Understanding the electronic and ionic conduction and lithium over-stoichiometry in LiMn$_2$O$_4$ spinel

We report a first-principles study of defect thermodynamics and transport in spinel-type lithium manganese oxide LiMn$_2$O$_4$, an important lithium-ion battery electrode material, using density-functional theory and the Heyd-Scuseria-Ernzerhof screened hybrid functional. We find that intrinsic point defects in LiMn$_2$O$_4$ have low formation energies and hence can occur with high concentrations. The electronic conduction proceeds via hopping of small polarons and the ionic conduction occurs via lithium vacancy and/or interstitialcy migration mechanisms. The total conductivity is dominated by the electronic contribution. LiMn$_2$O$_4$ is found to be prone to lithium over-stoichiometry, i.e., lithium excess at the manganese sites, and Mn$^{3+}$/Mn$^{4+}$ disorder. Other defects such as manganese antisites and vacancies and lithium interstitials may also occur in LiMn$_2$O$_4$ samples. In light of our results, we discuss possible implications of the defects on the electrochemical properties and provide explanations for the experimental observations and guidelines for defect-controlled synthesis and defect characterization.