Quantum criticality associated with dimensional crossover in the iso-electronic series Ca_2−xSr_xRuO₄

The iso-electronic series, Ca_2−xSr_xRuO₄, is studied within the GGA (and spin-orbit coupled GGA) plus DMFT formalism using the hybridization expansion of continuous time Quantum Monte Carlo (CT-QMC) impurity solver. GGA+DMFT, along with CT-QMC impurity solver we used, provides insights into the retarded electronic correlations at finite temperatures. We use GGA+U and energy considerations at T = 0 for complementary understanding of the ground state structural and electronic properties. While the dynamical correlations make Sr₂RuO₄ a Hund's metal, they drive Ca₂RuO₄ to a Mott insulating ground state. We study the single-particle and 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 observe that a structural distortion is likely to be responsible. 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. Ca₂RuO₄, though, is driven to the proximity of a Mott transition by the narrowing of band width (U/W > 1.5). We show that there is a critical end point of second-order structural transition at x = 0.5, where spin fluctuations become critical and follow the scaling of local quantum criticality. We argue that this critical end point of quasi-3D nature is associated with an effective dimensional cross-over from the quasi-2D structures of x = 2.0 and x = 0.0 end-members. Finally we draw an electronic and magnetic phase diagram in T-x plane with these novel inputs, with a fan like region starting from the quantum critical end point at x = 0.5. (paper)