  To explore the limitations of the mean field approximation, frequently used
in \textit{ab initio} molecular electronics calculations, we study an
out-of-equilibrium Anderson impurity model in a scattering formalism. We find
regions in the parameter space where both magnetic and non-magnetic solutions
are stable. We also observe a hysteresis in the non-equilibrium magnetization
and current as a function of the applied bias voltage. The mean field method
also predicts incorrectly local moment formation for large biases and a spin
polarized current, and unphysical kinks appear in various physical quantities.
The mean field approximation thus fails in every region where it predicts local
moment formation.
