Verifying Theoretical Models of Flux Pinning Using Heavy Ion Irradiated YBCO Thin Films

We have irradiated YBa <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula> Cu <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> O <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{6+x}$</tex-math></inline-formula> (YBCO) films without artificial pinning sites with Ag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^+$</tex-math></inline-formula> ions with energies of 75 MeV and 150 MeV and fluences between 2–8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cdot 10^{11}$</tex-math></inline-formula> ions/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> in order to create as controlled nanorod pinning sites as possible. The structural and superconducting properties were determined before and after the irradiation with x-ray diffraction and magnetic measurement. After the irradiation also transport and transmission electron microscopy measurements were made. It was noted that the ion tracks are all parallel to the YBCO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c$</tex-math></inline-formula> -axis of the sample and those done with 150 MeV ions formed continuous 5 nm diameter tracks, whereas with 75 MeV ions, the tracks were not continuous through the sample. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{\mathrm{c}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{\mathrm{c}}$</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(0 \mathrm{\,T})$</tex-math></inline-formula> decreased with the irradiation, but the in-field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{\mathrm{c}}$</tex-math></inline-formula> increased. The maximum increase was obtained with the 150MeV and 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cdot 10^{11}$</tex-math></inline-formula> ions/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> sample with continuous rods, where the distance between the rods was closest to the diameter of the rods. Thus, the previous theoretical models predicting optimal pinning when the pinning site diameter is approximately equal to the distance between the pinning sites, are experimentally verified for these very pure samples, with no other external pinning sites.