Spin-orbital entangled molecular jeff states in lacunar spinel compounds.

The entanglement of the spin and orbital degrees of freedom through the spin-orbit coupling has been actively studied in condensed matter physics. In several iridium oxide systems, the spin-orbital entangled state, identified by the effective angular momentum jeff, can host novel quantum phases. Here we show that a series of lacunar spinel compounds, GaM4X8 (M=Nb, Mo, Ta and W and X=S, Se and Te), gives rise to a molecular jeff state as a new spin-orbital composite on which the low-energy effective Hamiltonian is based. A wide range of electron correlations is accessible by tuning the bandwidth under external and/or chemical pressure, enabling us to investigate the cooperation between spin-orbit coupling and electron correlations. As illustrative examples, a two-dimensional topological insulating phase and an anisotropic spin Hamiltonian are investigated in the weak and strong coupling regimes, respectively. Our finding can provide an ideal platform for exploring jeff physics and the resulting emergent phenomena.