Nonlinear and Chaotic Dynamics of Two Dipolar-Coupled Anisotropic Spins under Periodic Excitation
Abstract
We investigate the non-linear magnetization dynamics of two identical anisotropic macrospins coupled by dipolar interaction and subjected to periodic transverse excitation. The coupled Landau- Lifshitz-Gilbert equations are solved numerically using a fourth-order Runge-Kutta method. By combining bifurcation diagrams, local-maxima analysis, Lyapunov exponents, and two-dimensional stability maps, we characterize how dipolar coupling, transverse driving amplitudes, and uniaxial anisotropy govern the long-time dynamics. The results reveal a non-monotonic reorganization of dynamical regimes, with alternating intervals of enhanced and suppressed instability. Analysis of symmetric and antisymmetric coordinates distinguishes the collective and relative spin responses, while Fourier spectra and three-dimensional trajectories provide complementary frequency-domain and geometrical characterizations. Simultaneous positivity of the two largest Lyapunov exponents identifies parameter regions consistent with hyperchaotic dynamics. Finally, analytical linearization and ferromagnetic-resonance calculations reveal the distinct coupling dependence of the collectivemode frequencies and clarify the limitations of the linearized description beyond the stability thresholds of the collinear reference state. These findings establish a unified framework for understanding the interplay of dipolar coupling, anisotropy, and periodic excitation in the non-linear dynamics of a minimal interacting-spin system.
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BibTeX
@misc{anand2026nonlinear,
title = {{Nonlinear and Chaotic Dynamics of Two Dipolar-Coupled Anisotropic Spins under Periodic Excitation}},
author = {Manish Anand},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30414},
eprint = {2610.30414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30414},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonlinear and Chaotic Dynamics of Two Dipolar-Coupled Anisotropic Spins under Periodic Excitation
AU - Manish Anand
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30414
UR - https://arxiv.org/abs/2610.30414
AB - We investigate the non-linear magnetization dynamics of two identical anisotropic macrospins coupled by dipolar interaction and subjected to periodic transverse excitation. The coupled Landau- Lifshitz-Gilbert equations are solved numerically using a fourth-order Runge-Kutta method. By combining bifurcation diagrams, local-maxima analysis, Lyapunov exponents, and two-dimensional stability maps, we characterize how dipolar coupling, transverse driving amplitudes, and uniaxial anisotropy govern the long-time dynamics. The results reveal a non-monotonic reorganization of dynamical regimes, with alternating intervals of enhanced and suppressed instability. Analysis of symmetric and antisymmetric coordinates distinguishes the collective and relative spin responses, while Fourier spectra and three-dimensional trajectories provide complementary frequency-domain and geometrical characterizations. Simultaneous positivity of the two largest Lyapunov exponents identifies parameter regions consistent with hyperchaotic dynamics. Finally, analytical linearization and ferromagnetic-resonance calculations reveal the distinct coupling dependence of the collectivemode frequencies and clarify the limitations of the linearized description beyond the stability thresholds of the collinear reference state. These findings establish a unified framework for understanding the interplay of dipolar coupling, anisotropy, and periodic excitation in the non-linear dynamics of a minimal interacting-spin system.
ER -