Hydrodynamic Spin Lattices

We introduce a hydrodynamic analog system that allows us to investigate simultaneously the wave-mediated self-propulsion and interactions of effective spin degrees of freedom in inertial and rotating frames. 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 counter-clockwise 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 the spontaneous emergence of ferromagnetic or antiferromagnetic order. Transitions between these two forms of order can be controlled by tuning the lattice parameters or by imposing a Coriolis force mimicking an external magnetic field. Theoretical predictions based on a generalized Kuramoto model derived from first principles rationalize our experimental observations.