Effects of dimensional crossover on flux pinning in a model high-${\mathit{T}}_{\mathit{c}}$ superconductor: ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$/(${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$)${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ superlattices

Superlattices of one-unit-cell-thick ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, layers with (${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$)${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ were fabricated as a model system to study the effects of magnetic coupling on flux pinning in high-${\mathit{T}}_{\mathit{c}}$ superconductors. The sample can be transformed from an S/S to an S/N structure by increasing the temperature from below to above the ${\mathit{T}}_{\mathit{c}}$ of the intercalating (${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$)${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ layer. Dramatic changes in the characteristics of the magnetic field and angle dependence of the critical current density, ${\mathit{J}}_{\mathit{c}}$(B,Θ), caused by a 3D to 2D crossover were observed. The result demonstrates the significance of the dimensionality to the flux pinning in these materials with layered structures.