Nematicity, magnetic fluctuation and ferro-spin-orbital ordering in BaFe$_2$As$_2$ family

Abstract: Through detailed electronic structure simulations we show that the electronic orbital ordering (between d${yz}$ and d${xz}$ bands) takes place due to local breaking of in-plane symmetry that generates two non-equivalent $a$, $b$ directions in 122 family of Fe-based superconductors. Orbital ordering is strongly anisotropic and the temperature dependence of the corner zone orbital order maps to that of the orthorhombicity parameter. Orbital anisotropy results in two distinct spin density wave nesting wave vectors and causes inter-orbital charge and spin fluctuations. Temperature dependence of the orbital order is proportional to the nematic order and it sets in at a temperature where magnetic fluctuation starts building. Magnetic fluctuations in the orthorhombic phase is characterized through evolution of Stoner factor which reproduces experimentalfindings very accurately. Orbital ordering becomes strongly spin dependent in presence of magnetic interaction. Occupation probabilities of all the Fe-d-orbitals exhibit temperature dependence indicating their possible contribution in orbital fluctuation. This need to be contrasted with the usual definition of nematic order parameter (n${d{xz}}$-n${d{yz}}$). Relationship among orbital fluctuations, magnetic fluctuations and nematicity are established.