科研之友
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摘要
We present a detailed analytical derivation of the spin wave (SW) dispersion relation in magnetic nanotubes with magnetization along the azimuthal direction. The obtained formula can be used to calculate the dispersion relation for any longitudinal and azimuthal mode. The obtained dispersion is asymmetric for all azimuthal modes traveling along the axial direction. As reported in our recent publication [Phys. Rev. Lett. 117, 227203 (2016)], the asymmetry is a curvature-induced effect originating from the dipole-dipole interaction. Here, we discuss the asymmetry of the dispersion for azimuthal modes by analyzing the SW asymmetry Delta f (k(z)) = f(n) (k(z)) - f(n) (-k(z)), where fn (k(z)) is the eigenfrequency of a magnon with a longitudinal and azimuthal wave vectors, kz and n, respectively; and the dependence of the maximum asymmetry with the nanotube radius R. The analytical results are in perfect agreement with micromagnetic simulations. Furthermore, we show that the dispersion relation simplifies to the thin-film dispersion relation with in-plane magnetization when analyzing the three limiting cases: (i) k(z) = 0, (ii) k(z) >> 1/R, and (iii) (k)z << 1/R. In the first case, for the zeroth-order modes the thin-film Kittel formula is obtained. For modeswith higher order the dispersion relation for theBackward-Volume geometry is recovered. In the second case, for the zeroth-order mode the exchange dominated dispersion relation for SW in Damon-Esbach configuration is obtained. For the case k(z) << 1/R, we find that the dispersion relation can be reduced to a formula similar to the Kalinikos-Slavin [J. Phys. C: Sol. State Phys. 19, 7013 (1986)] type.
- 出版日期2017-5-12
- 单位上海大学
