Magnonic φ Josephson junctions and synchronized precession

There has been a growing interest in non-Hermitian physics. One of its main goals is to engineer dissipation and to explore ensuing functionality. In magnonics, the effect of dissipation due to local damping on magnon transport has been explored. However, the effects of nonlocal damping on the magnonic analog of the Josephson effect remain missing, despite that nonlocal damping is inevitable and has been playing a central role in magnonics. Here, we uncover theoretically that a surprisingly rich dynamics can emerge in magnetic junctions due to intrinsic nonlocal damping, using analytical and numerical methods. In particular, under microwave pumping, we show that coherent spin precession in the right and left insulating ferromagnet (FM) of the junction becomes synchronized by nonlocal damping and thereby a magnonic analog of the phi Josephson junction emerges, where phi stands here for the relative precession phase of right and left FM in the stationary limit. Remarkably, phi decreases monotonically from pi to pi /2 as the magnon-magnon interaction, arising from spin anisotropies, increases. Moreover, we also find a magnonic diode effect giving rise to rectification of magnon currents. Our predictions are readily testable with current device and measurement technologies at room temperatures.