$\mathrm{LDA}+\mathrm{DMFT}$ computation of the electronic spectrum of NiO

The electronic spectrum, energy gap and local magnetic moment of paramagnetic NiO are computed using the local density approximation plus dynamical mean-field theory (LDA + DMFT). To this end the noninteracting Hamiltonian obtained within the LDA is expressed in Wannier function basis, with only the five antibonding bands with mainly Ni $3d$ character taken into account. Complementing it by local Coulomb interactions one arrives at a material-specific many-body Hamiltonian which is solved by DMFT together with quantum Monte Carlo (QMC) simulations. The large insulating gap in NiO is found to be a result of the strong electronic correlations in the paramagnetic state. In the vicinity of the gap region, the shape of the electronic spectrum calculated in this way is in good agreement with the experimental x-ray-photoemission and bremsstrahlung-isochromat-spectroscopy results of Sawatzky and Allen. The value of the local magnetic moment computed in the paramagnetic phase (PM) agrees well with that measured in the antiferromagnetic (AFM) phase. Our results for the electronic spectrum and the local magnetic moment in the PM phase are in accordance with the experimental finding that AFM long-range order has no significant influence on the electronic structure of NiO.

Figure 1

Nonmagnetic band structure of NiO obtained by the LMTO method; the Fermi energy is set to zero. The five “$d$-like” Bloch bands (in solid lines) are used for constructing Wannier functions.

Figure 2

(Color online). $t_{2g}$- and $e_g$-resolved LDA DOS in the basis of $d$-like Wannier functions ($t_{2g}$, red solid curve; $e_g$, green dot-dashed curve) and Ni $3d$ LMTOs ($t_{2g}$, black dotted dash curve; $e_g$, blue dash curve).

Figure 3

(Color online). Theoretical energy spectrum of NiO obtained by the $\mathrm{LDA}+\mathrm{DMFT}$ approach for $T=1160\mathrm{K}$, and $U=8\mathrm{eV}$, $J=1\mathrm{eV}$. $t_{2g}$ states (blue dashed curve) and $e_g$ states (green dotted curve) are resolved, and total states (red solid curve) are the sum of the two. Note the curve for total states coincides with that of the unoccupied $e_g$ states above the chemical potential.

Figure 4

(Color online). Theoretical spectrum is obtained by the $\mathrm{LDA}+\mathrm{DMFT}$ approach (red curve) for $U=8\mathrm{eV}$ and $J=1\mathrm{eV}$ at $T=1160\mathrm{K}$, compared with experimental $\mathrm{XPS}+\mathrm{BIS}$ data (black dots) after Sawatzky and Allen (Ref. 7). The zero energy point of the theoretical curve is shifted to fit the energy scale of the experimental data.

Figure 5

(Color online). Theoretical spectrum of NiO obtained by the $\mathrm{LDA}+\mathrm{DMFT}$ approach for $U=8\mathrm{eV}$, $J=1\mathrm{eV}$ at $T=1160\mathrm{K}$ (red solid curve) and $T=725\mathrm{K}$ (green dashed curve) respectively.

Figure 6

(Color online) Theoretical spectra obtained by the $\mathrm{LDA}+\mathrm{DMFT}$ approach for $U=7.5$, 8, and $8.5\mathrm{eV}$ (blue dashed, red solid, and green dashed curves, respectively) with fixed $J=1\mathrm{eV}$ and temperature $T=1160\mathrm{K}$. Experimental $\mathrm{XPS}+\mathrm{BIS}$ data from Sawatzky and Allen (Ref. 7) are also shown for comparison.