### Frequency Dependencies of the Exchange Spin Wave Reflection Coefficient on a One-Dimensional Magnon Crystal with Complex Interfaces

#### Abstract

**Background.** This work is devoted to theoretical study of the behavior of spin waves passing through multilayer ferromagnetic with complex interfaces.

**Objective. ****T**he aim of the paper is to calculate the reflection coefficient of multilayer ferromagnetic with complex interfaces as function of spin wave frequency at variable material parameter and constant value of external magnetic field. The formalism of geometric optics allows describing the spin wave refraction process and the reflection coefficient, as well as controlling this process by changing the frequency of the spin wave for given parameters of the medium.

**Methods.**** **To find the reflection coefficient from a multilayer** **ferromagnetic the mathematical apparatus of geometric optics was used**.**** **To describe the dynamics of the magnetization vector the formalism of the spin density order parameter was used allowing for the use of methods of quantum mechanics to calculate the reflection coefficient from a semi-infinite multilayer structure.

**Results.** The spin wave reflection coefficient of semi-infinite multilayer structure of ferromagnetic materials with complex interfaces has been found. The dependency graphs of the reflection coefficient from the frequency of the spin waves at different parameters of magnetic anisotropy inhomogeneity and constant value of the external magnetic field were obtained.

**Conclusions.**It is shown that the frequency dependencies are periodic, points of full transmission and areas, full of reflection. Decreasing exchange parameter value in interface causes the increase of reflectance coefficient. Changing the material parameters we get the necessary intensity value of the reflection coefficient depending on the frequency at a constant value of the external magnetic field.

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DOI: https://doi.org/10.20535/1810-0546.2017.4.105143

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