Observation of an extended magnetic field penetration in amorphous superconducting MoGe films

We have observed the magnetic field distribution of a vortex generated in amorphous $\left(\alpha \right)\text{−}\mathrm{Mo}\mathrm{Ge}$ thin films with various thicknesses $\left(d\right)$ ($<\lambda$, where $\lambda$ is the penetration depth) with a scanning superconducting quantum interference device microscope. From the analyses of the field distribution as functions of film thickness and temperature, it is found that an effective in-plane penetration depth $\left(\Lambda \right)$ extends with decreasing $d$, in accordance with the Pearl prediction $\Lambda =2{\lambda }^2∕d$. Temperature dependence of $\Lambda$ is also consistent with the two-fluid model involving the Pearl prediction.

Figure 1

(a) Magnetic images of vortices forming triangular lattice in the $400\mathrm{nm}$ thick $\alpha \text{−}\mathrm{Mo}\mathrm{Ge}$ film and (b) a disordered vortex arrangement in the $100\mathrm{nm}$ thick film at an applied magnetic field of $10\mu \mathrm{T}$ perpendicular to the film surface at $4.5\mathrm{K}$. The shade corresponds to a range of the magnetic flux density from $0\text{to}10\mu \mathrm{T}$.

Figure 2

Magnetic images of vortices in the $\alpha \text{−}\mathrm{Mo}\mathrm{Ge}$ films with thicknesses of (a) $400\mathrm{nm}$ and (b) $30\mathrm{nm}$ at a perpendicular magnetic field of $1\mu \mathrm{T}$ at $4.5\mathrm{K}$, respectively. [(c) and (d)] The magnetic field profiles of the vortices along the dashed lines in (a) and (b), respectively. The solid lines shown in (c) and (d) are the fits of numerical calculations (see text).

Figure 3

Thickness dependence of $\Lambda$ at $4.5\mathrm{K}$ in comparison with the Pearl relation $\Lambda =2{\lambda }^2∕d$, which is shown by a solid line (see text). The error bars are assigned by a doubling of the ${\chi }^2$ values of the fits.

Figure 4

Temperature dependence of $\Lambda$ for the $100\mathrm{nm}$ thick film is compared with theoretical expressions. The filled circles represent experimental data. The dotted and the broken curves show dependencies $\Lambda \left(0\right){[1-{(T∕T_c)}^4]}^{-1∕2}$ and $\Lambda \left(0\right){[1-{(T∕T_c)}^2]}^{-1∕2}$, respectively, where $\lambda \left(0\right)=550\mathrm{nm}$ and $T_c=5.7\mathrm{K}$. The solid curve represents the result obtained from Eq. (6) (see text). The error bars are assigned the same as Fig. 3.