Spin waves going 3D - chiral effects in curved magnetic nanowires

Recent progress in material science has enabled the first experimental studies concerning the static magnetization characterization of samples with tubular geometry to be carried out [1]. Although investigating spin-wave and domain-wall dynamics remains a challenge from an experimental point of view, theory predicts that it is fundamentally different than in previously investigated flat geometries. Here, we discuss the effect of the curvature on the dynamics of domain walls and spin waves. Using extensive finite element micromagnetic simulations, we demonstrate that a typical vortex-type domain wall formed in a ferromagnetic tube exhibits advantageous properties regarding the domain wall speed and stability. For topological reasons, these robust domain walls do not encounter the Walker breakdown in certain nanotubes and can propagate with velocities faster than the spin wave phase velocity [2]. Above a critical velocity, the domain wall triggers a Cherenkov-type spin wave radiation. A characteristic of ferromagnetic nanotubes is that the chiral symmetry of the domain wall propagation is broken [3]. This is attributed to the lack of local inversion symmetry due to the curved surface of the nanotube [4]. Our micromagnetic as well as analytical studies show that this lack of inversion symmetry leads to a non-reciprocal dispersion relation for the spin waves with regards to the sign of the propagation vector k. The split in the frequencies for spin waves traveling in opposite directions is of the order of several GHz for tubes below 100 nm in diameter. This effect is the largest when the nanotube radius is comparable with the wavelength of the traveling spin waves and is already present for bended thin films that form a half or even less than a half nanotube only. The split and the minima of the dispersion, however, can be tuned with a circular field. The analytical formula obtained for the dispersion allows for a systematic study of the dispersion relation of nanotubes