Phase stability and properties of manganese oxide polymorphs: Assessment and insights from diffusion Monte Carlo

We present an analysis of the polymorphic energy ordering and properties of the rocksalt and zinc-blende structures of manganese oxide using fixed node diffusion Monte Carlo (DMC). Manganese oxide is a correlated, antiferromagnetic material that has proven to be challenging to model from first principles across a variety of approaches. Unlike conventional density functional theory and some hybrid functionals, fixed node diffusion Monte Carlo finds the rocksalt structure to be more stable than the zinc-blende structure, and thus recovers the correct energy ordering. Analysis of the site-resolved charge fluctuations of the wave functions according to DMC and other electronic structure descriptions gives insights into elements that are missing in other theories. While the calculated band gaps within DMC are in agreement with predictions that the zinc-blende polymorph has a lower band gap, the gaps themselves overestimate reported experimental values.

Figure 1

The rocksalt (left) and zinc-blende (right) polymorphs of manganese oxide; both exhibit an antiferromagnetic ordering of Mn atoms. The grey atoms are oxygen and the blue or red are opposing spin manganese atoms. In the rocksalt structure each Mn atom possesses a neighboring octahedral field of O atoms; in the zinc-blende structure the neighboring field of O atoms surrounding each Mn atom is tetrahedral instead.

Figure 2

The energy difference $E_{\mathrm{ZB}}-E_{\mathrm{RS}}$ according to DFT-${\mathrm{PBE}1}_x$, obtained from all-electron calculations (orange) and with Burkatski-Filipi-Dolg (Hartree-Fock) pseudopotentials (blue). According to all-electron results, for $\alpha =0$ the ZB phase is lower in energy, but as $\alpha$ increases the RS phase becomes stable. The crossing occurs around $\alpha =10\%$. When Burkatski-Filipi-Dolg pseudopotentials are used, the trends are very similar.

Figure 3

The partial density of states for O $2s,2p$ and Mn $3d$ orbitals, as obtained within DFT for different degrees of exchange mixing $\alpha$. As $\alpha$ increases, the band gap becomes larger as expected. Also below the valence band maximum, the $p-d$ hybridization increases as the relative Mn $3d$ orbital energies near the VBM drop.

Figure 4

The total absolute spin on the manganese atoms increases with increasing exchange weight $\alpha$. The spin on the ZB phase is always lower than that of the RS phase.

Figure 5

The effect of varying the trial wave function in DMC using different DFT-${\mathrm{PBE}1}_x$ exchange weights $\alpha$ on the DMC total energies for RS and ZB (error bars are smaller than the marker size). Both phases demonstrate a minimum energy around $\alpha =25\%$, and maintain similar relative energies over the domain.

Figure 6

The DMC energies of the RS and ZB phases (eV/fu), relative to the extrapolated zero time step DMC energy of the ZB phase, plotted as a function of time step, for a 4-atom supercell. The inset shows the energy difference $E_{\mathrm{ZB}}-E_{\mathrm{RS}}$ (eV/fu) vs time step.

Figure 7

Extrapolated values of lattice constants according to DMC for ZB and RS MnO are $4.73\pm 0.004\AA$ and $4.47\pm 0.005\AA$ respectively. The RS value is within 1% of experiment, 4.43 Å [33]. The experimental value for ZB is unknown, but the DMC value matches the PBE0 value of $4.73\AA$.

Figure 8

(a) The extrapolated DMC total energies of the RS and ZB phases; the RS phase is found to be lower in energy by $E_{\mathrm{ZB}}-E_{\mathrm{RS}}=132\pm 6.5$ meV/formula unit. (b) Compiled existing results and current DMC results on the energy ordering of MnO ZB and RS polymorphs.

Figure 9

The charge fluctuations $\langle \mathrm{\Psi }\left|{({\widehat{n}}_i-\langle {\widehat{n}}_i\rangle )}^2\right|\mathrm{\Psi }\rangle$ site-resolved onto Mn and O atoms from Slater determinants of PBE, PSE0, and HSE06 orbitals, in comparison to DMC and Hartree-Fock for rocksalt (top) and zinc blende (bottom). The trends demonstrate that both PBE0 and HSE06 improve the description of the materials, bringing the fluctuations closer to that of the DMC values.