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Using {\it ab initio} molecular dynamics we investigate the electronic andlattice structure of $A$Fe$_2$As$_2$ ($A$=Ca, Sr, Ba) under pressure. We findthat the structural phase transition (orthorhombic to tetragonal symmetry) isalways accompanied by a magnetic phase transition in all the compounds, whilethe nature of the transitions is different for the three systems. Ourcalculations explain the origin of the existence of a collapsed tetragonalphase in CaFe$_2$As$_2$ and its absence in BaFe$_2$As$_2$. We argue thatchanges of the Fermi surface nesting features dominate the phase transitionunder pressure rather than spin frustration or a Kondo scenario. Theconsequences for superconductivity are discussed.

Microscopic origin of pressure-induced phase transitions in iron-pnictide $AFe_2As_2$ superconductors: an {ab initio} molecular-dynamics study