  Surface curvature of magnetic systems can lead to many static and dynamic
effects which are not present in flat systems of the same material. These
emergent magnetochiral effects can lead to frequency nonreciprocity of spin
waves, which has been shown to be a bulk effect of dipolar origin and is
related to a curvature-induced symmetry breaking in the magnetic volume
charges. So far, such effects have been investigated theoretically mostly for
thin shells, where the spatial profiles of the spin waves can be assumed to be
homogeneous along the thickness. Here, using a finite-element dynamic-matrix
approach, we investigate the transition of the spin-wave spectrum from thin to
thick curvilinear shells, at the example of magnetic nanotubes in the vortex
state. With increasing thickness, we observe the appearance of higher-order
radial modes which are strongly hybridized and resemble the
perpendicular-standing-waves (PSSWs) in flat films. Along with an increasing
dispersion asymmetry, we uncover the curvature-induced non-reciprocity of the
mode profiles. This is explained in a very simple picture general for thick
curvilinear shells, considering the inhomogeneity of the emergent geometric
volume charges along the thickness of the shell. Such curvature-induced
mode-profile asymmetry also leads to non-reciprocal hybridization which can
facilitate unidirectional spin-wave propagation. With that, we also show how
curvature allows for nonlinear three-wave splitting of a higher-order radial
mode into secondary modes which can also propagate unidirectionally. We believe
that our study provides a significant contribution to the understanding of the
spin-wave dynamics in curvilinear magnetic systems, but also advertises these
for novel magnonic applications.
