Dynamic Exchange Coupling between Magnets Mediated by Attenuating Elastic Waves

Abstract: Coupling between spatially separated magnets can be mediated by excitations such as photons and phonons, which can be characterized as coherent coupling and dissipative coupling with real and imaginary coupling rate. We theoretically predict the existence of dynamic exchange coupling in a closed magneto-elastic system mediated by attenuating elastic waves and whose coupling rate is complex in general, leading to alternating repulsive or attractive spectrum depending on thickness of the elastic media. The presence of dynamic exchange coupling and its competition with coherent coupling are numerically verified according to the generalized Hooke's law in magneto-elastic systems. The predicted mechanism provides a new strategy to synchronize precessing magnets as well as other excitations over long distance and pave the way for non-Hermitian engineering of collective modes in hybrid magnonics, phononics and photonics.