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.

arXiv commentsome additions and clarifications added

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• Unified description of electronic orderings and cross correlations by complete multipole representation
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• Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry
• Antisymmetric Thermopolarization by Electric Toroidicity
• Odd-parity multipole fluctuation and unconventional superconductivity in locally noncentrosymmetric crystal
• Evidence of an improper displacive phase transition in Cd${}_2$Re${}_2$O${}_7$ via time-resolved coherent phonon spectroscopy
• Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca${}_5$Ir${}_3$O${}_{12}$
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• Low-Temperature Phase of the Cd${}_2$Re${}_2$O${}_7$ Superconductor: Ab initio Phonon Calculations and Raman Scattering
• Successive phase transitions of the spin-orbit-coupled metal Cd2Re2O7 probed by high-resolution synchrotron x-ray diffraction
• Multiple-$q$ dipole-quadrupole instability in spin-1 triangular-lattice systems
• Implications of second harmonic generation for hidden order in Sr${}_2$CuO${}_2$Cl${}_2$
• Chirality/Axiality-Induced Axiality/Chirality via Surface Polarization
• Metal-insulator transitions in pyrochlore oxides
• Spin-orbit-coupled metal candidate PbRe2O6
• Domain Control by Adjusting Anisotropic Stress in Pyrochlore Oxide Cd2Re2O7
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States