Abstract

Magnetochiral properties are enriched in curved magnetic nanostructures, in which dipole-dipole and exchange couplings are their physical sources. In such systems, direct implications are evidenced in the magnetization dynamics, where a noticeable frequency shift appears between two counterpropagating spin waves. In this paper, the spin-wave asymmetry induced by the curvature is theoretically studied in thick ferromagnetic nanotubes with a vortex ground state. The spin-wave spectra are obtained using semianalytical calculations and the dynamical matrix method for thin and thick nanotubes. Under the thickness increase, radial standing spin waves are observed at low frequencies, while the nonreciprocal properties are improved. Such standing waves exhibit a nonreciprocal spin-wave dispersion, but it is not as prominent as the asymmetry of the low-frequency in-phase modes. In the limit of small wave vectors, analytical expressions are reported for the spin-wave dispersion, where the resonance frequency, the frequency shift of two counterpropagating waves, and the critical field that destabilizes the vortex state are determined. The obtained frequency shift allows us to estimate the influence of thickness and curvature on the nonreciprocity of the spin waves. These results constitute a significant advance in the fundamental understanding of the spin-wave dynamics of ferromagnetic nanotubes, predicting new phenomena and providing expressions that are easy to interpret and that allow us, therefore, to promote the study of magnetization dynamics in curved structures.