Theory of Spin Waves in a Circular Nanotube Composed of an Easy-Plane Ferromagnet. Consideration of the Dissipation for a Non-metallic External Medium

Authors V.V. Kulish 

National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», 37, Beresteisky Ave., 03056 Kyiv, Ukraine

Issue Volume 15, Year 2023, Number 5
Dates Received 18 August 2023; revised manuscript received 15 October 2023; published online 30 October 2023
Citation V.V. Kulish, J. Nano- Electron. Phys. 15 No 5, 05021 (2023)
PACS Number(s) 75.75. + a, 75.30.Ds, 75.30.Gw
Keywords Spin wave, Nanomagnetism, Dipole-exchange theory, Ferromagnetic nanotube, Easy-plane ferromagnet.

The paper extends study of dipole-exchange spin waves in a circular nanotube composed of an easy-plane ferromagnet started by the author in the previous paper. The proposed model considers the magnetic dipole-dipole interaction, the exchange interaction, the anisotropy effects, the damping effects and the general boundary conditions. An equation for the magnetic potential has been obtained for such waves and solved for the case of longitudinal-radial waves. As a result, the dispersion law for the investigated waves has been obtained. After implying boundary conditions, this dispersion law has been complemented with the relation between the wave vector components. This relation has been shown to degenerate into a quasi-one-dimensional values’ spectrum of the orthogonal wave vector component for a thin nanotube. For the obtained spectral characteristics, graphical representations have been given and numerical evaluations have been performed. The spin wave frequency (calculated according to the obtained dispersion law) for typical values of the nanotube parameters corresponds to typical values observed in experiments, thus substantiating the obtained results. Comparative analysis of the dispersion law obtained in the paper and the analogous law for a nanotube composed of an easy-axis ferromagnet has been performed; differences and similarities have been outlined. It has been shown that branches (that correspond to different orthogonal modes) of the dependencies on the longitudinal wave vector components for both real and imaginary parts of the spin wave frequency are close to parabolic and are essentially apart from each other. The area of application of the obtained results is essentially extended compared to the previous paper. The method that is proposed in the paper can be applied to nanotubes of more complex configurations.

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