  We describe a theoretical scheme for generating scalable spin squeezing with
nearest-neighbour interactions between spin-1/2 particles in a 3D lattice,
which are naturally present in state-of-the-art 3D optical lattice clocks. We
propose to use strong isotropic Heisenberg interactions within individual
planes of the lattice, forcing the constituent spin-1/2s to behave as large
collective spins. These large spins are then coupled with XXZ anisotropic
interactions along a third direction of the lattice. This system can be
realized via superexchange interactions in a 3D optical lattice subject to an
external linear potential, such as gravity, and in the presence of spin-orbit
coupling (SOC) to generate spin anisotropic interactions. We show there is a
wide range of parameters in this setting where the spin squeezing improves with
increasing system size even in the presence of holes.
