Pressure-Induced Metal-Insulator Transition in ${\mathrm{LaMnO}}_3$ Is Not of Mott-Hubbard Type

Calculations employing the local density approximation combined with static and dynamical mean field theories ($\mathrm{LDA}+U$ and $\mathrm{LDA}+\mathrm{DMFT}$) indicate that the metal-insulator transition observed at 32 GPa in paramagnetic ${\mathrm{LaMnO}}_3$ at room temperature is not a Mott-Hubbard transition, but is caused by orbital splitting of the majority-spin $e_g$ bands. For ${\mathrm{LaMnO}}_3$ to be insulating at pressures below 32 GPa, both on-site Coulomb repulsion and Jahn-Teller distortion are needed.

Figure 1

${\mathrm{LaMnO}}_3$ orthorhombic translational cell ($Pbnm$) and LDA-NMTO Mn $e_g$ crystal-field orbitals $|1⟩$ (left) and $|2⟩$ (right) of, respectively, lowest and highest energy. For the sake of clarity, the orbitals have been placed only in subcells 3 and 2; those in subcells 1 and 4 may be obtained by the LaO mirror plane perpendicular to the $c(=z)$ axis. Since they have antibonding O $2p$ tails, orbitals $|1⟩$ and $|2⟩$ are directed, respectively, along and perpendicular to the longest Mn-O bond. Red/blue indicates a positive/negative sign.

Figure 2

Top: paramagnetic LDA band structure for orthorhombic (right) and hypothetical cubic (left) ${\mathrm{LaMnO}}_3$ at 0 GPa plotted along the high-symmetry lines in the $k_x=k_y$ plane. Energies are in eV, the $\mathbf{k}$ unit is $\pi$ [11], and the $\mathbf{k}$ points marked are $\Gamma \mathrm{MRX}\Gamma$ in the cubic, and $\Gamma \mathrm{YTZ}\Gamma$ in the orthorhombic BZ. The latter is folded in from the former and has the following smallest inequivalent reciprocal-lattice vectors: $\mathbf{Q}=000$, 110, 111, and 001. Dashed blue bands: large NMTO basis set; red bands: Mn $e_g$ NMTO basis set employed in Eq. (1). The $\mathrm{N}+1$ support energies $E_i$ are shown at the right-hand sides. The zero of energy corresponds to configuration $t_{2g}^4$. Second row: 0 and 11 GPa orthorhombic (0 GPa cubic) $e_g$ bands folded out (in) to the $(000,110)$-BZ. The dimensionless band-shape parameter, $X$, is the LDA crystal-field splitting in units of the effective hopping integral $t\equiv |t_{dd\sigma }|\sim W/6$, both obtained from the NMTO Mn $e_g$ Wannier functions. Third row: as second row, but obtained by spin-polarized $\mathrm{LDA}+U$ for random spin orientations (room temperature). Bands are labeled by their main character. The zero of energy is the Fermi level. Bottom: spectra calculated by $\mathrm{LDA}+\mathrm{DMFT}$. The full and dashed lines give the projections onto orbitals $|1⟩$ and $|2⟩$, respectively.

Figure 3

Left: LDA $e_g$ bandwidths, $W\sim 6t$, calculated as functions of compression, $V/V_0$. The top abscissa gives the experimental pressures, with 32 GPa marking the observed IM transition [5]. Right: 300 K $\mathrm{LDA}+\mathrm{DMFT}$ (solid lines) and $\mathrm{LDA}+U$ (dashed lines) results calculated as functions of $W$. For insulators, we plot the DOS gap (top scale) and for metals the quasiparticle weights (bottom scale). Full symbols indicate actual experimental structures and connecting black dotted lines are extrapolations. Each curve was calculated with fixed structure type (band shape): orthorhombic 0 GPa (green, $X=1.85$), orthorhombic 11 GPa (blue, $X=0.94$), cubic plus crystal-field splitting (dark red, $X=0.52$), and cubic (red, $X=0$).