Emergent order in hydrodynamic spin lattices

Macroscale analogues of microscopic spin systems offer direct insights into fundamental physical principles, thereby advancing our understanding of synchronization phenomena and informing the design of novel classes of chiral metamaterials. Here we introduce hydrodynamic spin lattices (HSLs) of 'walking' droplets as a class of active spin systems with particle-wave coupling. HSLs reveal various non-equilibrium symmetry-breaking phenomena, including transitions from antiferromagnetic to ferromagnetic order that can be controlled by varying the lattice geometry and system rotation. Theoretical predictions based on a generalized Kuramoto model derived from first principles rationalize our experimental observations, establishing HSLs as a versatile platform for exploring active phase oscillator dynamics. The tunability of HSLs suggests exciting directions for future research, from active spin-wave dynamics to hydrodynamic analogue computation and droplet-based topological insulators.