Masataka Kawano

We investigate the magnetic phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC). While extensive research has been focused on Rashba metals and insulating magnets, the understanding of the intermediate interaction regime has remained limited due to the lack of appropriate theoretical tools for unbiasedly describing large-scale magnetic structures. In this study, we employ four complementary methods: sine-square deformed mean-field theory, random phase approximation (RPA), Luttinger-Tisza method, and density matrix embedding theory, to clarify the magneic phases of this model. We successfully identify previously overlooked incommensurate spin-density-wave (SDW) phases characterized by very long spatial periods. The transition from the metallic phase to the SDW phases is driven by an instability that arises from the nesting of Fermi surface carrying opposite spins. In the case of strong SOC, we observe the emergence of spiral, stripe, and vortex phases when four Dirac points are located near the Fermi level, and their linear dispersions collectively nest with a wavelength of $\pi$, opening of a band gap. These two types of transitions give rise to unique Fermiology that distinguishes the antisymmetric SOC systems, resulting in a rich variety of magnetic phases that span from the relatively weak correlation regime to the strongly interacting limit.