Origin of Spinel Nanocheckerboards via First Principles

Self-organizing nanocheckerboards have been experimentally fabricated in Mn-based spinels but have not yet been explained with first principles. Using density-functional theory, we explain the phase diagram of the ZnMn_{x}Ga_{2-x}O_{4} system and the origin of nanocheckerboards. We predict total phase separation at zero temperature and then show the combination of kinetics, thermodynamics, and Jahn-Teller physics that generates the system's observed behavior. We find that the {011} surfaces are strongly preferred energetically, which mandates checkerboard ordering by purely geometrical considerations.