  We present a set of self-consistent chemo-dynamical simulations of MW-type
galaxies formation to study the origin of the bimodality of $\alpha$-elements
in stellar populations. We explore how the bimodality is related to the
geometrically and kinematically defined stellar discs, gas accretion and radial
migration. We find that the two $\alpha$-sequences are formed in quite
different physical environments. The high-$\alpha$ sequence is formed early
from a burst of star formation (SF) in a turbulent, compact gaseous disc which
forms a thick disc. The low-$\alpha$ stellar populations is the result of
quiescent SF supported by the slow accretion of enriched gas onto a radially
extended thin disc. Stellar feedback-driven outflows during the formation of
the thick disc are responsible for the enrichment of the surrounding gaseous
halo, which subsequently feeds the disc on a longer time-scale. During the thin
disc phase, chemical evolution reaches an equilibrium metallicity and
abundance, where the stars pile-up. This equilibrium metallicity decreases
towards the outer disc, generating the ridgeline that forms the low-$\alpha$
sequence. We identify a second mechanism capable of creating a low-$\alpha$
sequence in one of our simulations. Rapid shutdown of the SF, provoked by the
feedback at the end of the thick disc phase, suppresses the chemical enrichment
of the halo gas, which, once accreted onto the star-forming disc, dilutes the
ISM at the beginning of the thin disc formation. Both mechanisms can operate in
a galaxy, but the former is expected to occur when SF efficiency ceases to be
dominated by the formation of the thick disc, while the latter can occur in the
inner regions. Being the result of the presence of low and high gas density
environments, the bimodality is independent of any particular merger history,
suggesting that it could be much more widespread than has been claimed.
