From antiferromagnetic ordering to magnetic textures in the two-dimensional Fermi-Hubbard model with synthetic spin-orbit interactions

We study the interacting Fermi-Hubbard model in two spatial dimensions with synthetic gauge coupling of the spin-orbit Rashba type, at half-filling. Using real-space mean-field theory, we numerically determine the phase as a function of the interaction strength for different values of the gauge-field parameter. For a fixed value of the gauge field, we observe that when the strength of the repulsive interaction is increased, the system enters into an antiferromagnetic phase, then undergoes a first-order phase transition to a noncollinear magnetic phase. Depending on the gauge-field parameter, this phase further evolves to the one predicted from the effective Heisenberg model obtained in the limit of large interaction strength. We explain the presence of the antiferromagnetic phase at small interaction from the computation of the spin-spin susceptibility, which displays a divergence at low temperatures for the antiferromagnetic ordering. We discuss, how the divergence is related to the nature of the underlying Fermi surfaces. Finally, the fact that the first-order phase transitions for different gauge-field parameters occur at unrelated critical interaction strengths arises from a Hofstadter-like situation, i.e., for different magnetic phases, the mean-field Hamiltonians have different translational symmetries.