First-principles calculations of dynamical screened interactions for the transition metal oxides $M$O ($M$=Mn, Fe, Co, Ni)

To facilitate reliable and accurate modeling of the late transition metal oxides from first principles, we present detailed and systematic calculations of the dynamical screened Coulomb interactions (Hubbard $U$) of MnO, FeO, CoO, and NiO within the constrained random-phase approximation. The matrix elements of the screened interactions are calculated in maximally localized Wannier functions. We consider the screened interactions not only for conventional models that include only the $d$-like bands but also for models that include both the transition metal $d$ bands and the oxygen $p$ bands. The screened interaction is found to be sensitive to the screening channels subtracted from the polarization function. The frequency dependence of the screened interactions of these oxides is characterized by the two sharp peaks in low-energy region that may be called “subplasmons,” which arise from the particle-hole transitions between $d$ and oxygen $p$ states.

Figure 1

Band structure (left) and density of states (right) of the paramagnetic TMOs calculated with the LDA. In the left panels the Wannier-interpolated band structures[33] are also plotted by circles.

Figure 2

(a) Diagonal part [Eq. (9)] of the bare Coulomb interaction matrix in the Wannier function basis for each model. (b) Spread of the Wannier functions.

Figure 3

(a) Fully screened Coulomb interaction $W$ of $3d$ Wannier functions. (b) Partially screened Coulomb interaction $U$ of $3d$ Wannier functions. The values for the transition metals (TMs) are calculated with the methods in Refs. 36 and 37 for open circles and crosses, respectively.

Figure 4

Fully screened interaction ($W$) and partially screened interaction $U$ of oxygen $2p$-like Wannier functions.

Figure 5

Fully screened interaction ($W$) and partially screened interaction $U$ between $d$ and $2p$ Wannier functions.

Figure 6

(a) Fully screened interaction [$W\left(\omega \right)$] in the $d$ model. (b) Partially screened interaction [$U\left(\omega \right)$] in the $d$ model. (c) Partially screened interaction [$U\left(\omega \right)$] in the $dp$ model.

Figure 7

Partially screened interaction [$U\left(\omega \right)$] in the $d$-$dp$ model (b).

Figure 8

(a) Fully screened interaction [$W\left(\omega \right)$] of the transition metals. (b) Partially screened interaction [$U\left(\omega \right)$] of the transition metals.