Tuning the Magnetic and Superconducting Properties of Hole Doped BaFe₂As₂: A Universal Scaled Phase Diagram

Embarking on an extensive effort in which more than fifty hole-doped BaFe₂As₂ samples have been produced and characterized by neutron diffraction allowed us to extract universal behaviors and properties of this rich system. All the measured magnetic and superconducting transitions values collapse into a single phase diagram. Strontium, calcium, and sodium subsitutions at the barium site enabled the production of many samples in which both the re-entrant tetragonal double-Q magnetic C₄ and the orthorhombic SDW magnetic C₂ phases coexist and compete with superconductivity just before reaching the peak of the superconductivity-only region of the phase diagram. The evolution of T_N, T_r and the internal structual parameters are in agreement with recent theoretical models that correlate the stabiity of these observed phases with approaching a perfect tetrahedral FeAs₄ angle and perfect Fermi surface nesting. Our results separate the individual roles played by either the As-Fe-As bond angles or the Fe-As bond lengths and demonstrate their combined effects in tuning the magnetic and superconducting properties.