Emergent honeycomb lattice in LiZn2Mo3O8

We introduce the idea of emergent lattices, where a simple lattice decouples into two weakly-coupled lattices as a way to stabilize spin liquids. In LiZn2Mo3O8, the disappearance of 2/3rds of the spins at low temperatures suggests that its triangular lattice decouples into an emergent honeycomb lattice weakly coupled to the remaining spins, and we suggest several ways to test this proposal. We show that these orphan spins act to stabilize the spin-liquid in the $J_1-J_2$ honeycomb model and also discuss a possible 3D analogue, Ba2MoYO6 that may form a "depleted fcc lattice."