Long-distance coupling of standing spin waves mediated by a charge current

We propose an experimentally feasible dynamic coupling of ferromagnets mediated by a charge current in a nonmagnetic heavy metal. Dynamic magnetic moments generate a spin current via spin pumping, subsequently converted into charge current through the inverse spin Hall effect. This charge current, in turn, generates another spin current via the spin Hall effect, exerting an anti-damping-like torque on the adjacent ferromagnet. Our theoretical framework reveals the dissipative nature of this dynamic coupling, characterized by energy-level attraction that promotes synchronization of frequency, phase, and amplitude information. Experimental validation is realized on submicrometer-sized Py rectangles interconnected by Pt strips using spin-torque ferromagnetic resonance techniques. The standing spin waves excited in Py arrays exhibit high spin pumping efficiency, enabling the demonstration of the proposed dynamic coupling. A notably long coupling length exceeding 2 \textmu{}m is achieved. These findings underscore a promising pathway for integrated magnonic devices, particularly in applications related to spin synchronization and transmission.