Green Function Method for Ferromagnetic Superlattice Nanotubes

Authors V.A. Tanriverdiyev

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

Е-mail [email protected]
Issue Volume 12, Year 2020, Number 3
Dates Received 03 February 2020; revised manuscript received 15 June 2020; published online 25 June 2020
Citation V.A. Tanriverdiyev, J. Nano- Electron. Phys. 12 No 3, 03028 (2020)
PACS Number(s) 75.70.Cn, 75.40.Gb
Keywords 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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