Spin lattices of walking droplets*

We present experiments that demonstrate the spontaneous emergence of collective behavior in spin lattices of droplets walking on a vibrating fluid surface. Circular wells at the bottom of the fluid bath encourage individual droplets to walk in clockwise or counter-clockwise direction along circular trajectories centered at the lattice sites. A thin fluid layer between the wells enables wave-mediated interactions between neighboring walkers resulting in coherent rotation dynamics across the lattice. When the pair-coupling is sufficiently strong, interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or anti-ferromagnetic order. Results for different lattice geometries are discussed.