Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: the Ti$_4$O$_7$ Magn\'eli phase

TL;DR

This study uses advanced Quantum Monte Carlo methods to analyze the magnetic states of Ti4O7, revealing detailed insights into its charge, spin, and lattice interactions and highlighting the limitations of density functional theory approximations.

Contribution

It provides highly accurate quantum Monte Carlo calculations of Ti4O7's magnetic states, improving understanding of its electronic structure beyond density functional theory.

Findings

Quantum Monte Carlo confirms state ordering and nature.

Energy differences and spin distributions differ from DFT results.

Non-local exchange-correlation functionals are needed for better accuracy.

Abstract

The Magn\'eli phase Ti$_4$O$_7$ is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low-lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate Quantum Monte Carlo methods. We compare our results to those obtained from density functional theory-based methods that include approximate corrections for exchange and correlation. Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. A detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.