First-principles investigation of cubic ${\mathrm{BaRuO}}_3$: A Hund's metal

A first-principles investigation of cubic ${\mathrm{BaRuO}}_3$, by combining density functional theory with dynamical mean-field theory and a hybridization expansion continuous time quantum Monte Carlo solver, has been carried out. Nonmagnetic calculations with appropriately chosen on-site Coulomb repulsion $U$ and Hund's exchange $J$ for single-particle dynamics and static susceptibility show that cubic ${\mathrm{BaRuO}}_3$ is in a spin-frozen state at temperatures above the ferromagnetic transition point. A strong redshift with increasing $J$ of the peak in the real frequency dynamical susceptibility indicates a dramatic suppression of the Fermi liquid coherence scale as compared to the bare parameters in cubic ${\mathrm{BaRuO}}_3$. The self-energy also shows clear deviation from Fermi liquid behavior that manifests in the single-particle spectrum. Such a clean separation of energy scales in this system provides scope for an incoherent spin-frozen (SF) phase that extends over a wide temperature range, to manifest in non-Fermi liquid behavior and to be the precursor for the magnetically ordered ground state.

Figure 1

Band structure of cubic ${\mathrm{BaRuO}}_3$ in its nonmagnetic phase. Energies are scaled to the Fermi level (dotted line).

Figure 2

Projected density of states (PDOS) of ${\mathrm{BaRuO}}_3$. Green (shaded light gray), violet (shaded dark gray), black (thick line), orange (dashed line), and gray (dot-dashed line) represent the DOS of the whole system, Ru-atom, O-atom, Ru-$e_g$, and Ru-$t_{2g}$, respectively.

Figure 3

Orbital plots of maximally localized Wannier functions used to reproduce the low-energy subspace Hamiltonian.

Figure 4

Low-energy subspace band structure obtained from: (a) Plane-wave basis and (b) Wannier basis.

Figure 5

Imaginary part of the Matsubara self-energy $[-\mathrm{Im}\mathrm{\Sigma }\left(i{\omega }_n\right)]$ for $U=2.3$ eV and different $J$ values for (a) $T=60$ K and (b) $T=116$ K.

Figure 6

Imaginary part of the self-energy for $T=60$ K and different $J$ values (see legend) with (a) $U=3$ eV and (b) $U=4$ eV.

Figure 7

Exponent $\alpha$ (circles, left axis) and intercept $C$ (squares, right axis) obtained by fitting the data to $-\text{Im}\mathrm{\Sigma }\left(i{\omega }_n\right)=C+A{\left|{\omega }_n\right|}^{\alpha }$ at different $J$ values, $U=2.3$ eV and $T=60$, 116, and 232 K.

Figure 8

Imaginary part of the self-energy $[-\text{Im}\mathrm{\Sigma }\left(i{\omega }_n\right)]$ fitted to a fourth order polynomial: (a) zeroth order coefficient $C_0$, (b) $Z=1/(1+C_1)$, where $C_1$ is the linear coefficient, for different $J$ values, $U=2.3$ and 3.0 eV and $T=60$ K.

Figure 9

Local static spin susceptibility as a function of temperature for different $J$ values and $U=2.30$ eV. The dashed curve represents a $1/T$ fit at high temperatures. Inset: The screened magnetic moment as a function of temperature.

Figure 10

Imaginary part of dynamical spin susceptibility on real frequency axis obtained from maximum entropy method for various $J$ values, $U=2.3$ eV and $T=60$ K.

Figure 11

(a) Imaginary part of the self-energy. (b) Single-particle spectral function on the real frequency axis obtained from the maximum entropy method for different temperatures and $U=2.3$ eV, $J=0.5$ eV.

Figure 12

Intensity map of the spectral function $A(k,\omega )$ obtained from DFT (top panel) and DFT+DMFT (lower panel) for $U=2.3$ eV, $J=0.5$ eV at $T=154$ K plotted along high symmetry directions in the irreducible Brillouin zone.