The magnetization dynamics in two dipolarly coupled ferromagnet–normal metal (FM–NM) structures is investigated under symmetric and asymmetric compensation of intrinsic spin-wave damping mediated by the spin Hall effect. Within the framework of a linear model of complex amplitudes, the spectral characteristics of the normal modes are analyzed, including their degeneracy at an exceptional point in the asymmetric case. It is demonstrated that asymmetric compensation leads to a transition from a two-frequency to a single-frequency regime at the exceptional point, accompanied by a narrowing of the spectral linewidth, whereas symmetric compensation preserves the two-frequency regime. The results are of relevance for the development of magnonic devices such as filters and sensors.
Temnaya et al. (Wed,) studied this question.