Ca$_{3}$Ru$_{2}$O$_{7}$: Interplay among degrees of freedom and the role of the exchange-correlation

TL;DR

This paper analyzes the complex electronic and structural behavior of Ca$_{3}$Ru$_{2}$O$_{7}$ using density functional theory, highlighting how different degrees of freedom and exchange-correlation functionals influence its properties.

Contribution

It provides a comparative density-functional analysis of Ca$_{3}$Ru$_{2}$O$_{7}$, clarifying the role of exchange-correlation methods in its electronic and structural transitions.

Findings

Ca$_{3}$Ru$_{2}$O$_{7}$ exhibits metallic, semimetallic, and insulating states depending on Hubbard-U.

Structural transitions depend on the choice of exchange-correlation functional.

Exchange-correlation effects are crucial in understanding the material's electronic and structural phases.

Abstract

Ca$_{3}$Ru$_{2}$O$_{7}$ is a fascinating material that displays physical properties governed by spin-orbit interactions and structural distortions, showing a wide range of remarkable electronic phenomena. Here, we present a density-functional-based analysis of the interplay among degrees of freedom, such as magnetism, Coulomb repulsion (Hubbard-U), and structural degrees of freedom, considering two exchange-correlation methods: Local-Density Approximation (LDA) and Perdew-Burke-Ernzerhof revised for solids (PBEsol). Our goal is twofold: first, to provide a brief overview of the current state of the art on this compound underpinning the last proposed theoretical models and experimental research, and second, to give another view to model the electronic properties compared with the previous theoretical models. Our findings show that Ca$_{3}$Ru$_{2}$O$_{7}$ displays several electronic states (metal, semimetal, and narrow insulator) as a function of Hubbard-U while it exhibits structural transition depending on the functional. We disentangle the effect of the different degrees of freedom involved, clarifying the role of exchange-correlation in the observed electronic and structural transitions.