Scaling in the angular dependence of the critical current and temperature-dependent anisotropy ratio in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$

We present measurements of the critical current in an epitaxial ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ film as a function of the magnetic field, the temperature, and of the angle ϑ between the field and the a,b planes. The orientational study reveals an increasing anisotropy in ${\mathit{J}}_{\mathit{c}}$ with increasing temperature. The isothermal curves ${\mathit{J}}_{\mathit{c}}$(H) taken at various angles 0°≤ϑ≤90° are found to collapse to a single curve when the magnetic field is normalized to a scaling function f(ϑ): ${\mathit{J}}_{\mathit{c}}$(H,ϑ)=${\mathit{J}}_{\mathit{c}}$[H/f(ϑ)]. The best fit for f(ϑ) is obtained using an expression originally derived for ${\mathit{H}}_{\mathit{c}2}$(T,ϑ) by Tinkham. The increase in ${\mathit{J}}_{\mathit{c}}$(0°)/${\mathit{J}}_{\mathit{c}}$(90°) with increasing temperature is reflected by the increase in the anisotropy ratio f(0°)/f(90°), consistent with the quasi-two-dimensional Tinkham expression. Consistently, the same model quantitatively describes the increasing anisotropy with increasing temperature.