Emergent order in hydrodynamic spin lattices

Macroscale analogues(1-3) of microscopic spin systems offer direct insights into fundamental physical principles, thereby advancing our understanding of synchronization phenomena(4) and informing the design of novel classes of chiral metamaterials(5-7). 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(8). Theoretical predictions based on a generalized Kuramoto model(4) 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. A macroscopic analogue of a spin system is shown to emerge in an ensemble of droplets bouncing on the surface of a vibrating bath, revealing symmetry-breaking phenomena such as 'magnetic' ordering.