Symmetry of the coupling between surface acoustic waves and spin waves in synthetic antiferromagnets

Synthetic antiferromagnets host spin waves that are highly tunable. It is of practical interest to analyze the symmetry of their coupling to surface acoustic waves with the design of hybrid devices in view. For this we calculate the layer-resolved susceptibility tensor of a synthetic antiferromagnet, the effective magneto-elastic and magneto-rotation fields associated to a travelling elastic wave, and the power irreversibly transferred by the elastic wave to the magnetic layers. We consider Rayleigh-type surface acoustic waves: (a) that travel in an elastically isotropic, non-piezoelectric substrate, or (b) that propagate along the X direction at the surface of a Z-cut LiNbO$_3$ substrate, or (c) that are guided in a thin Z-cut LiNbO$_3$ film grown on a sapphire substrate. In particular, we show that the complementary angular dependencies of the acoustic and optical spin wave modes in synthetic antiferromagnets makes it possible to excite spin waves for any relative orientation of magnetization and acoustic wavevector. In addition, we discuss the symmetries of the driving fields and of the energy transferred to the magnetic degree of freedom. We evidence new interaction channels coupling the magnetization eigenmodes when elastic anisotropy and piezoelectricity of the substrate are considered.