Roles of intrinsic anisotropy and π-band pairbreaking effects on critical currents in tilted- c -axis Mg B 2 films probed by magneto-optical and transport measurements

Investigations of $\mathrm{Mg}{\mathrm{B}}_{2}$ and Fe-based superconductors in recent years have revealed many unusual effects of multiband superconductivity, but manifestations of anisotropic multiband effects in the critical current density ${J}_{c}$ have not been addressed experimentally, mostly because of the difficulties in measuring ${J}_{c}$ along the $c$ axis. To investigate the effect of very different intrinsic anisotropies of \ensuremath{\sigma} and \ensuremath{\pi} electron bands in $\mathrm{Mg}{\mathrm{B}}_{2}$ on current transport, we grew epitaxial films with a tilted $c$ axis (\ensuremath{\theta} \ensuremath{\sim} 19.5\ifmmode^\circ\else\textdegree\fi{}), which enabled us to measure the components of ${J}_{c}$ along both the $ab$ plane and the $c$ axis using magneto-optical and transport techniques. These measurements were combined with scanning and transmission electron microscopy, which revealed terraced steps on the surface of the tilted-$c$-axis films. The measured field and temperature dependencies of the anisotropic ${J}_{c}(H)$ show that ${J}_{c,\mathrm{L}}$ parallel to the terraced steps is higher than ${J}_{c,\mathrm{T}}$ perpendicular to the terraced steps, and ${J}_{c}$ of thinner films (50 nm) obtained from transport experiments at 0.1 T reaches \ensuremath{\sim}10% of the depairing current density ${J}_{d}$ in the $ab$ plane, while magneto-optical imaging revealed much higher ${J}_{c}$ at lower fields. To analyze the experimental data we developed a model of anisotropic vortex pinning which accounts for the observed behavior of ${J}_{c}$ in the tilted-$c$-axis films and suggests that the apparent anisotropy of ${J}_{c}$ is affected by current pairbreaking effects in the weaker \ensuremath{\pi} band. Our results indicate that the out-of-plane current transport mediated by the \ensuremath{\pi} band could set the ultimate limit of ${J}_{c}$ in $\mathrm{Mg}{\mathrm{B}}_{2}$ polycrystals.