The nature of the tensor order in Cd2Re2O7

TL;DR

This paper develops a formalism to identify tensor components in SHG reflectivity, revealing the primary and secondary order parameters in Cd2Re2O7's phase transition as magnetic and axial toroidal quadrupoles, respectively.

Contribution

It introduces a general formalism for analyzing SHG data to determine tensor components and clarifies the nature of order parameters in Cd2Re2O7's phase transition.

Findings

Secondary order parameter is the x2-y2 component of the axial toroidal quadrupole.

Primary order parameter is the 3z2-r2 component of the magnetic quadrupole.

Differentiates between atomic displacement symmetry and order parameters in phase transition.

Abstract

The pyrochlore metal Cd2Re2O7 has been recently investigated by second-harmonic generation (SHG) reflectivity. In this paper, we develop a general formalism that allows for the identification of the relevant tensor components of the SHG from azimuthal scans. We demonstrate that the secondary order parameter identified by SHG at the structural phase transition is the x2-y2 component of the axial toroidal quadrupole. This differs from the 3z2-r2 symmetry of the atomic displacements associated with the I-4m2 crystal structure that was previously thought to be its origin. Within the same formalism, we suggest that the primary order parameter detected in the SHG experiment is the 3z2-r2 component of the magnetic quadrupole. We discuss the general mechanism driving the phase transition in our proposed framework, and suggest experiments, particularly resonant X-ray scattering ones, that could clarify this issue.