Untangling the structural, magnetic dipole, and charge multipolar orders in Ba$_2$MgReO$_6$

TL;DR

This study uses density functional theory to analyze the complex interplay of structural, magnetic, and charge quadrupolar orders in Ba$_2$MgReO$_6$, revealing hidden charge quadrupolar components and their relationship with structural and magnetic phases.

Contribution

It introduces a method to disentangle and analyze structural, magnetic, and charge multipolar orders in 5d$^1$ double perovskites, including the discovery of a hidden charge quadrupolar component.

Findings

Confirmation of charge quadrupolar order in Ba$_2$MgReO$_6$

Discovery of a previously hidden charge quadrupolar component

Establishment of the relationship between structural, magnetic, and charge orders

Abstract

We present a density functional theory study of the low-temperature structural, magnetic, and proposed charge-quadrupolar ordering in the double perovskite, Ba$_2$MgReO$_6$. Ba$_2$MgReO$_6$ is a spin-orbit-driven Mott insulator with a symmetry-lowering structural phase transition at 33\,K and a canted antiferromagnetic ordering of $5d^1$ Re magnetic moments at 18\,K. Our calculations confirm the existence of the proposed charge quadrupolar order and discover an additional, previously hidden, ordered charge quadrupolar component. By separately isolating the structural distortions and the orientations of the magnetic dipoles, we determine the relationship between the charge quadrupolar, structural and magnetic orders, finding that either a local structural distortion or a specific magnetic dipole orientation is required to lower the symmetry and enable the existence of charge quadrupoles. Our work establishes the crystal structure -- magnetic dipole -- charge multipole relationship in Ba$_2$MgReO$_6$ and related 5$d^1$ double perovskites, and illustrates a method for separating and analyzing the contributions and interactions of structural, magnetic, and charge orders beyond the usual dipole level.