Determining the absolute value of magnetic penetration depth in small-sized superconducting films

In the previous four decades, a two-coil mutual inductance (MI) technique has been widely employed in characterizing magnetic penetration depth, $\lambda$, of superconducting films. However, the conventional methods used to obtain $\lambda$ are not applicable to small-sized films with common shapes, which limits the application of the MI technique in superconductivity research. Here, we first employed the fast wavelet collocation (FWC) method to a two-coil system and then proposed the possibility of directly obtaining the absolute $\lambda$ of polygonal superconducting films with arbitrary sizes. To verify its accuracy and advantages, we extracted the $\lambda$ values of square NbN films with different sizes using the FWC and conventional flux leakage subtraction (FLS) methods. Notably, the FLS method fails for a $5\times 5 \, \rm mm^2$ film, which is attributed to the significant current peak at the film edge. In contrast, the absolute $\lambda$ extracted using the FWC method was independent of the film size. Finally, we established the applicability of the FWC method to large coil spacings, which may pave the way for integrating high-accuracy $\lambda$ measurements with the ionic liquid gating technique.