Spin-orbital entangled matter can yield a rich variety of phases. In a 5d4 (t2g4) Mott insulator, the Hund’s coupling yields local S = 1 and Leff = 1 moments. Spin-orbit coupling in the large U limit should lead to a nonmagnetic ground state with Jeff = 0, which interestingly is a Mott insulator without a magnetic dipole moment. With increasing electron hopping strength, the excited Jeff = 1 triplet states will interact appreciably, and their dispersion will cross the Jeff = 0 level, where an unconventional magnetic ground state may emerge. This process can be viewed as a condensation of magnetic excitations and therefore may be called excitonic magnetism . The excitonic magnetism becomes even more exotic if it appears in the edge-shared honeycomb network of 5d4 transition-metal ions as in 5d5 candidates to realization of the Kitaev model. Due to the bond-dependent interactions, a hallmark of spin-orbital entangled systems, an exotic spin-superfluid state and/or nematic dimerized states are theoretically proposed.
Some 5d4 Ir5+ compounds are pointed out to be Jeff = 0 Mott insulators . However, the splitting of the ground Jeff=0 and the first exited Jeff=1 states, proportional to the spin-orbit coupling strength of around half an eV, is too large to induce the excitonic magnetism by increasing the exchange coupling. It might therefore be more realistic to consider 4d4 Ru4+ compounds as candidates for the realization of this exotic magnetism. However, most of insulating Ru4+ oxides known so far are either magnetic insulators or strong dimer insulators, but not the elusive Jeff = 0 Mott insulators. Recently, 4d4 Ca2RuO4 has been suggested to be an excitonic magnet with strong interaction beyond the critical point . Nevertheless, the most important part of the proposed phase diagram, the Jeff = 0 Mott insulator and its associated excitonic critical point remains to be fully explored. With this project, we propose a comprehensive search for the Jeff = 0 Mott insulators through material synthesis of honeycomb Ru4+ oxides, as well as RIXS, NMR, Raman and thermodynamic measurements to exploring the ground state and the properties of the phase diagram.
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