Dramatic Role of Critical Current Anisotropy on Flux Avalanches in ${\mathrm{MgB}}_2$ Films

Anisotropic penetration of magnetic flux in ${\mathrm{MgB}}_2$ films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, the anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate perpendicular to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability.

Figure 1

(Left) X-ray diffraction data for a sapphire substrate slightly miscut with respect to the $[1-102]$ direction. (Right) Sketch of the square substrate with surface steps. The angle $\Delta \theta$ defines the deviation from the $[1-102]$ surface, $\Delta \varphi$ describes the orientation of the steps with respect to the substrate edge, which is equivalent to the 0° orientation of the diffractometer.

Figure 2

Magneto-optical image of the remanent state in an anisotropic $5\times 5{\mathrm{mm}}^2$ ${\mathrm{MgB}}_2$ film at 12 K. The angle $\alpha$ indicates the orientation of the discontinuity line which allows determination of the critical current density ratio $j_{c1}/j_{c2}$.

Figure 3

Flux penetration into the same ${\mathrm{MgB}}_2$ film as in Fig. 2, but at lower temperatures and an applied field of 16 mT. At 8 K the flux pattern is dendritic and isotropic, while at 10 K dendritic avalanches are formed only along one direction.

Figure 4

Remanent states of the anisotropic ${\mathrm{MgB}}_2$ film. The flux pattern is isotropic at 8 K, but strongly anisotropic at 10 K, similar to the virgin penetration behavior in Fig. 3.

Figure 5

Big plot: Threshold field for the dendritic instability as a function of the critical current density, calculated using (1, 2). Two dashed lines show the values of $j_c$ in an ${\mathrm{MgB}}_2$ film at 10 K for the directions along and across the substrate steps. Large difference in the corresponding $H_{\mathrm{th}}$’s implies a strong anisotropy of the dendritic avalanches specifically at $T=10\mathrm{K}$. Two small plots illustrate the behavior at higher temperatures (there is no instability) and lower temperatures (isotropic instability, $H_{\mathrm{th}1}\approx H_{\mathrm{th}2}$).