Frequency Characteristics of Reflection and Refraction Coefficients of Bulk Spin Waves in Spin Lens with Non-Ideal Interphaces

Background. This work is devoted to the application of geometrical optics formalism to describe the behavior of spin waves, which is propagating in a ferromagnetic medium with non-uniform distribution of magnetic parameters. Use of this approach allows to describe the process of refraction of spin waves to determine the focal length of spin lenses or mirrors and to operate it by changing the frequency of the spin wave with a given magnetic parameters of a medium. Objective. The objective is to calculate the index of refraction, reflection coefficient and focal length of spin lens as function of frequency of spin waves, the external magnetic field and magnetic parameters of the medium. Methods. In this paper, to find the refractive index and the focal length was used the geometrical optics approach. To describe the dynamics of the magnetization vector the formalism was used of the parameter of order of spin density that also gives an opportunity to use the methods of quantum mechanics to calculate the spin wave reflection coefficient. Results. In the paper the refractive index and focal length of a bulk spin lens have been found. By considering the generalized boundary conditions the expression has been found for the reflection coefficient of spin lens. In addition, results of investigation says that strong dependence exists of transparency of spin lens on the frequency of spin waves that is characterized by corresponding magnetic parameters of structure. Conclusions. It is shown the possibility to change “optical” spin lens parameters in a wide range of values by changing only the frequency of spin waves and keeping constant the values of the external magnetic field and magnetic structure parameters. In addition, the results of studies prove that exists a strong dependence of the spin lens transparency on the quality of its borders, which is characterized by appropriate parameters of interface.