Localization of spin wave in a magnetic ultra-thin film

A quantum statistic Green's-function method is used to study the localization of in-plane propagating spin waves in a magnetic film consisting of two different atomic planes. It is known that, in a three dimensions magnetic system with randomness, there is a mobility edge at which the states of spin wave change their character from extended to localized. However, we find a mobility edge in the magnetic film at finite temperature. In low-frequency range, the spin waves ω₁ and ω₂ are extended, they can propagate in layers 1 as well as 2. Whereas, in high-frequency range, the spin waves ω₁ and ω₂ are localized, i.e., they propagate in layers 2 and 1, respectively. We use the ratio of frequency width of localized spin wave to that of extended spin wave to characterize the degree of localization of spin wave in the magnetic film. The effects of the temperature, the interlayer coupling and the external magnetic field on the mobility edge energy ω * and the degree of localization of spin wave have been investigated. In the present work, a quantum approach is developed to study the localization of spin wave and the results show the method to adjust the transition from localized to extended states of spin wave in a magnetic film consisting of two different atomic planes.