Large nematic susceptibility in the double- Q C 4 magnetic phase of Ba 1 − x Na x Fe 2 As 2

The nematic susceptibility of ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{Na}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ single crystals is studied by measuring the Young's modulus using a three-point-bending setup in a capacitance dilatometer over a wide doping range. Particular emphasis is placed on the behavior within the double-Q antiferromagnetic ${C}_{4}$ re-entrant phase. Here, we surprisingly still observe a sizable nematic susceptibility in spite of the well-developed magnetic order, consistent with recent theoretical calculations. Outside the ${C}_{4}$ re-entrant region, the behavior is very similar to that of K-doped ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$. A significant coupling of superconductivity to the shear modulus is observed and is discussed in terms of strong competition between the superconducting and magnetic phases.