Orbital glass conceals missing magnetic entropy in a relativistic Mott insulator

TL;DR

This study introduces a phase-sensitive method to disentangle coupled spin and orbital orders in a relativistic Mott insulator, revealing an orbital glass state and its role in magnetic ordering.

Contribution

The paper demonstrates a novel phase-sensitive technique to directly detect and analyze orbital glass and nematic states in complex correlated materials.

Findings

Detected short-range orbital order up to 380 K.

Observed orbital dispersion increase near magnetic transition.

Established orbital nematic state induces magnetic order.

Abstract

Coupling between different degrees of freedom (DOF) in an electronic material leads to exotic phases of matter characterized by complex and competing order parameters as well as emergent excitations. Building a microscopic understanding of these order parameters and their mutual relationship is hindered by the fact that different orders often mask each others' response to conventional experimental probes. Here, we reveal how to disentangle responses from distinct orders that arise from the coupling between the spin and orbital DOF. Our method uses a phase sensitive technique that measures ground state properties by independently resolving interactions of different symmetries. This allows us to directly detect an orbital glass state caused by competing interactions in the $5d^1$ relativistic Mott insulator Ba$_2$NaOsO$_6$. We observe short-range orbital order up to 380 K and a dramatic increase of orbital dispersion near the magnetic phase transition. This orbital dispersion generates a directional ordering, $\textit{i.e.}$, it forms an orbital nematic state which breaks the rotational symmetry of the crystal. We establish that the orbital nematic state induces the magnetic ordering. The presence of this short-range orbital order well above the magnetic phase transition solves the long-standing puzzle of missing entropy in this material.