We predict that surface acoustic waves are generated preferentially in one direction in a heterostructure of a thin magnetic film on a non-magnetic substrate. The non-reciprocity arises from magneto-elastic coupling and magneto-rotation coupling, the former being dominant for YIG/GGG heterostructures. For YIG films thinner than about 100 nm, the surface acoustic wave amplitude is nearly unidirectional at certain angles of the in-plane equilibrium magnetisation. We compute the full magnetic field dependence of the effect for a selected device.
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