  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.
