Symmetry- and curvature effects on spin waves in vortex-state hexagonal nanotubes

TL;DR

This study investigates how the shape and curvature of hexagonal magnetic nanotubes influence spin wave behavior, revealing symmetry-induced mode localization and splitting, with experimental validation using advanced microscopy and simulations.

Contribution

It provides the first experimental demonstration of spin-wave propagation in 3D nano-objects and analyzes the effects of discrete rotational symmetry on spin-wave spectra.

Findings

Polygonal shape causes mode localization at corners and edges.

Discrete symmetry lifts degeneracy of azimuthal modes.

Microwave absorption calculations highlight importance of antenna design.

Abstract

Analytic and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from intrinsic Dzyaloshinskii-Moriya interaction or interface-induced anisotropies. In constrast, these chiral effects stem from isotropic exchange or dipole-dipole interaction, present in all magnetic materials, which acquire asymmetric contributions in case of curved geometry of the specimen. As a result, for example, the spin-wave dispersion in round magnetic nanotubes becomes asymmetric, namely spin waves of the same frequency propagating in opposite directions along the nanotube exhibit different wavelenghts. Here, using time-resolved scanning transmission X-ray microscopy experiments, standard micromagntic simulations and a dynamic-matrix approach, we show that the spin-wave spectrum undergoes additional drastic changes when transitioning from a continuous to a discrete rotational symmetry, i.e. from round to hexagonal nanotubes, which are much easier to fabricate. The polygonal shape introduces localization of the modes both to the sharp, highly curved corners and flat edges. Moreover, due to the discrete rotational symmetry, the degenerate nature of the modes with azimuthal wave vectors known from round tubes is partly lifted, resulting in singlet and duplet modes. For comparison with our experiments, we calculate the microwave absorption from the numerically obtained mode profiles which shows that a dedicated antenna design is paramount for magnonic applications in 3D nano-structures. To our knowledge these are the first experiments directly showing real space spin-wave propagation in 3D nano objects.