The Iso-electronic Series $C{a}_{2-x}S{r}_{x}Ru{O}_4$: Structural Distortion, Effective Dimensionality, Spin Fluctuations and Quantum Criticality

Abstract

The iso-electronic $d^4$ compounds of the $4d$ series show rich phase diagrams due to competing spin, charge and orbital degrees of freedom in presence of strong correlations and structural distortions. One such iso-electronic series, $C{a}_{2-x}S{r}_{x}Ru{O}_4$, is studied within the GGA (and spin-orbit coupled GGA) plus DMFT formalism using the hybridization expansion of continuous time Quantum Monte Carlo solver. While the local dynamical correlations make $S{r}_{2}Ru{O}_4$ a Hund's metal, they drive $C{a}_{2}Ru{O}_4$ to a Mott insulating ground state. We study the dynamic and static single-particle and local irreducible vertex-corrected two-particle responses at three different points ($x=2.0,0.5,0.0$) to understand the anomalous cross-over from Hund's metal ($x=2.0$) to a Mott insulator ($x=0$) and find that a structural distortion is likely to be responsible for the cross-over. Further, dynamical correlations reveal that the band-width ($W$) of the Hund's metal is larger than its effective local Hubbard $U$, and a finite Hund's coupling $J_H$ helps it remain in a bad metallic and nearly spin-frozen state over a large temperature range. $C{a}_{2}Ru{O}_4$, on the other hand, is intrinsically driven to the proximity of a Mott transition due to narrowing of band width ($U/W>1.5$), though its finite temperature excitations indicate bad metallicity. We show that there is a critical end point of second-order structural transition at $x=0.5$, where spin fluctuations become critically singular and follow the exact scaling of conformally invariant boundary field theory. The critical end point of quasi-$3D$ nature is associated with an effective dimensional cross-over between the $x=2.0$ and $x=0.0$ quasi-$2D$ structures. Finally we draw a modified magnetic phase diagram of the material, showing a fan-like region starting from the quantum critical end point at $x=\mathrm{0.5.}$

13 pages, 10 figures

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• Evening out the spin and charge parity to increase T${}_c$ in unconventional superconductor Sr_{2}RuO_{4}