Chaotic dynamics of a magnetic nanoparticle

Abstract

We study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a magnetic field with a constant longitudinal and a time-dependent transverse component using the Landau-Lifshitz-Gilbert equation. We characterize the dynamical behavior of the system through calculation of the Lyapunov exponents, Poincaré sections, bifurcation diagrams, and Fourier power spectra. In particular we explore the positivity of the largest Lyapunov exponent as a function of the magnitude and frequency of the applied magnetic field and its direction with respect to the main anisotropy axis of the magnetic particle. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated structure of intricately intermingled chaotic and regular phases.

Energy dissipation in single-domain ferromagnetic nanoparticles: Dynamical approach

“…In particular, the regimes of quasiperiodic [25] and chaotic [29][30][31] motion of m can be realized in circularly and linearly polarized magnetic fields, respectively. Therefore, to find the power loss in these and other cases, Eqs.…”

“…In particular, the circularly polarized magnetic field, whose polarization plane is perpendicular to the anisotropy axis, can generate the periodic and quasiperiodic regimes of * lyutyy@oeph.sumdu.edu.ua † denisov@sumdu.edu.ua precession of the magnetic moment [25][26][27][28]. Moreover, the precessional motion of the magnetic moment induced by the linearly polarized magnet field can exhibit chaotic behavior [29][30][31].…”

Chaotic convection in a ferrofluid

“…The latter is the hallmark of a chaotic behavior. Our basically 3-dimensional phase space carries 3 LEs [58][59][60][61][62], which can be ordered in descending form, with the largest Lyapunov exponent denoted by k max . The error Err in the evaluation of the LEs has been checked by using Err ¼ r k M ð Þ= max k M ð Þ, where rðk M Þ is the standard deviation of k max .…”

Hyper-chaotic Magnetisation Dynamics of Two Interacting Dipoles

“…In such a circumstance the magnetisation of the particles may exhibit complex behaviour as. e.g., quasi-periodicity, and chaos [12,18,19,20]. The next section provides an exhaustive characterisation of the chaotic regime including its dependence on the longitudinal field |H 0 |, the frequency Ω and the distance between particles d. This will reveal a rather complicated topology in the parameter space.…”

“…The standard approach to study the magnetisation dynamics is based on the LandauLifshitz system, which was derived 80 years ago [11]. Using this model (or its generalisations), theoretical descriptions and phase diagrams of the chaotic regions have been given and explored [12,13,14,15,16,17,18,19,20,21,22]. Some of these models show new possible roots and ranges of physical parameters in chaotic domains that could motivate new experiments in this area.…”