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The in-plane London penetration depth, $\Delta\lambda(T)$, was measured usinga tunnel diode resonator technique in single crystals ofBa$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ with doping levels $x$ ranging from heavilyunderdoped, $x$=0.16 ($T_{c}$=7~K) to nearly optimally doped, $x$= 0.34($T_{c}=$39 K). Exponential saturation of $\Delta\lambda(T)$ in the $T\to0$limit is found in optimally doped samples, with the superfluid density$\rho_{s}(T)\equiv(\lambda(0)/\lambda(T))^{2}$ quantitatively described by aself-consistent $\gamma$-model with two nodeless isotropic superconductinggaps. As the doping level is decreased towards the extreme end of thesuperconducting dome at $x$=0.16, the low-temperature behavior of$\Delta\lambda(T)$ becomes non-exponential and best described by the power-law$\Delta\lambda(T)\propto T^{2}$, characteristic of strongly anisotropic gaps.The change between the two regimes happens within the range of coexistingmagnetic/nematic order and superconductivity, $x<0.25$, and is accompanied by arapid rise in the absolute value of $\Delta\lambda(T)$ with underdoping. Thiseffect, characteristic of the competition between superconductivity and otherordered states, is very similar to but of significantly smaller magnitude thanwhat is observed in the electron-doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$compounds. Our study suggests that the competition between superconductivityand magnetic/nematic order in hole-doped compounds is weaker than inelectron-doped compounds, and that the anisotropy of the superconducting statein the underdoped iron pnictides is a consequence of the anisotropic changes inthe pairing interaction and in the gap function promoted by both magnetic andnematic long-range order.

physical review. b, condensed matter and materials physics

Competition between superconductivity and magnetic/nematic order as a  source of anisotropic superconducting gap in underdoped  Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$