Title: The nature of the tensor order in Cd2Re2O7,
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.