Large nematic susceptibility in the double-$Q{C}_4$ magnetic phase of ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$

The nematic susceptibility of ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ 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.

Figure 1

(a) Orthorhombic distortion versus temperature of ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystals determined using capacitance dilatometry. The inset shows the phase diagram from Ref. [18] and the Na concentrations for the present measurements (arrows on top of inset). (b) Corresponding normalized Young' s modulus $Y_{\left[110\right]}/Y_{{\left[110\right]}_0}$ from static three-point bending measurements on the same crystals used for dilatometry.

Figure 2

(a) Normalized Young's modulus $Y_{\left[110\right]}/Y_{{\left[110\right]}_0}$ of ${\mathrm{Ba}}_{0.735}{\mathrm{Na}}_{0.265}{\mathrm{Fe}}_2{\mathrm{As}}_2$ under different maximal compressive (tensile) stress conditions. (b) The temperature derivative of $Y_{\left[110\right]}/Y_{{\left[110\right]}_0}$. (c) The corresponding orthorhombic distortion, δ $\equiv (b-a)/(b+a)$, of the same crystal. The dashed lines indicated the transition temperature $T_{\mathrm{s},\mathrm{N}}$, $T_{dQ}$, and $T_{\mathrm{C}}$. (See text for details.)

Figure 3

Thermal expansion coefficient $\alpha \left(T\right)$ along the ${\left[110\right]}_{\mathrm{Tet}}$ direction of ${\mathrm{Ba}}_{0.735}{\mathrm{Na}}_{0.265}{\mathrm{Fe}}_2{\mathrm{As}}_2$ under two different uniaxial pressures. The inserts illustrate the pressure induced shift of the transition temperatures $T_{\mathrm{s},\mathrm{N}}$ and $T_{dQ}$, respectively.

Figure 4

(a) Nematic $\mathrm{susceptibility}{\chi }_{\phi }$ in units of ${\lambda }^2{\chi }_{\phi }/C_{66,0}$. The black dotted lines are Curie-Weiss fits in the underdoped region. The dashed colored lines are guides to the eye. (b) Inverse nematic susceptibility exhibiting clear deviations from Curie-Weiss behavior for $x>20\%$ Na.

Figure 5

Magnified view of the shear modulus response near $T_{\mathrm{C}}$ for various Na concentrations.