Electronic structure of black sodalite

The electronic structure of black sodalite, ${\mathrm{Na}}_8{(\mathrm{A}\mathrm{l}\mathrm{S}\mathrm{i}\mathrm{O}}_4{)}_6,$ is determined in the local-spin-density approximation (LSDA). This structure has six Na atoms to compensate the six Al atoms, leaving two excess Na atoms. A band-gap electronic state is induced in the wide oxide gap by the excess sodium, and has “particle in a box” behavior. Magnetic orderings of these gap states are studied. Analytic models show that an antiferromagnetic ordering is lowest in energy in the LSDA. A self-consistent LSDA calculation shows the system to change from a metal to an antiferromagnetic insulator when spin orderings are allowed. Hopping and Hubbard-U parameters are estimated, and the many-body correlated Hubbard model is solved using a constrained path Monte Carlo technique, which again predicts the system to be antiferromagnetic with a $T_c$ of order 50 K.