Electronic structure and effects of dynamical electron correlation in ferromagnetic bcc Fe, fcc Ni, and antiferromagnetic NiO

We have constructed a $\text{LDA}+\text{DMFT}$ method in the framework of the iterative perturbation theory with local density approximation (full-LDA) Hamiltonian without mapping onto the effective Wannier orbitals. We then apply this $\text{LDA}+\text{DMFT}$ method to ferromagnetic bcc Fe and fcc Ni as a test of transition metal, and to antiferromagnetic NiO as an example of transition metal oxide. In Fe and Ni, the width of occupied $3d$ bands is narrower than those in LDA and Ni 6 eV satellite appears. In NiO, the resultant electronic structure is of charge-transfer insulator type and the band gap is 4.3 eV. These results are in good agreement with the experimental x-ray photoemission spectroscopy. The configuration mixing and dynamical correlation effects play a crucial role in these results.

Figure 1

Left (1a)–(1d): Energy spectrum in ferromagnetic bcc Fe. Right (2a)–(2d): Energy spectrum in ferromagnetic fcc Ni. (1a)(2a): LDA. (1b)(2b): $\text{LDA}+\text{DMFT-IPT}\left(1\right)$. [(1c) and (2c)] Atomic ionization spectrum by the LFT. [(1d) and (2d)] Atomic affinity spectrum by the LFT. The energy zeroth is set at the Fermi level $\left(E_F=0\right)$, and temperature is set at 1000 K $\left(T=1000\text{K}\right)$.

Figure 2

(Color) The $\mathit{k}$-resolved spectrum $-\text{Im}\mathcal{G}\left(\mathit{k},\omega \right)$ by $\text{LDA}+\text{DMFT-IPT}\left(1\right)$ (shaded regions) with the energy bands (dashed lines) by LDA. Left: ferromagnetic bcc Fe: (a) majority spin and (b) minority spin. The high-symmetry $\mathit{k}$ points are $\Gamma \left(0,0,0\right)$, $N\left(\frac{1}{2},\frac{1}{2},0\right)$, $P\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$, and $H\left(0,0,1\right)$. Right: ferromagnetic fcc Ni: (a) majority spin and (b) minority spin. The high-symmetry $\mathit{k}$ points are $L\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$, $\Gamma \left(0,0,0\right)$, $X\left(0,1,0\right)$, $W\left(\frac{1}{2},1,0\right)$, and $K\left(0,\frac{3}{4},\frac{3}{4}\right)$. The energy zeroth is set at the Fermi energy $E_F=0$, and temperature is set to be 1000 K $\left(T=1000\text{K}\right)$.

Figure 3

Energy spectra $-\text{Im}\mathcal{G}\left(\omega \right)$ of antiferromagnetic NiO. (1) Partial $-\text{Im}\mathcal{G}\left(\omega \right)$ by LDA. (2) Partial $-\text{Im}\mathcal{G}\left(\omega \right)$ by $\text{LDA}+\text{DMFT-IPT}\left(1\right)$. (3) Partial $-\text{Im}\mathcal{G}\left(\omega \right)$ in the atomic spectra of Ni by LFT. (4) Total $-\text{Im}\mathcal{G}\left(\omega \right)$ by $\text{LDA}+\text{DMFT-IPT}\left(1\right)$ and XPS. The energy zeroth is set at the Fermi energy $\left(E_F=0\right)$, and temperature is set to be 1000 K $\left(T=1000\text{K}\right)$. Characteristic atomic spectra for $e_g$ $\left(t_{2g}\right)$ orbitals is labeled by white (black) letter in (3). Note that the index of nickel “majority (minority) spin” denotes up (down) spin component on up spin Ni site and down (up) spin component on down spin Ni site.

Figure 4

(Color) (a) Partial $-\text{Im}\mathcal{G}\left(\omega \right)$ for antiferromagnetic NiO by LDA corresponding to Fig. 3(1). (b) $\mathit{k}$-resolved spectrum of $\text{LDA}+\text{DMFT-IPT}\left(1\right)$ and energy bands of LDA for antiferromagnetic NiO. Shaded regions: $\mathit{k}$-resolved spectrum $-\text{Im}\mathcal{G}\left(\mathit{k},\omega \right)$ by $\text{LDA}+\text{DMFT-IPT}\left(1\right)$. Dashed lines: energy bands by LDA. Dots: the angle-resolved photoemission spectrum (ARPES) (Ref. 49). The high-symmetry $\mathit{k}$ points are $K\left(0,\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.,\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)$, $L\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$, $\Gamma \left(0,0,0\right)$, and $X\left(0,0,1\right)$. (c) Partial $-\text{Im}\mathcal{G}\left(\omega \right)$ for antiferromagnetic NiO by $\text{LDA}+\text{DMFT-IPT}\left(1\right)$ corresponding to Fig. 3(2). The energy zeroth is set at the Fermi energy $\left(E_F=0\right)$, and temperature is set to be 1000 K $\left(T=100\text{K}\right)$. Each figure shows the total of both majority and minority spins.