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The tetragonal-to-orthorhombic phase transition at $T_s$, which precedes theantiferromagnetic phase transition at $T_N$ in many iron-based superconductors,is considered as one of the manifestations of electronic \textit{nematic}order. By constructing temperature-pressure phase diagrams of pure and Co-dopedBaFe$_2$As$_2$, we study the relation of $T_s$ and $T_N$ under pressure $p$.Our data disclose two qualitatively different regimes in which $\DeltaT\,=\,T_s-T_N$ either increases or decreases with $p$. We provide experimentalevidence that the transition between the two regimes may be associated withsudden changes of the Fermi surface topology. Therefore, our results not onlysupport the electronic origin of the structural order, but also emphasize theimportance of details of the Fermi surface for the evolution of nematic orderunder pressure.

Role of Fermi surface for the pressure-tuned nematic transition in the BaFe$_2$As$_2$ family