Nonreciprocal propagation of surface acoustic wave in Ni/LiNbO3

We have investigated surface acoustic wave propagation in Ni/LiNbO$_3$ hybrid devices. We have found the absorption and phase velocity are dependent on the sign of wave vector in a device, which indicates the nonreciprocal propagation characteristic of systems with time reversal and spatial inversion simultaneously broken symmetries. The nonreciprocity is reversed by the 180$^\circ$ rotation of magnetic field. Nonreciprocity seems largely dependent on the shape of ferromagnetic Ni film. The origin of these observations is ascribed to film shape dependent magnetoelastic coupling.