A model for the phenomena in which magnetic waves excite elastic waves and vice versa, is formulated and used to explore magnetic and anti-plane elastic interactions in piecewise homogeneous ferromagnetic media. The magnetization vectors in each medium are perpendicular to the wave propagation direction. The space is in an external homogeneous magnetic field, the direction of which coincides with direction of the initial magnetization vector. A joint contact on the interface of two ferromagnetic semi-spaces is considered. The existence of new type of waves is shown. These waves are localized on the interface of two ferromagnetic media and accompany to the reflection and transmission waves. These types of waves named as an accompanying surface magnetoelastic (ASM) waves. An analytical expression for the coefficients of reflection, transmission, and accompanying surface magnetoelastic waves is derived. Coefficients of mentioned waves are strongly dependent on applied magnetic field, material properties of each medium as well as the frequency and the angle of an incident elastic wave. Conclusions and directions for the design of magnetoelastic devises are outlined.

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