Suppression of the structural phase transition and lattice softening in slightly underdoped ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ with electronic phase separation

We present x-ray powder diffraction (XRPD) and neutron-diffraction measurements on the slightly underdoped iron-pnictide superconductor ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$, $T_c=32\text{K}$. Below the magnetic-transition temperature $T_m=70\text{K}$, both techniques show an additional broadening of the nuclear Bragg peaks, suggesting a weak structural phase transition. However, macroscopically the system does not break its tetragonal symmetry down to 15 K. Instead, XRPD patterns at low temperature reveal an increase in the anisotropic microstrain proportionally in all directions. We associate this effect with the electronic phase separation previously observed in the same material and with the effect of lattice softening below the magnetic phase transition. We employ density-functional theory to evaluate the distribution of atomic positions in the presence of dopant atoms both in the normal and magnetic states and to quantify the lattice softening, showing that it can account for a major part of the observed increase in the microstrain.

Figure 1

(Color online) Neutron-diffraction data showing the temperature-dependent longitudinal broadening of the ${\left(110\right)}_{\mathrm{T}}$ nuclear Bragg reflection (circles) overlayed with the intensity of the ${\left(\frac{1}{2}\frac{1}{2}\overline{3}\right)}_{\mathrm{T}}$ magnetic Bragg peak (triangles).

Figure 2

(Color online) Panels (a) and (b) present XRPD data measured at 300 and 15 K, respectively. (i) Scattered x-ray intensity as a function of the diffraction angle $2\Theta$ $\left(\lambda =0.7\text{Å}\right)$ fitted to the tetragonal $I4/mmm$ space group. For $2\Theta >17°$ the plots are enlarged by a factor of 3. The fit includes a few $\text{wt}\%$ of tetragonal $\beta$ tin from the flux as an impurity phase and some reflections of the brass sample holder as indicated by the reflection markers in (ii). (iii) The difference $\Delta$ between the experimental points and the fitting curve. Insets show tensor surfaces representing the normalized anisotropic microstrain distribution along different crystallographic directions. The distance of the surface from the origin corresponds to the squared FWHM of the microstrain $B_{\epsilon }^2$ along the corresponding directions in real space. The $x\text{−}z$ and $x\text{−}y$ cross sections of both surfaces are shown in panel (c) for comparison.

Figure 3

(Color online) The $2\sqrt{2}a\times 2\sqrt{2}b\times c$ supercell with 50% of the Ba atoms randomly substituted by the K dopants that we used in our density functional calculations. The calculated statistical distributions of the five interatomic distances, which are marked in the figure, are presented in Fig. 4.

Figure 4

(Color online) Histograms of the calculated interatomic distances for the supercell as defined in Fig. 3. The plots at the top of each panel are a result of the normal-state (nonmagnetic) calculation, whereas the upsidedown plots below represent the magnetic ground state. Solid lines are fits to a normal distribution.