  The interplay between the structural and magnetic phase transitions occurring
in the Fe-based pnictide superconductors is studied within a Ginzburg-Landau
approach. We show that the magnetoelastic coupling between the corresponding
order parameters is behind the salient features observed in the phase diagram
of these systems. This naturally explains the coincidence of transition
temperatures observed in some cases as well as the character (first or
second-order) of the transitions. We also show that magnetoelastic coupling is
the key ingredient determining the collinearity of the magnetic ordering, and
we propose an experimental criterion to distinguish between a pure elastic from
a spin-nematic-driven structural transition.

Strongly Correlated Electrons;Superconductivity