Origin of structural and magnetic transitions in BaFe$_{2-x}$Ru$_x$As$_2$ materials

Using the experimentally measured temperature and doping dependent structural parameters on Ru doped BaFe$_2$As$_2$, orbital-dependent reconstruction of the electronic structure across the magnetostructural transition is found, through first principle simulations. Below structural transition there exists two distinct Fe - Fe bond distances which modifies the Fe-d$_{xy}$ orbital largely due to its planar spatial extension leading to Lifshitz transition, while the otherwise degenerate Fe-d$_{xz}$ and d$_{yz}$ orbitals become non-degenerate, giving rise to orbital order. The orbital order follows the temperature dependence of orthorhombocity and is also the cause of two distinct Fe - Fe bond distances. Doping dependent Fermi surfaces show nearly equal expansion of both the electron and hole like Fermi surfaces whereas the hole Fermi surface shrinks with temperature but the electron Fermi surface expands comparatively slowly. The observed structural transition in this compound is electronic in origin, occurs close to the Lifshitz transition whereas the suppression of the concurrent magnetic transition is due to loss of temperature dependent nesting of Fermi surface.