Ground-state properties of multivalent manganese oxides: Density functional and hybrid density functional calculations

We present density functional theory (DFT) calculations for MnO, ${\mathrm{Mn}}_3{\mathrm{O}}_4$, $\alpha \text{−}{\mathrm{Mn}}_2{\mathrm{O}}_3$, and $\beta \text{−}\mathrm{Mn}{\mathrm{O}}_2$, using different gradient corrected functionals, such as Perdew-Burke-Ernzerhof (PBE), $\mathrm{PBE}+\mathrm{U}$, and the two hybrid density functional Hartree-Fock methods PBE0 and Heyd-Scuseria-Ernzerhof (HSE). We investigate the structural, electronic, magnetic, and thermodynamical properties of the mentioned compounds. Despite the lack of sufficient experimental information allowing for a comprehensive comparison of our results, we find overall that hybrid functionals provide a more consistent picture than standard PBE. Although $\mathrm{PBE}+\mathrm{U}$ is limited due to the uncertainty of choosing the parameter U, it nevertheless provides satisfactory results in terms of magnetic properties and energies of formation. This is in line with results of PBE0 and HSE calculations, but the $\mathrm{PBE}+\mathrm{U}$ approach tends to overestimate the equilibrium volumes, and also it favors a half-metallic state for the more reduced oxides ${\mathrm{Mn}}_3{\mathrm{O}}_4$, $\alpha \text{−}{\mathrm{Mn}}_2{\mathrm{O}}_3$, and $\beta \text{−}\mathrm{Mn}{\mathrm{O}}_2$, rather than an insulating character as derived from the hybrid functional approaches. The comparison of measured valence-band spectra with the HSE density of states offers a further assessment of the capability of hybrid approaches in overcoming the deficiencies of DFT in treating these kinds of materials.

Figure 1

(Color online) Schematic ball and stick representation of (a) MnO, (b) ${\mathrm{Mn}}_3{\mathrm{O}}_4$, (c) $\alpha \text{−}{\mathrm{Mn}}_2{\mathrm{O}}_3$, and (d) $\beta \text{−}\mathrm{Mn}{\mathrm{O}}_2$. White spheres indicate oxygen atoms whereas black (red) and gray (pink) balls indicate spin-up and spin-down Mn atoms, respectively. Magnetic ordering corresponds to optimal HSE low-energy structure.

Figure 2

(Color online) Comparison between calculated (by the PBE, $\mathrm{PBE}+\mathrm{U}$, PBE0, and HSE approaches) and experimental equilibrium volumes (${\mathrm{\AA }}^3$/atom). The manganese oxidation states are also indicated.

Figure 3

(Color online) Calculated spin resolved DOS for (a) MnO, (b) ${\mathrm{Mn}}_3{\mathrm{O}}_4$, (c) $\alpha \text{−}{\mathrm{Mn}}_2{\mathrm{O}}_3$, and (d) $\beta \text{−}\mathrm{Mn}{\mathrm{O}}_2$ within PBE, $\mathrm{PBE}+\mathrm{U}$ $(\mathrm{U}=4\mathrm{eV})$, PBE0, and HSE. Shadowed areas depict the gap region.

Figure 4

(Color online) Comparison between the $d$-like DOS of the HSE calculation (full line) in comparison to the experimental XPS valence-band spectra for (a) MnO, (b) ${\mathrm{Mn}}_3{\mathrm{O}}_4$, (c) $\alpha \text{−}{\mathrm{Mn}}_2{\mathrm{O}}_3$, and (d) $\beta \text{−}\mathrm{Mn}{\mathrm{O}}_2$, according to Ref. 55. The levels of the experimental and calculated valence-band maxima are aligned. The calculated DOS is convoluted by a Gaussian with a width of $\sigma =0.6\mathrm{eV}$.

Figure 5

(Color online) Comparison of calculated and experimental energies of formation (eV). The numerical labels indicate the oxidation state.