-form solutions for typical THz or ultrahigh-frequency magnetization observables as well as the GHz ones associated with the usual ferromagnetic resonance due to precessional motion.