Magnetic Stability for the Hatree-Fock Ground State in Two Dimensional Rashba-Gauge Electronic Systems

The magnetic Hartree Fock ground state stability for a two-dimensional interacting electron system with Rashba-type coupling is studied by implementing the standard many body Green's function formalism. The externally applied electrical field $\mathbf{E}$ enters into the Hamiltonian model through a local gauge-type transformation $\sim E_{j}\mathcal{A}_{j}(\mathbf{k})$, with $\mathcal{A}_{j}(\mathbf{k})$ as the spin gauge vector potential. Phase diagrams associated to the average spin polarization, the Fermi energy, electron density and energy band gap at zero temperature are constructed. The magnetic polarization state as a function of $\mathbf{E}$ is obtained by minimizing the Helmholtz energy functional $\mathcal{F}$ with respect to the average $Z$-spin: $\langle\hat{\sigma}_{Z}\rangle$. We have found that the electric field might reverse the magnetic ground state, unlike the characteristic decreasing associated to the linear $\hat{\boldsymbol{\sigma}}\cdot(\mathbf{k\times E})$ spin-momentum-field coupling.