Spin waves in rings of classical magnetic dipoles

TL;DR

This paper explores spin wave phenomena in classical magnetic dipole rings, providing analytical solutions for specific cases and numerical analysis for thermal excitations, advancing understanding of dipolar magnetic systems.

Contribution

It offers new analytical and numerical insights into spin waves in dipole rings, including exact solutions and the behavior in the infinite chain limit.

Findings

Analytical dispersion relation for infinitesimal spin waves.

Comparison of theoretical frequencies with Monte Carlo simulations.

Exact solution for synchronized oscillations at zero wave number.

Abstract

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system's ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with $N\longrightarrow \infty$ is investigated and completely solved.