Critical currents ofex situYBa2Cu3O7−δthin films on rolling assisted biaxially textured substrates: Thickness, field, and temperature dependencies

The critical current density ${J}_{c}$ flowing in thin $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) films of various thicknesses $d$ has been studied magnetometrically, both as a function of applied field $H$ and temperature $T$, with a central objective to determine the dominant source of vortex pinning in these materials. The films, grown by a $\mathrm{Ba}{\mathrm{F}}_{2}$ ex situ process and deposited on buffered rolling assisted biaxially textured substrates (``RABiTS'') substrates of $\mathrm{Ni}\text{\ensuremath{-}}5%\phantom{\rule{0.3em}{0ex}}\mathrm{W}$, have thicknesses $d$ ranging from $28\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ to $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. Isothermal magnetization loops $M(H;T)$ and remanent magnetization ${M}_{\mathit{rem}}(T)$ in $H=0$ were measured with $H\ensuremath{\Vert}c$-axis (i.e., normal to film plane). The resulting ${J}_{c}(d)$ values (obtained from a modified critical state model) increase with thickness $d$, peak near $d\ensuremath{\sim}120\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and thereafter decrease as the films get thicker. For a wide range of temperatures and intermediate fields, we find ${J}_{c}\ensuremath{\propto}{H}^{\ensuremath{-}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\sim}(0.56--0.69)$ for all materials. This feature can be attributed to pinning by large random defects, which theoretically has power-law exponent $\ensuremath{\alpha}=5∕8$. Calculated values for the size and density of defects are comparable with those observed by TEM in the films. As a function of temperature, we find ${J}_{c}(T,sf)\ensuremath{\sim}{[1\ensuremath{-}{(T∕{T}_{c})}^{2}]}^{n}$ with $n\ensuremath{\sim}1.2--1.4$. This points to ``$\ensuremath{\delta}{T}_{c}$ pinning'' (pinning that suppresses ${T}_{c}$ locally) in these YBCO materials.