For the 122 iron arsenide superconducting systems, we have refined the synthesis procedures and successfully generated high quality samples with precise compositions in both polycrystalline and single crystal across the entire phase diagram of alkaline earth (AE) alkali metal (A) iron arsenide (AE_1-xA_xFe₂As₂) including Ba_1-xNa_xFe₂As₂, Sr_1-xNa_xFe₂As₂, Ca_1-xNa_xFe₂As₂, BaFe₂(As_1-xP_x)₂ as well as other combinations that we published in the past years. The recent discovery of coexistence of the C4 symmetry phase in the superconducting region in the Sr_1-xNa_xFe₂As₂ phase diagram led to the double Q model which involves the coexistence of magnetic and non-magnetic Fe sites observed by Mössbauer spectroscopy (Fig. 1).

While for Ba_1-xK_xFe₂As₂ and Ba_1-xNa_xFe₂As₂, the very narrow doping extent of the C4 phase leads to an incomplete transformation and phase coexistence with the C2 phase, there is complete transformation into the C4 phase over an extended range of concentrations in Sr_1-xNa_xFe₂As₂ and Ca_1-xNa_xFe₂As₂. In all these systems, we find microscopic phase coexistence of the C4 phase and superconductivity, although the C4 phase competes more strongly with superconductivity than the C2 phase. Neutron diffraction study by collaboration with the X-ray and Neutron Scattering group (S. Rosenkranz) indicates that the magnetism of the C4 phase is related to the stripe-SDW structure of the C2 state. Within an itinerant model of SDW order, a tetragonal phase arises from a double-Q structure, in which the magnetization of the two components cancels on half the iron sites, so that they are non-magnetic, and doubles on the other half. This can only be tested by a local probe of the magnetization, and Mossbauer spectroscopy show that, in the C4 state, just such a non-uniform magnetization exists. This remarkable observation demonstrates conclusively that the magnetism in these iron pnictides is itinerant in character. By establishing conclusively that the magnetic structure is a double-Q spin-density-wave, we settle two of the most important questions in the iron-based superconductors: i) The best starting model for understanding the magnetism in these materials is one of itinerant electrons. ii) Orbital order cannot be the primary order parameter in generating the combined magnetic/orthorhombic transitions. The double-Q structure is incompatible with any orbital order, hence the single-Q structures, from which it is derived, also cannot be driven by orbital interactions.

“Double-Q spin-density wave in iron arsenide superconductors” J. M. Allred,  K. M. Taddei, D. E. Bugaris, M. J. Krogstad, S. H.Lapidus, D. Y. Chung, H. Claus, M. G. Kanatzidis, D. E. Brown, J. Kang, R. M. Fernandes, I. Eremin, S. Rosenkranz, O. Chmaissem, and R. Osborn Nature Physics 2016, 12, 493-498. (DOI: 10.1038/NPHYS3629)