Improved pseudopotential transferability for magnetic and electronic properties of binary manganese oxides from $\mathrm{DFT}+U+J$ calculations

We employ the fully anisotropic $\mathrm{DFT}+U+J$ approach with the PBEsol functional to investigate ground-state magnetic and electronic properties of bulk binary manganese oxides: MnO, ${\mathrm{Mn}}_3{\mathrm{O}}_4, \alpha -{\mathrm{Mn}}_2{\mathrm{O}}_3$, and $\beta -{\mathrm{MnO}}_2$, in order of increasing Mn valence. The computed crystal structures, noncollinear magnetic ground states, and corresponding electronic structures are in good agreement with the experimental data and hybrid functional calculations available in the literature. We take into account the nonlinear core-valence interaction in our Mn pseudopotential designed by ourselves, as it has been proven to be important for transition-metal systems. Although the Hubbard $U$ term is capable by itself of opening a band gap, the explicitly defined exchange parameter $J$ plays an important role in improving the detailed electronic and noncollinear magnetic structure profiles. Appropriate band gaps are obtained with $U$ values smaller than those used in previously reported calculations. Our results suggest that pseudopotential design together with $\mathrm{DFT}+U+J$ enables the acquisition of accurate properties of complex magnetic systems using a nonhybrid density functional.

Figure 1

Optimized crystal structures of the manganese oxides in their magnetic ground states: (a) AFM-II MnO, (b) YK-FiM ${\mathrm{Mn}}_3{\mathrm{O}}_4$, (c) NC-AFM2 $\alpha -{\mathrm{Mn}}_2{\mathrm{O}}_3$, and (d) spiral $\beta -{\mathrm{MnO}}_2$. Spin-up and spin-down Mn are colored in purple and gold for MnO, respectively, with red O atoms. The magnetic ground states of ${\mathrm{Mn}}_3{\mathrm{O}}_4, \alpha -{\mathrm{Mn}}_2{\mathrm{O}}_3$, and $\beta -{\mathrm{MnO}}_2$ are noncollinear; these spin structures are further discussed and illustrated in the Results and Discussion section. Bonds are not shown in (c) for clearer observation of the O chains along $\mathit{a}$ or $\mathit{b}$.

Figure 2

Projected density of states of the manganese oxides computed with PBEsol+$U$+$J$: (a) MnO shows a collinear AFM-II ground state with a band gap of 2.81 eV; the valence bands are governed by the overlap between O $2p$ and Mn $e_g$ orbitals, and the conduction bands by Mn $t_{2g}$ orbitals. The rest of the systems have noncollinear magnetic ground states: (b) ${\mathrm{Mn}}_3{\mathrm{O}}_4$ shows a YK-FiM ground state with a band gap of 1.01 eV, where ${\mathrm{Mn}}_A$ and ${\mathrm{Mn}}_B$ refer to the tetrahedral and the octahedral sites, respectively; (c) $\alpha -{\mathrm{Mn}}_2{\mathrm{O}}_3$ shows a NC-AFM2 ground state with a small band gap of 0.081 eV; (d) $\beta -{\mathrm{MnO}}_2$ shows a spiral magnetic ground state with a band gap of 0.25 eV. The band gap regions are indicated with a light blue color.

Figure 3

Computed YK-FiM structure of ${\mathrm{Mn}}_3{\mathrm{O}}_4$: (a) Magnetic moments are colored in green within the Mn tetrahedral (purple) and octahedral (gold) cages. (b) Side view showing the top and bottom bilayers used to illustrate the noncollinear spin pattern. (c) Top bilayer exhibiting a sinusoidal ${\mathrm{Mn}}_B$ spin pattern (along the green dashed lines), with ${\mathrm{Mn}}_A$ spin alignment along the $b$ axis. (d) The bottom bilayer shows a similar spin structure, but the pattern is related by mirror symmetry to the one shown in (c).

Figure 4

Magnetic and electronic structures of $\alpha -{\mathrm{Mn}}_2{\mathrm{O}}_3$: (a) Computed NC-AFM2 structure, with green and yellow spins indicating up and down directions, respectively. (b) The corresponding band structure shows an insulating state with a gap of 0.081 eV. (c) Four magnetic sublattices based on Mn Wyckoff positions. (d) The magnetic sublattices from (c) untangled for clarity, where sublattice I consists of Mn 4(a) and 4(b) in a C-type magnetic structure, sublattice II consists of Mn 8(c) in an A-type magnetic structure, sublattice III consists of Mn 8(c) in a G-type magnetic structure, and sublattice IV consists of Mn 8(c) in a unique magnetic structure, where each magnetic ion has three nearest neighbors, one with identical spin direction and two with opposite spin direction, similar to E type [107].

Figure 5

Computed spiral magnetic structure of $\beta -{\mathrm{MnO}}_2$: (a) Side view showing the seven unit cell period of the spin spiral, numbered for clarity, with magnetic moments colored in green. (b) Top view showing the spin rotation of ${129}^{\circ }$ from each layer. The darker the spin, the closer it is to the viewer.