Curvature-Induced Asymmetry of Spin-Wave Dispersion

We show using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in flat thin films. The dispersion relation is asymmetric regarding the sign of the wave vector. This is a purely curvatureinduced effect and its fundamental origin is identified to be the classical dipole-dipole interaction. In certain cases the Damon-Eshbach modes in nanotubes behave as the volume-charge-free backward volume modes in flat thin films. Such non-reciprocal spin-wave propagation [1] is known for flat thin films with Dzyalonshiinsky-Moriya interaction (DMI), an antisymmetric exchange due to spin-orbit coupling.
The analytical expression of the dispersion relation has the same mathematical form as in flat thin films with DMI. The influence of curvature on spin waves is thus equivalent to an effective dipole-induced Dzyalonshiinsky-Moriya interaction [2].
[1] K. Zakeri, et. al., Phys. Rev. Lett. 104, 137203 (2010).
[2] J.A. Otálora, et. al., Phys. Rev. Lett. 117, 227203 (2016).