By combining first-principles calculations and experimental x-ray photoemission (XPS) spectroscopy measurements, we investigate the electronic structure of potential Li-ion battery cathode materials Li$M$PO${}_4$ ($M=\mathrm{Mn}$, Fe, Co, Ni) to uncover the underlying mechanisms that determine small hole polaron formation and migration. We show that small hole polaron formation depends on features in the electronic structure near the valence-band maximum and that, calculationally, these features depend on the methodology chosen for dealing with the correlated nature of the transition-metal $d$-derived states in these systems. Comparison with experiment reveals that a hybrid functional approach is superior to $\mathrm{GGA}+U$ in correctly reproducing the XPS spectra. Using this approach, we find that LiNiPO${}_4$ cannot support small hole polarons, but that the other three compounds can. The migration barrier is determined mainly by the strong- or weak-bonding nature of the states at the top of the valence band, resulting in a substantially higher barrier for LiMnPO${}_4$ than for LiCoPO${}_4$ or LiFePO${}_4$.

• Received 21 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.115106