  We study the well-posedness of the reduced Hartree-Fock model for molecules
and perfect crystals when taking into account a self-generated magnetic field.
We exhibit a critical value $\alpha_c > 0$ such that, if the fine structure
constant $\alpha$ is smaller than $\alpha_c$, then the corresponding system is
stable, whereas if $\alpha$ is greater than $\alpha_c$, it is unstable. We give
an explicit characterisation of $\alpha_c$ as a minimisation problem over the
set of zero-modes, and we prove that the critical values for the molecular case
and the periodic case coincide. Finally, we prove the existence of minimisers
when the system is neutral or positively charged.
