The magnetic phase diagram of a periodic system of identical quantum wells subject to a strong magnetic field is investigated within the Hartree-Fock approximation. Weak tunneling between the wells accounts for the broadening of the individual energy levels of a single well into minibands of bandwidth $\Delta$. For integer, even values of the filling factor the nature of the ground state is found to depend critically on the magnitude of $\Delta$. For small tunneling probability, the quasi-two dimensional system undergoes a ferromagnetic to paramagnetic transition as in the case of a single electron gas layer. For larger tunneling probability a critical value of $\Delta_{c}$ is reached for which spin flip excitations between minibands can become soft and lead to a spin density wave coupling between the bands with $Q = \frac{\pi}{a}$, with $a$ the superlattice period.
