Scaling laws for ion irradiation effects in iron-based superconductors

<jats:title>Abstract</jats:title><jats:p>We report on ion irradiation experiments performed on compounds belonging to the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\hbox {BaFe}_2\hbox {As}_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>BaFe</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mtext>As</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> family, each one involving the partial substitution of an atom of the parent compound (K for Ba, Co for Fe, and P for As), with an optimal composition to maximize the superconducting critical temperature <jats:inline-formula><jats:alternatives><jats:tex-math>$$T_c$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>. Employed ion beams were 3.5-MeV protons, 250-MeV Au ions, and 1.2-GeV Pb ions, but additional data from literature are also considered, thus covering a wide range of ions and energies. Microwave characterization based on the use of a coplanar waveguide resonator allowed us to investigate the irradiation-induced <jats:inline-formula><jats:alternatives><jats:tex-math>$$T_c$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> degradation, as well as the increase of normal state resistivity and London penetration depth. The damage was quantified in terms of displacements per atom (dpa). From this broad and comprehensive set of experimental data, clear scaling laws emerge, valid in the range of <jats:italic>moderate</jats:italic> irradiation-induced disorder (dpa up to 5 <jats:inline-formula><jats:alternatives><jats:tex-math>$$\times$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math></jats:alternatives></jats:inline-formula> 10 <jats:inline-formula><jats:alternatives><jats:tex-math>$$^{-3}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> were investigated). In these conditions, linear trends with dpa were found for all the modification rates, while a power law dependence on the ion energy was found for heavy-ion irradiation. All these scaling laws are reported and discussed throughout the paper.</jats:p>