5d1 Mott insulators, with one electron in the t2g orbital, may open an additional route to explore multipolar degrees of freedom in the physics of transition metals, going beyond the paradigm of the dipolar moment. The multipolar states so far were popular in nuclear physics and, more recently, in f-electron systems. In 5d1 Mott insulators, one electron is in the Jeff = 3/2 quartet stabilized by the large spin-orbit coupling. Unlike the Jeff = 1/2 state which has its spin-orbital entangled wave function fixed in the cubic environment, the Jeff = 3/2 quartet is composed of the two Kramers doublets with the axial and planar orbital shapes. The ideal Jeff = 3/2 quartet hosts “zero” magnetic dipolar moment (<M>=0) because of the complete cancellation of spin- and orbital angular moment. This contrasts with the Jeff = 1/2 state with the finite magnetic dipolar moment of 1 mB. Jeff = 3/2 states are therefore characterized by higher multipoles, such as a charge quadrupole and a magnetic octupole, which are often silent to the conventional experimental probes . A hidden ordering of the interacting multipoles may be anticipated. The materialization of the pure Jeff = 3/2 state and the experimental verification of hidden multipolar ordering remain as a challenge. 5d1 and 4d1 transition metal (Os7+ and Mo5+) oxides with double-perovskite structure have been primarily studied as a candidate of Jeff = 3/2 electron system [2,3]. They exhibit rather conventional orderings of magnetic dipoles and the clear signature of multipolar ordering was not observed. Those may be attributed to the strong covalency that causes imperfect cancellation of spin- and orbital- angular moments. New 5d compounds better representing the Jeff = 3/2 physics should be developed.
Placing the 5d1 Jeff = 3/2 quartets on the edge shared honeycomb network of transition metal anion (oxygen) octahedra, as in the 5d5 Jeff = 1/2 Kitaev case, an exotic state even beyond multipolar ordered state is expected to emerge . Bond-dependent hopping between the four orbital states of Jeff = 3/2 through the two edge anions is apparently not SU(4)-symmetric. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit of the 5d1 configuration, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. Another interesting direction is charge carrier doping into the d1 Jeff = 3/2 Mott insulator, which might yield itinerant Jeff = 3/2 multipoles. Properties of such carrier doped Jeff = 3/2 Mott insulators are still an open question both experimentally and theoretically. It is not clear if the multipolar excitations, like phonons in metals, could provide a novel scattering channel and an exotic pairing channel of superconductivity among the itinerant multipoles. Another interesting viewpoint on the itinerant Jeff = 3/2 may be the possibility of discovering thermoelectric materials, as Jeff = 3/2 electrons carry at high temperatures the large electronic entropy of kBln4 associated with the degeneracy of quartet. For this project, we propose a wide-ranging search for multipolar physics in 5d1 systems through new material synthesis.
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 M. G. Yamada et al., arXiv: 1709.05252.