Quantitative assessment of pinning forces and magnetic penetration depth in NbN thin films from complementary magnetic force microscopy and transport measurements

Epitaxial niobium nitride thin films with a critical temperature of ${T}_{\mathrm{c}}=16$ K and a thickness of 100 nm were fabricated on MgO (100) substrates by pulsed laser deposition. Low-temperature magnetic-force-microscopy (MFM) images of the supercurrent vortices were measured after field cooling in a magnetic field of 3 mT at various temperatures. The temperature dependence of the penetration depth has been evaluated by a two-dimensional fitting of the vortex profiles in the monopole-monopole model. Its subsequent fit to a single $s$-wave-gap function results in the superconducting gap amplitude, $\ensuremath{\Delta}(0)=(2.9\ifmmode\pm\else\textpm\fi{}0.4)$ meV $=(2.1\ifmmode\pm\else\textpm\fi{}0.3){k}_{\mathrm{B}}{T}_{\mathrm{c}}$, which perfectly agrees with the previous reports. The pinning force has been independently estimated from the local depinning of individual vortices by the lateral forces exerted by the MFM tip and from transport measurements. A good quantitative agreement between the two techniques shows that for low fields, $B\ensuremath{\ll}{\ensuremath{\mu}}_{0}{H}_{\text{c2}}$, MFM is a powerful and reliable technique to probe the local variations of the pinning landscape. We also demonstrate that the monopole model can be successfully applied even for thin films with a thickness comparable to the penetration depth.