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Low-temperature (22~K) irradiation with 2.5~MeV electrons was used to studythe competition between stripe ${\rm C_2}$ and tetragonal ${\rm C_4}$antiferromagnetic phases which exist in a narrow doping range around $x=$0.25in hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$. In nearby compositions outside ofthis range, at $x=$0.22 and $x=$0.19, the temperatures of both the concomitantorthorhombic/stripe antiferromagnetic transition $T_{\rm C2}$ and thesuperconducting transition $T_{\rm c}$ are monotonically suppressed by addeddisorder at similar rates of about 0.1~K/$\mu \Omega$cm, as revealed throughusing resistivity variation as an intrinsic measure of scattering rate. In astark contrast, a rapid suppression of the ${\rm C_4}$ phase at the rate of0.24 K/$\mu \Omega \cdot$cm is found at $x=$0.25. Moreover, this suppression ofthe ${\rm C_4}$ phase is accompanied by unusual disorder-induced stabilizationof the ${\rm C_2}$ phase, determined by resistivity and specific heatmeasurements. The rate of the ${\rm C_4}$ phase suppression is notably higherthan the suppression rate of the spin-vortex phase in the Ni-dopedCaKFe$_4$As$_4$ (0.16 K/$\mu \Omega$cm).

physical review. b./physical review. b

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