Momentum-dependent band spin splitting in semiconducting MnO2: a density functional calculation†
Recently, manganese-oxide compounds have attracted considerable attention, in particular, as candidate materials for photochemical water-splitting reactions. Here, we investigate electronic states of pristine manganese dioxides (MnO2) in different crystal phases using spin-polarized density functional theory (DFT) with Hubbard U correction. Geometrical structures and band dispersions of α-, β-, δ-, and λ-MnO2 crystals with collinear magnetic [ferromagnetic (FM) and antiferromagnetic (AFM)] orders are discussed in detail. We reveal that penalty energies that arise by violating the Goodenough–Kanamori rule are important and the origin of the magnetic interactions of the MnO2 crystals is governed by the superexchange interactions of Mn–O–Mn groups. In addition, it is found that momentum-dependent band spin splitting occurs in the AFM α-, β-, and δ-MnO2 crystals while no spin splitting occurs in the AFM λ-MnO2 crystal. Our results show that spin-split band dispersions stem from the different orientations of Mn-centred oxygen octahedra. Such interesting electronic states of the MnO2 crystals are unraveled by our discussion on the relationship between the effective (spin-dependent) single-electron potentials and the space-group symmetry operations that map up-spin Mn atoms onto down-spin Mn atoms. This work provides a basis to understand the relationship between the spin-dependent electronic states and the crystallography of manganese oxides. Another relationship to the recent experimental observations of the photochemical oxygen evolution of MnO2 crystals is also discussed.