Anisotropic superconducting strip in an oblique magnetic field

The critical state of a thin superconducting strip in an oblique applied magnetic field ${H}_{a}$ is analyzed without any restrictions on the dependence of the critical current density ${j}_{c}$ on the local magnetic induction $\mathbf{B}$. In such a strip, ${j}_{c}$ is not constant across the thickness of the sample and differs from ${J}_{c}∕d$, where ${J}_{c}$ is the critical sheet current. It is shown that in contrast to the case of $\mathbf{B}$-independent ${j}_{c}$, the profiles ${H}_{z}(x)$ of the magnetic-field component perpendicular to the strip plane generally depend on the in-plane component ${H}_{ax}$ of the applied magnetic field ${H}_{a}$ and on how ${H}_{a}$ is switched on. On the basis of this analysis, we explain how and under what conditions one can extract ${j}_{c}(\mathbf{B})$ from the magnetic-field profiles ${H}_{z}(x)$ measured by magneto-optical imaging or by Hall-sensor arrays at the upper surface of the strip.