Regions of existence of surface spin-waves in surface Brillouin zones of hexagonal simple ferromagnetic thin films

Abstract

Abstract A quantum statistic Green's-function method is used to study the surface in-plane propagating spin-waves (k// ≠ 0) in a symmetric magnetic film consisting of twelve atomic layers with damping. The effects of temperature, external magnetic field, surface exchange coupling, surface anisotropy and thickness on the regions of existence of low- and high-frequency surface spin-waves in the surface two-dimensional Brillouin zone have been investigated. The regions of existence of surface spin-waves increase first and then decrease with increasing temperature or external magnetic field. There is a special temperature or external magnetic field, at which the regions of existence of surface spin-waves exhibit a maximum. Additionally, the spatial distribution of spin-waves in different spin-wave frequency range is also studied. For a film with low-frequency surface spin-waves, there is a special spin-wave frequency range, in which no spin-waves propagate in surfaces, the spin-waves propagate only in internal layers of the film. Namely, in this frequency range, the film is a spin-waves surface insulator . For a film with high-frequency surface spin-waves, there is also a special spin-wave frequency range, in which the spin-waves propagate only in surfaces. Namely, in this frequency range, the film is a spin-waves internal insulator . In the present work, a quantum statistic approach is developed to study the surface spin-wave of magnetic film. The results show the method to adjust the regions of existence of surface spin-waves in the surface two-dimensional Brillouin zone and are beneficial for building future microwave device based upon magnetic film.