Spin waves in rings of classical magnetic dipoles

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 −→ ∞ is investigated and completely solved.

Fourier-Taylor series for the figure eight solution of the three body problem

“…One remarkable feature of it is that all three bodies follow the same curve but with a constant phase shift ("choreography"). This is similar to the property of a spin wave in a finite spatial structure, see [6]. Nevertheless, an analytical solution is not known.…”

“…We choose the solution A 0 0 = −a in view of (8). The coefficient of λ 1 vanishes at both sides of (6). Comparison of coefficients of λ 2 cos n ω t for n = 0, 1, 2 yields the following three equations:…”

“…The detailed results of the FT series method for the three examples are too complicated to be presented in a paper and will be given in three MATHEMATICA 10.1 notebooks that can be downloaded from [5]. Further applications of the FT method will be given elsewhere [6].…”

{ScnGdn} Heterometallic Rings: Tunable Ring Topology for Spin-Wave Excitations

“…Therefore, its effect strongly depends on the topology of the molecule. For a symmetric eight-spin-ring structure, one would expect two distinct dipolar spin-wave peaks, but there is none visible in Sc 8 Gd 8 despite its shorter Gd···Gd distance than that of Sc 6 Gd 6 . We attribute this to the relatively bent structure of Sc 8 Gd 8 .…”

“…Molecular rings with the same topological charge radiate spin waves with spiral and antispiral spatial profiles. The propagating spin waves have a preferred radiation direction, with clear dipole signatures in their radiation pattern, suggesting that the molecular ring forms an efficient spin-wave antenna. , …”