Coexistence of odd-parity and even-parity order parameters in the multipole order phase of the spin-orbit coupled metal Cd2Re2O7

Magnetic torque measurements have been performed to investigate the phase transitions of the metallic pyrochlore compound $\mathrm{C}{\mathrm{d}}_{2}\mathrm{R}{\mathrm{e}}_{2}{\mathrm{O}}_{7}$, in which a spin-orbit (SO) interaction leads to unique multipole orders associated with an inversion symmetry breaking. We find that the magnetic torque signals with a fourfold symmetry (${\ensuremath{\tau}}_{4}\ensuremath{\propto}{H}^{4}$) as well as a twofold symmetry (${\ensuremath{\tau}}_{2}\ensuremath{\propto}{H}^{2}$) are significantly enhanced at low temperatures below a structural phase transition temperature (\ensuremath{\sim}200 K). The analyses of the torque curve symmetries show that the ${\ensuremath{\tau}}_{4}$ term arises from an even-parity order parameter (OP) with the irreducible representation ${E}_{\mathrm{g}}$, whereas the ${\ensuremath{\tau}}_{2}$ term from an odd-parity OP with ${E}_{\mathrm{u}}$, ${T}_{1\mathrm{u}}$ or ${T}_{2\mathrm{u}}$. The parity mixing of the primary OPs shows a peculiar phase transition in the SO coupled $\mathrm{C}{\mathrm{d}}_{2}\mathrm{R}{\mathrm{e}}_{2}{\mathrm{O}}_{7}$. The coexistence of the two OPs provides important insights into the origin of the multipole orders induced by the SO interaction.