Metal-Insulator and Magnetic Phase Diagram of Ca$_2$RuO$_4$ from Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory

TL;DR

This study combines advanced many-body computational methods to map the low-temperature phase diagram of Ca$_2$RuO$_4$, revealing pressure-driven metal-insulator and magnetic transitions with detailed orbital character insights.

Contribution

It presents the first application of Auxiliary Field Quantum Monte Carlo to an orbitally-degenerate system with Mott and Hund's physics, comparing it with Dynamical Mean Field Theory.

Findings

Pressure induces a metal-insulator transition.

Ferromagnetic state is dominated by the $d_{xy}$ orbital.

Antiferromagnetic state is dominated by the $d_{xz}$ and $d_{yz}$ orbitals.

Abstract

Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work, we combine results from two complementary state of the art many-body methods, Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory, to determine the low-temperature phase diagram of Ca$_2$RuO$_4$. Both methods predict a low temperature, pressure-driven metal-insulator transition accompanied by a ferromagnetic-antiferromagnetic transition. The properties of the ferromagnetic state vary non-monotonically with pressure and are dominated by the ruthenium $d_{xy}$ orbital, while the properties of the antiferromagnetic state are dominated by the $d_{xz}$ and $d_{yz}$ orbitals. Differences of detail in the predictions of the two methods are analyzed. This work is theoretically important as it presents the first application of the Auxiliary Field Quantum Monte Carlo method to an orbitally-degenerate system with both Mott and Hunds physics, and provides an important comparison of the Dynamical Mean Field and Auxiliary Field Quantum Monte Carlo methods.