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We investigate the metal-insulator transition (MIT) and phase diagram of thehalf-filled Fermi Hubbard model with Rashba-type spin-orbit coupling (SOC) on asquare optical lattice. The interplay between the atomic interactions and SOCresults in distinctive features of the MIT. Significantly, in addition to thediverse spin ordered phases, a nonmagnetic insulating phase emerges in aconsiderably large regime of parameters near the Mott transition. This phasehas a finite single-particle gap but vanishing magnetization and spincorrelation exhibits a power-law scaling, suggesting a potential algebraicspin-liquid ground state. These results are confirmed by the non-perturbativecluster dynamical mean-field theory.

Emergence of Quantum Nonmagnetic Insulating Phase in Spin-Orbit Coupled Square Lattices