Green Function Method for Ferromagnetic Superlattice Nanotubes

Автор(ы) V.A. Tanriverdiyev

Institute of Physics of the National Academy of Sciences of Azerbaijan, 33, H. Javid Ave., Baku AZ 1143, Azerbaijan

Выпуск Том 12, Год 2020, Номер 3
Даты Received 03 February 2020; revised manuscript received 15 June 2020; published online 25 June 2020
Ссылка V.A. Tanriverdiyev, J. Nano- Electron. Phys. 12 No 3, 03028 (2020)
PACS Number(s) 75.70.Cn, 75.40.Gb
Ключевые слова Nanotubes (15) , Superlattice (7) , Spin waves, Green function, Interlayer exchange coupling.

Spin-waves excitations propagating along the superlattice nanotubes are investigated by use of the many-body Green function method of quantum statistical theory. The elementary unit cell of superlattice nanotubes constructed of l atomic layers of ferromagnetic material a and r atomic layers of different ferromagnetic material b. The exchange coupling between two neighboring magnetic atoms of material a (or b) in intralayer and interlayer are Ja(Jb) and Ya(Yb), respectively. Exchange interactions between neighboring spins of two adjacent a and b materials is Y. An external magnetic field h is applied along the z-direction. Continuous and discrete components of the total wave vector are used to take into account the periodicity of the nanotubes along the z-axis and circumferential direction. Within the framework of random-phase approximation the expressions of Green functions for different spins of nanotubes, which are modeled as having a hexagonal cross section, are derived by recurrence relation technique. The results are illustrated numerically for a particular choice of parameters. The spin-wave spectra for reduced frequency /Ja versus the wave-vector component, which characterizes periodicity in the z direction for the system under consideration, are demonstrated. Moreover, in order to clarify the effect of exchange interaction and the number of atomic layers l and r in the elementary unit cell on dispersion law, the results are presented for the various values of discrete components of wave-vector. It is found that four energy ranges exist for the spin waves propagating along the z direction. When both ka and kb are real superlattices, dispersion curve exhibits brood pass band and narrow stop bands.

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