Abstract:We present the results of Synchrotron XRD measurements on powdered single crystal samples of BaFe2-xRuxAs2, as a function of Ru content, and as a function of temperature, across the spin density wave transition in BaFe1.9Ru0.1As2. The Rietveld refinements reveal that with Ru substitution, while the a-axis increases, the c-axis decreases. In addition the variation of positional co-ordinates of As (zAs), the Fe-As bond length and the As-Fe-As bond angles have also been determined. In the sample with x=0.1, temperature dependent XRD measurements, indicate that the orthorhombicity shows the characteristic increase with decrease in temperature, below the magnetic transition. It is seen that the c-axis, the As-FeAs bond angles, Fe-As bond length and positional co-ordinate of the As show definite anomalies close to the structural transition. The observed anomalies in structural parameters are analysed in conjunction with geometric optimization of the structure using ab-initio electronic structure calculations.

Using the experimentally measured temperature and doping dependent structural parameters on Ru doped BaFe2As2, 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-dxy orbital largely due to its planar spatial extension leading to Lifshitz transition, while the otherwise degenerate Fe-dxz and dyz 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.

Fermiology of various 122 systems are studied through first principles simulation. Electron doping causes expansion of electron and shrinkage of hole Fermi pockets. Isovalent Ru substitution (up to 35%) makes no visible modification in the electron-and hole-like Fermi surfaces (FSs) providing no clue regarding the nature of charge carrier doping. However, in case of 32% P doping there are considerable changes in the hole FSs. From our calculations, it is very clear that two-dimensionality of FSs may favour electron pair scattering between quasi-nested FSs which has important bearings in various orders (magnetic, orbital, superconducting) present in Fe-based superconductors.

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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 experimental findings 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 dxz -n dyz ). Relationship among orbital fluctuations, magnetic fluctuations and nematicity are established.

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In the quest of why there should be a single transition temperature in a multi-gapped system like Fe-based materials we use two band model for simplicity. The model comprises of spin density wave (SDW), orbital density wave (ODW) arising due to nested pieces of the electron and hole like Fermi surfaces; together with superconductivity of different pairing symmetries around electron and hole like Fermi surfaces. We show that either only intra or only inter band pairing is insufficient to describe some of the experimental results like large to small gap ratio, thermal behaviour of electronic specific heat jump etc. It is shown that the inter-band pairing is essential in Fe-based materials having multiple gaps to produce a single global Tc. Some of our results in this scenario, matches with the earlier published work [19], and also have differences. The origin of difference between the two is also discussed. Combined intra-inter band pairing mechanism produces the specific heat jump to superconducting transition temperature ratio proportional to square of the transition temperature, both in the electron and hole doped regime, for sign changing s ± wave symmetry which takes the d+s pairing symmetry form. Our work thus demonstrates the importance of combined intra-inter band pairing irrespective of the pairing mechanism.PACS numbers: 74.25.Bt

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