Characterization of the Chaotic Magnetic Particle Dynamics

In this paper, we study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a time-dependent magnetic field using the Landau-Lifshitz equation. In particular, we study the case when the magnetic field is homogeneous with a fixed direction perpendicular to the anisotropy direction and consists of a constant and a time-periodic part. We characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and by bifurcation diagrams. We focus on the dependence of the largest Lyapunov exponent on the magnitude and frequency of the applied magnetic field as well as on the anisotropy parameter of the particle. We find rather complicated landscape of sometimes closely intermingled chaotic and nonchaotic areas in parameter space with rather fuzzy boundaries in-between. For actual experiments that means the system can exhibit multiple transitions between regular and chaotic behavior.