Screened Coulomb interactions of localized electrons in transition metals and transition-metal oxides

The screened Coulomb interactions of localized electrons, often treated as adjustable parameters in constructing model Hamiltonians, are important quantities for studying strongly correlated materials. Using a recently implemented constrained random phase approximation approach, we have calculated the screened Coulomb and exchange interactions of $3d$ electrons in transition metals, late transition-metal monoxides, and VO${}_2$. For monoxides, we have also calculated the on-site screened Coulomb interaction for oxygen $p$ electrons as well as the intersite $pd$ interaction. Our results compare reasonably well with available experimental and theoretical results. We find that for oxide systems, a self-consistent procedure is very important for an accurate account of the screening effect.

Figure 1

Total and projected DOS of CoO and NiO calculated within the LSDA.

Figure 2

Total and projected DOS of CoO and NiO calculated within the LSDA+$U$.

Figure 3

Comparison of present calculated Coulomb $U$ and exchange $J$ (filled circles) with previous results calculated within the cLDA approach[4, 15] (unfilled symbols) and empirical values[4] (stars). Data points from the same work are connected by dashed lines as a guide to the eye.

Figure 4

LDA band structure of fcc paramagnetic manganese.

Figure 5

Diagonal averaged (a) bare Coulomb $V$ and (b) screened Coulomb $U$ for $3d$ electrons in TMs calculated in this work (black dots) compared with previous cRPA results. Previous results are taken from Refs. 22 (diamonds), 23 (squares), and 27 (triangles).

Figure 6

Comparison of screened Coulomb $U$ (a) and exchange $J$ (b) for paramagnetic TMs between this work (closed circles) and empirical values (open circles) from Ref. 38. Effective dielectric constants for the direct Coulomb interaction (c) and the exchange interaction (d) are also presented. Result for the ferromagnetic phase of Fe, Co, and Ni are shown with star symbols.

Figure 7

Total and projected DOS of R phase and M${}_1$ phase of VO${}_2$ calculated using the LDA+$U$ method.