Interplay between spin-orbit coupling and Van Hove singularity in the Hund's metallicity of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

We investigate the roles of spin-orbit coupling and the Van Hove singularity in the dynamical properties of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, which become prominent at zero and very low temperature, by means of density functional theory plus dynamical mean-field theory with an exact diagonalization solver. We examine the crossover between a Fermi liquid and a Hund's metal for a wide range of temperatures and Hund's coupling. In the absence of doping, we confirm that the Fermi liquid persists at zero temperature even with nonzero Hund's coupling. The freezing-moment mechanism suggests that thermal fluctuations lead to a suppression of the Fermi liquid phase and promote Hund's metallicity with incoherence. We show that the Van Hove singularity is an additional key ingredient to drive the suppression at very low temperature by observing a doping dependence of the freezing or long-lived paramagnetic moments. The role of spin-orbit coupling is marked by an amplified Van Vleck contribution of spin susceptibility, significantly promoting Hund's metallicity. Together with the known doping dependence of Hund's metallicity, the additional Van Hove singularity doping dependence found here may allow for the control of the Hund's metallicity of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4\left(t_{2g}^4\right)$ by a fine tuning of the doping or possibly even strain.

Figure 1

(a) Power exponent $\alpha$ of the imaginary part of the Matsubara self-energy and (b) long-time correlator ${\chi }_{zz}^S(\tau =\beta /2)$ in the $T\text{−}{J}_H$ plane. The dashed line in (a) denotes the crossover between the Fermi liquid and Hund's metal regimes, and the yellow star marks a realistic value of $J_H$ for ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

Figure 2

Doping dependence around the Van Hove singularity. (a) Power exponent of the imaginary part of the Matsubara self-energy and (b) long-time correlator ${\chi }_{zz}^S(\tau =\beta /2)$ in the $T\text{−}{n}_{\mathrm{el}}$ plane. Inset: Projected density of states on $t_{2g}$ for the noninteracting case. The vertical dotted lines denote the Fermi level when $n_{\mathrm{el}}=4$ and 4.35 around the VHS of the $d_{xy}$ band.

Figure 3

Spectral density of (a) the Fermi surface and its projection onto the (b) $t_{2g}$- and (c) $j_{\text{eff}}$-basis states. (d) Dispersion along different angles $\theta$ between the $\mathrm{\Gamma }M$ and $\mathrm{\Gamma }X$ lines depicted in (a). All data are obtained with $U=2.5\mathrm{eV}$, $J_H=0.4\mathrm{eV}$, and ${\lambda }_{\mathrm{SOC}}^{}=0.1\mathrm{eV}$ at $T=23\mathrm{K}$.

Figure 4

Static spin susceptibilities ${\chi }_{zz}^S$ in the presence or absence of SOC (a) as a function of temperature for $n_{\mathrm{el}}=4$ and (c) as a function of $n_{\mathrm{el}}$ at $T=11.33$ K. Static orbital susceptibilities ${\chi }_{zz}^L$ are plotted in (b) and (d). We also plot their Van Vleck contributions ${\chi }_{zz}^{S/L;\mathrm{VV}}$ in (a) and (b). The data are from $(U,J_H)=(2.5,0.4)\mathrm{eV}$.