Effect of uniaxial stress on structural and electronic properties of BaFe$_2$As$_2$ and CaFe$_2$As$_2$

We investigate the effects of the uniaxial tensile and compressive stresses applied along {\bf a}, {\bf b} and {\bf a}+{\bf b} directions in BaFe$_2$As$_2$ and CaFe$_2$As$_2$ in the framework of ab initio density functional theory calculations. While the systems remain in the orthorhombic phase at moderate pressures, we observe an inversion of magnetism at a critical strain happening when the {\bf a} and {\bf b} axes approach the tetragonal condition. We discuss our results in view of recent reports of modified magnetic and structural transitions in BaFe$_2$As$_2$ under externally applied uniaxial strain and make a connection to phenomenological models proposed for these transitions.