Effects of Nematic Fluctuations on the Elastic Properties of Iron Arsenide Superconductors

We demonstrate that the changes in the elastic properties of the FeAs systems, as seen in our resonant ultrasound spectroscopy data, can be naturally understood in terms of fluctuations of emerging nematic degrees of freedom. Both the softening of the lattice in the normal, tetragonal phase as well as its hardening in the superconducting phase are consistently described by our model. Our results confirm the view that structural order is induced by magnetic fluctuations.

Figure 1

Left-hand panel: In-plane magnetic ordering of the pnictides. The two iron atoms present in one tetragonal unit cell (open blue circles and filled red circles) form two coupled AFM sublattices with coplanar staggered magnetization ${\mathbf{m}}_1$ and ${\mathbf{m}}_2$. Right-hand panel: In the disordered phase, the spins in the two sublattices fluctuate around two arbitrary staggered magnetization directions. In the nematic phase, these two Néel vectors are locked either parallel ($\phi >0$) or antiparallel ($\phi <0$) to each other, but still with $⟨{\mathbf{m}}_1⟩=⟨{\mathbf{m}}_2⟩=0$. The coupling between the nematic and the elastic order parameters makes the bonds between neighboring parallel (antiparallel) spins contract (expand).

Figure 2

Temperature dependence of the RUS measured squared resonant frequency $f^2$ (red points), and of the calculated shear modulus $C_s\equiv C_{66}$ of the tetragonal phase (solid blue line), for both (a) undoped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and (b) optimally doped ${\mathrm{BaFe}}_{1.84}{\mathrm{Co}}_{0.16}{\mathrm{As}}_2$.

Figure 3

Shear modulus $C_s$ in the tetragonal, SC phase. The inset shows a schematic ($x,T$) phase diagram for $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$, with the green arrow denoting optimal doping. In the main panel, the solid line refers to the optimally doped system, whereas the dashed and dotted curves refer to systems that are, respectively, deeper in the overdoped region. The red points refer to the RUS data of Fig. 2b.