Electronic structures, magnetism, and phonon spectra in the metallic cubic perovskite ${\mathrm{BaOsO}}_3$

By using ab initio calculations, we investigated a cubic perovskite ${\mathrm{BaOsO}}_3$ and a few related compounds that have been synthesized recently and formally have a metallic $d^4$ configuration. In ${\mathrm{BaOsO}}_3$, which shows obvious three-dimensional fermiology, a nonmagnetism is induced by a large spin-orbit coupling (SOC), which is precisely equal to an exchange splitting $\sim 0.4$ eV of the $t_{2g}$ manifold. However, the inclusion of on-site Coulomb repulsion as small as $U^c\approx 1.2$ eV, only $1/3$ of the $t_{2g}$ bandwidth, leads to the emergence of a spin-ordered moment, indicating that this system is on the verge of magnetism. In contrast to ${\mathrm{BaOsO}}_3$, our calculations suggest that the ground state of an orthorhombic ${\mathrm{CaOsO}}_3$ is a magnetically ordered state due to the reduction of the strength of SOC (about a half of that of ${\mathrm{BaOsO}}_3)$ driven by the structure distortion, although the magnetization energy is only a few tenths of meV. Furthermore, in the cubic ${\mathrm{BaOsO}}_3$ and ${\mathrm{BaRuO}}_3$, our full-phonon calculations show several unstable modes, requiring further research.

Figure 1

(a) GGA NM band structure of ${\mathrm{BaOsO}}_3$ in the regime including O $2p$ and Os $5d$ orbitals. The bands above 0.5 eV are the Os $e_g$ manifold. (b) Blowup GGA FM band structure (black solid lines are for spin up and green dot-dashed lines are for spin down), which is overlapped by the $\mathrm{GGA}+\mathrm{SOC}$ one (red dashed lines). The horizontal dashed lines denote the Fermi energy $E_F$, which is set to zero.

Figure 2

Orbital-projected densities of states (PDOSs) per atom in (a) GGA, and (b) atom PDOSs in GGA and in (c) $\mathrm{GGA}+\mathrm{SOC}$ of NM ${\mathrm{BaOsO}}_3$. The corresponding FM DOS is not shown here, since this is very similar to that of NM, except for the positions of $E_F$ at 0.25 eV and –0.15 eV for the spin-up and spin-down channels, respectively, relative to $E_F$ of NM. For NM, the single-spin DOS at $E_F$ is $N\left(E_F\right)=3.38$ states per eV.

Figure 3

NM Fermi surfaces (FSs) in both GGA (top panel) and $\mathrm{GGA}+\mathrm{SOC}$ (bottom panel) colored with Fermi velocity, which show three-dimensional character. In the GGA case the $R$-centered hole FS is not shown for better visualization, since this FS is very similar to that of $\mathrm{GGA}+\mathrm{SOC}$, except for a little larger size. The $R$ and $M$ points are at each corner and midway of each side, respectively.

Figure 4

Total spin moment versus strength of the effective on-site Coulomb repulsion $U_{\mathrm{eff}}$ in $\mathrm{GGA}+U+\mathrm{SOC}$. For comparison, results of $\mathrm{GGA}+U$ are also given. In $\mathrm{GGA}+U+\mathrm{SOC}$, a small moment appears at $U_{\mathrm{eff}}^c=0.6$ eV and is saturated to $\sim 2{\mu }_B$ above $U_{\mathrm{eff}}\approx 4$ eV. For almost all range of $U_{\mathrm{eff}}$ studied here, the Os orbital moment is negligible, but $0.1{\mu }_B$ to $0.2{\mu }_B$ appears above $U_{\mathrm{eff}}=6$ eV due to an enhanced orbital polarization in the large-$U$ regime.

Figure 5

Enlarged PDOSs in GGA (top panel) and in $\mathrm{GGA}+\mathrm{SOC}$ (bottom panel) of FM ${\mathrm{CaOsO}}_3$ in the region of the partially filled $t_{2g}$ manifold, which is 25% narrower than in ${\mathrm{BaOsO}}_3$. $N\left(E_F\right)$ is 4.40 (3.71) and 3.16 (2.82) in NM and FM, respectively, in units of states/eV per formula unit. The values inside parentheses are obtained from $\mathrm{GGA}+\mathrm{SOC}$ calculations.

Figure 6

Top: Cubic ${\mathrm{BaOsO}}_3$ phonon dispersion curve and atom-projected phonon DOSs, obtained from $\mathrm{GGA}+\mathrm{SOC}$ by using our optimized volume and the 4% and 8% reduced volumes from the optimized value. Bottom: The same plots of cubic ${\mathrm{BaRuO}}_3$ in GGA with our optimized and 5%-reduced volumes. The latter corresponds to the experimental value. SOC is excluded, since the strength of SOC is small [22]. In both plots, each atom-projected phonon DOS is given for the optimized volume. Negative values in the phonon dispersion curves correspond to imaginary phonon frequencies.