Spin-orbit coupling in the metallic and spin-liquid phases of Na ₄Ir₃O₈

It has recently been proposed that Na₄Ir₃O ₈ is a weak Mott insulator at ambient pressure, supporting a three-dimensional spin-liquid phase with a spinon Fermi surface. This proposal is consistent with recent experimental findings that the material becomes a metal upon increasing pressure or doping. In this work, we investigate the effect of the spin-orbit coupling arising from 5d Ir moments in both the metallic and the spin-liquid phases of Na₄Ir₃O ₈. The effective Hubbard model in terms of pseudospin j=1/2 Ir states is derived and its consequences to both metallic and spin-liquid phases are studied. In particular, the model leads to an enhanced Wilson ratio and strong temperature dependence of the Hall coefficient.