Hydrodynamic Spin Lattices

In this talk, we introduce hydrodynamic spin lattices (HSLs) of walking droplets as a new class of highly tunable active spin analog systems. Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding wave fields. A walking droplet, or walker, may be trapped by a submerged circular well at the bottom of the fluid bath, leading to a clockwise or counterclockwise angular motion centered at the well. When a collection of such wells is arranged in a 1D or 2D lattice geometry, a thin fluid layer between wells enables wave-mediated interactions between neighboring walkers. For sufficiently strong pair-coupling, wave interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or antiferromagnetic order. Transitions between these two forms of magnetic order can be induced through variations in non-equilibrium driving, lattice geometry and Coriolis forces mimicking an external magnetic field. Our experimental results agree with theoretical predictions from a generalized Kuramoto model, establishing HSLs as a generic paradigm for active phase oscillator dynamics with complex particle-wave coupling.