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 i
s 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.
