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.