From antiferromagnetic order to magnetic textures in the two dimensional Fermi Hubbard model with synthetic spin orbit interaction

Abstract

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 parameters. 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 an non collinear 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.

13 pages, 4 figures

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• Half-skyrmion and meron pair in spinor condensates
• Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling
• Weyl Semimetallic State in the Rashba-Hubbard Model
• $SU(3)$ Topological Insulators in the Honeycomb Lattice
• Phase diagram, band structure and density of states in two-dimensional attractive Fermi-Hubbard model with Rashba spin-orbit coupling
• Incommensurate spin density wave as a signature of spin-orbit coupling
• Weyl semimetallic, Néel, spiral, and vortex states in the Rashba-Hubbard model
• Transient dynamics and quantum phase diagram for the square lattice Rashba-Hubbard model at arbitrary hole doping