Electric toroidal quadrupoles in the spin-orbit-coupled metal Cd2Re2 O7

We report our theoretical results on the order parameters for the pyrochlore metal Cd2Re2O7, which undergoes enigmatic phase transitions with inversion symmetry breaking. By carefully examining active electronic degrees of freedom based on the lattice symmetry, we propose that two parity-breaking phases at ambient pressure are described by unconventional multipoles, electric toroidal quadrupoles (ETQs) with different components, x2-y2 and 3z2-r2, in the pyrochlore tetrahedral unit. We elucidate that the ETQs are activated by bond or spin-current order on Re bonds. Our ETQ scenario provides a key to reconciling the experimental contradictions, by measuring ETQ specific phenomena, such as peculiar spin splittings in the electronic band structure, magnetocurrent effect, and nonreciprocal transport under a magnetic field.