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Abridged general form of the boundary conditions at an interface between antiferromagnetic (AFM) and ferromagnetic (FM) materials have been obtained in the continuous medium approximation [1], taking into account the fact that the interface is a composite material with finite thickness $\delta$ which is much less than the length of the spin wave (SW) $\lambda_{\text{sw}}$ and penetration depth $\lambda$ into second material [2]. Three order parameters have been considered inside an interface of finite thickness with magnetizations of both sublattices $\mathbf{M}_{1}$ and $\mathbf{M}_{2}$ of AFM, and magnetization $\mathbf{M}$ of FM. Using these boundary conditions, the excitation of a volume SW has been considered in FM when SW in AFM falls onto this interface. The uniform and non-uniform exchange between all order parameters have been taken into account in the interface energy as the coordinate dependencies of the magnetic parameters characterizing two-sublattice AFM, FM, and the interface region on the coordinate along the axis perpendicular to the interface in the energy. Interconnection between the magnitudes of the amplitudes of the incident spin waves in both sublattices and the reflected spin waves in both sublattices of the two-sublattice AFM have been derived. All possible variants of the energy transfer to the second material in the current system via the Poynting vector have been considered and the dependency between the amplitudes of the incident, transferred and the reflected SWs in the positive cases has been demonstrated [3]. The amplitude coefficients of the scattering and the phases of transmission and reflection of SW through the AFM/FM interface have been derived in general case.
[1] O. P. Busel, O. Yu. Gorobets and Yu. I. Gorobets, “Boundary conditions at the interface of finite thickness between ferromagnetic and antiferromagnetic materials”, J. Magn. Magn. Mater. 462, 226-229 (2018)
[2] V. V. Kruglyak, O. Yu. Gorobets, Yu. I. Gorobets, and A. N. Kuchko, “Magnetization boundary conditions at a ferromagnetic interface of finite thickness”, J. Phys.: Condens. Matter 26, 406001 (2014).
[3] A. I. Akhiezer, V. G. Bar’yakhtar, and S. V. Peletminskii, “Spin waves“ (North-Holland, Amsterdam, 1968).
