Magnetization dynamics of a linear dipole chain with accounting for all-to-all interactions

Abstract

The study presents an analysis of pure dipolar spin waves in a one-dimensional chain under external constant magnetic field. The ‘all-to-all’ interactions are taken into account. The magnetization spectrum of an ensemble of randomly oriented chains are similar to the Pake doublet. The wave dispersion relation is obtained in terms of special Clausen function for the secular dipole terms. The full dipole interaction leads to non-analyticity of the dispersion relation in the limit of small wave numbers even in a one-dimensional case. The non-secular terms produce weak oscillations at multiple frequencies. Their contribution in whole spectrum is negligible as expected from the common magnetic resonance theory. The motion equation for spin components in weak-nonlinear case lead to the Schrodinger equation with cubic nonlinearity and nonlinear diffusion.