Symmetry Analysis of Tensors in the Honeycomb Lattice of Edge-Sharing Octahedra

TL;DR

This paper derives the most general forms of rank-2 and rank-3 tensors consistent with the symmetries of honeycomb lattice materials, providing insights into their thermal responses under magnetic fields.

Contribution

It presents a comprehensive symmetry analysis of tensors in honeycomb lattice materials, including new predictions for thermal conductivity tensor components in various symmetry settings.

Findings

Derived tensor forms for different point groups

Identified unexpected tensor component equalities

Made testable predictions for thermal conductivity behavior

Abstract

We obtain the most general forms of rank-2 and rank-3 tensors allowed by the crystal symmetries of the honeycomb lattice of edge-sharing octahedra for crystals belonging to different crystallographic point groups, including the monoclinic point group $2/m$ and the trigonal (or rhombohedral) point group $\bar{3}$. Our results are relevant for two-dimensional materials, such as $\alpha$-RuCl$_3$, CrI$_3$, and the honeycomb iridates. We focus on the magnetic-field-dependent thermal conductivity tensor $\kappa_{ij}(\mathbf{H})$, which describes a system's longitudinal and thermal Hall responses, for the cases when the magnetic field is applied along high-symmetry directions, perpendicular to the plane and in the plane. We highlight some unexpected results, such as the equality of fully-longitudinal components to partially-transverse components in rank-3 tensors for systems with three-fold rotational symmetry, and make testable predictions for the thermal conductivity tensor.