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   Magnetoelastic coupling is considered as one of the most reliable method to induce nonreciprocity of propagation losses of microwave‐frequency surface acoustic waves (SAW) and other acoustic modes propagating in nonmagnetic‐ferromagnetic heterostructures. Here, it is demonstrated theoretically that magnetoelastic coupling can also induce phase nonreciprocity of SAW, which is necessary for the development of SAW circulators and other nonreciprocal solid‐state‐acoustic devices. In contrast to previous studies, induction of the phase nonreciprocity requires the coupling of SAW to a strongly nonreciprocal spin wave (SW), having the nonreciprocal splitting of the SW spectrum much larger than the strength of the magnetoelastic coupling, which, in turn, should be much larger than the geometric mean of the SW and SAW damping rates. In this case, the hybridized SAW in the spectral region between the magnetoelastic gaps demonstrate significant phase nonreciprocity, retaining, at the same time, propagation losses that are close to those of unhybridized SAW. Possible practical realization of nonreciprocal SAW phase shifters and SAW‐ring‐based circulators based on hybridized waves in acoustic crystal and synthetic antiferromagnetic heterostructures is discussed.

    

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