Magnetic torque in spin-orbit coupled metal Cd₂Re₂O₇

Spin-orbit (SO) interactions lead to peculiar symmetry-broken phases in highly correlated systems. Among various SO coupled metals, a metallic pyrochlore Cd₂Re₂O₇ is known to show unique multipole orders associated with the inversion symmetry breaking below ~200 K, whose order parameter has E_u symmetry. We have measured the magnetic torque of Cd₂Re₂O₇ in a wide temperature and field range. We find that a four-fold symmetry of the magnetic torque signal as well as a two-fold symmetry is significantly enhanced at low temperatures below ~200 K. The symmetry analysis of the torque signal strongly suggests the presence of the primary order parameter (OP) with the even parity E_g symmetry, which induces the four-fold term, whereas the two-fold arises from the odd parity E_u OP. It is very likely that the E_g symmetry OP is purely of electronic origin and the coexistence with the odd-parity E_u OP provides important insights into the origin of the multipole orders induced by the SO coupling.