Effect of temperature and magnetic field on the thickness dependence of the critical current density of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ films

In order to shed light on the puzzling thickness $\left(t\right)$ dependence of the critical current density $\left(J_c\right)$ in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ (YBCO) films at $77\mathrm{K}$ and self-field, we have investigated $J_c\text{−}t$ behavior as a function of temperature $\left(T\right)$ and applied magnetic field $\left(H\right)$ in the thickness range that is within the modified Larkin length $L_c$. It has been found that the $J_c\text{−}t$ behavior can be well described by the collective pinning (CP) model as monotonically decreasing $J_c\sim t^{-1∕2}$ when thermal assisted flux motion (TAFM) is suppressed at low $T$ close to zero. TAFM becomes increasingly important at elevated temperatures and causes deviation of the $J_c\text{−}t$ from the CP model in the thickness range below the magnetic penetration depth. The deviation is more pronounced at smaller thickness and increases with $T$ and $H$. Consequently, a completely reversed $J_c\text{−}t$ from monotonically decreasing to monotonically increasing occurs when TAFM dominates in high $T$ and $H$ ranges. This result suggests that the monotonic decreasing $J_c\text{−}t$ behavior is an intrinsic property of uniform YBCO films, while extrinsic effects such as material nonuniformity can greatly complicate it.

Figure 1

(Color online) Normalized $M[M∕M\left(10\mathrm{K}\right)]$ as a function of $T$ for YBCO films with various thicknesses. Shown in the inset are the $T_c$ and $\delta T_c$ as a function of thickness.

Figure 2

(Color online) (a) $J_c\left(\mathrm{SF}\right)\text{−}t$ at various temperatures. The error bar corresponds to the average over different sets of samples with the same thickness. (b) The reduced $J_c^r=J_c∕J_c\left(0.6\mu \mathrm{m}\right)$ as a function of thickness at various temperatures. The dashed line represents the fitting of $1∕t^{1∕2}$.

Figure 3

(Color online) $J_c^r\text{−}t$ curves at (a) $77\mathrm{K}$ and (b) $50\mathrm{K}$ at various $H$ fields. The dashed line represents the fitting of $1∕t^{1∕2}$.

Figure 4

$J_c^r\left(10\mathrm{K}\right)\text{−}t$ curves at SF and $1.0\mathrm{T}$, respectively. The dashed line represents the fitting of $1∕t^{1∕2}$.