Competition between orthorhombic and re-entrant tetragonal phases in underdoped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ probed by the response to controlled disorder

Low-temperature (22 K) irradiation with 2.5-MeV electrons, creating point defects affecting elastic scattering, was used to study the competition between stripe ${\mathrm{C}}_2$ and tetragonal ${\mathrm{C}}_4$ antiferromagnetic phases which exist in a narrow doping range around $x=0.25$ in hole-doped ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$. In nearby compositions outside of this range, at $x=0.22$ and $x=0.19$, the temperatures of both the concomitant orthorhombic/stripe antiferromagnetic transition $T_{\mathrm{C}2}$ and the superconducting transition $T_{\mathrm{c}}$ are monotonically suppressed by added disorder at similar rates of about 0.1 K/$\mu \mathrm{\Omega }\mathrm{cm}$, as revealed through using resistivity variation as an intrinsic measure of scattering rate. In a stark contrast, a rapid suppression of the ${\mathrm{C}}_4$ phase at the rate of 0.24 K/$\mu \mathrm{\Omega }\mathrm{cm}$ is found at $x=0.25$. Moreover, this suppression of the ${\mathrm{C}}_4$ phase is accompanied by unusual disorder-induced stabilization of the ${\mathrm{C}}_2$ phase, determined by resistivity and specific heat measurements. The rate of the ${\mathrm{C}}_4$ phase suppression is notably higher than the suppression rate of the spin-vortex phase in the Ni-doped ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ (0.16 K/$\mu \mathrm{\Omega }\mathrm{cm})$.

Figure 1

(a) Temperature-dependent resistivity of selected samples of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2,x=0.19$ (green), 0.22 (blue), and 0.25 (red). The curves are offset vertically. Inset: Low-temperature region showing differences in the superconducting transition temperatures and resistivity values at $T_{\mathrm{c}}$. (b) Resistivity derivative, revealing a sharp feature at the structural transitions at $T_{\mathrm{C}2}$ and $T_{\mathrm{C}4}$. (c) Doping phase diagram of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the range of ${\mathrm{C}}_4$ phase formation, as proposed by Böhmer et al. [15] (lines). The positions of ${\mathrm{C}}_2$ (circles), ${\mathrm{C}}_4$ (square), and superconducting (triangle) transitions for samples with $x=0.19$ and $x=0.22$ are matching well with the diagram, but the position of $x=0.25$ sample was adjusted to 0.264 to match the ${\mathrm{C}}_2$ line with the concomitant match of the ${\mathrm{C}}_4$ line. Symbols with crosses show the positions of the features in the heat capacity measurements (see Fig. 3 below).

Figure 2

Temperature-dependent resistivity (left panels) and resistivity derivative (right panels) of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ with $x=0.22$ (top panels) and $x=0.25$ (bottom panels). Black curves in panels (a) and (b) are for the pristine $x=0.22$ sample, and red curves are for the sample after electron irradiation with 2.35 C/${\mathrm{cm}}^2$. Panels (c) and (d) show systematics of the evolution of the temperature-dependent electrical resistivity in the sample with $x=0.25$ with irradiation, bottom to top: pristine sample (black), 0.212 C (red), 0.438 C (green), 0.893 C (blue), 1.835 C (cyan), 2.115 C (magenta), 3.115 C (dark yellow), and 4.115 C (navy). The inset in panel (a) shows resistivity at 95 K as a function of electron irradiation dose for the samples with $x=0.22$ (blue) and $x=0.25$ (green). Inset in panel (c) shows the evolution of the superconducting transition temperature in the sample with $x=0.25$ as a function of the change of resistivity at 95 K, above $T_{\mathrm{C}2}$.

Figure 3

Temperature-dependent heat capacity, $C/T$, of the ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_{2}x=0.25$ sample before (a) and after (b) electron irradiation with 5.045 C/${\mathrm{cm}}^2$. The right-hand insets zoom in on the $T_{\mathrm{C}2}$ phase transition, and the left-had insets zoom in on the low-temperature transitions.

Figure 4

Transition temperatures of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_{2}x=0.19$ (a), $x=0.22$ (b), and $x=0.25$ (c) samples as a function of scattering rate increase characterized with resistivity increase in the paramagnetic tetragonal phase above $T_{\mathrm{C}2}$. Note the similar rates of superconducting $T_{\mathrm{c}}$ suppression in all compositions (blue open circles), the fast suppression of the ${\mathrm{C}}_2$ phase (black solid up-triangles) in $x=0.19$ and 0.22 samples, the two times faster suppression of the ${\mathrm{C}}_4$ phase in $x=0.25$ samples (open red squares from resistivity measurements, crossed squares from heat capacity measurements), and the slight increase of $T_{\mathrm{C}2}$ with irradiation in $x=0.25$ samples (solid up-triangles resistivity measurements, crossed triangles from heat capacity measurements). Blue crossed circles are $T_{\mathrm{c}}$ from heat capacity measurements.