Magneto-Elastic Coupling of Surface Spin and Surface Acoustic Waves

Nonreciprocal propagation of surface acoustic waves (SAWs) may be achieved through magneto-elastic coupling with surface spin waves (SSWs). Here, we studied theoretically SAW–SSW coupling in yttrium–iron garnet (YIG)/ gadolinium–gallium garnet (GGG) bilayers magnetized in-plane at an oblique angle to the direction of wave propagation. An expression for the coupling rate that considers actual thickness profiles of both waves has been derived. The effects of the SAW–SSW coupling are most pronounced at the crossing point of the SAW and SSW spectra, which, for typical experimental parameters, occurs at a frequency of about 2 GHz and wavelength 2 µm. Under these conditions, the coupling rate for SSWs localized near the free surface of the YIG layer weakly depends on system parameters and exceeds 25 MHz. In contrast, for the opposite direction of wave propagation, when the SSW is localized near the YIG/GGG interface, the coupling rate rapidly decreases with the increase of YIG thickness, and strong nonreciprocity of the coupling is observed for thicknesses over 0.5 µm. With the increase of YIG thickness above 2.5 µm, coupling of SAW to higher order standing spin waves becomes important, which pollutes the spectrum of hybrid magneto-elastic waves, making observation and practical use of nonreciprocal SAW–SSW coupling more difficult.