Magnetic force microscopy versus scanning quantum-vortex microscopy: Probing pinning landscape in granular niobium films

Abstract

We provide an overview of the methodology and fundamental principles associated with newly developed experimental technique -- scanning quantum-vortex microscopy [Hovhannisyan et al., Commun. Mater., vol. 6, 42 (2025)]. This approach appears promising for experimental studies of vortex pinning phenomena in superconducting films and nanodevices. In particular, we studied the magnetic properties of magnetron-sputtered niobium (Nb) films by low-temperature magnetic force microscopy. As the temperature approaches the superconducting critical temperature, the pinning potential caused by structural defects weakens; consequently, the attractive interaction between the magnetic tip of the cantilever and a single-quantum vortex begins to dominate. In this scenario the magnetic probe is capable of trapping a vortex during the scanning process. Because the dragged vortex continues interacting with structural defects, it serves as an efficient nano-probe to explore pinning potentials and visualize grain boundaries in granular Nb films, achieving resolutions (30 nm) comparable to the superconducting coherence length.

Figures (13)

• Figure 1: a -- Schematic presentation of a cantilever used both in non-contact atomic-force microscopy and magnetic-force microscopy. Inset shows schematically instantaneous displacements of the piezo-actuator (red line) and the probe (blue line); the phase of the probe oscillations lags behind the excitation at about $-\pi/2$. b -- Frequency dependence of the phase shift between the excitation and the displacement of the probe.
• Figure 2: Typical frequency dependences of the amplitude of the driven oscillations (panel a) and their phase (panel b) acquired in the MFM measurements at low temperatures. Dashed black lines show the optimal fitting of the experimental data by Eqs. (\ref{['Eq:NC-AFM-Ampl']}) and (\ref{['Eq:NC-AFM-Freq']}) with the following parameters: $f^{\,}_0=66.935\,$kHz, $Q=1570$. The phase shift is presented in degrees with respect to an unperturbed baseline value of $-90^{\circ}$.
• Figure 3: a -- Schematic illustration depicting the magnetostatic interaction between an extended magnetic probe and a vortex-free superconducting film due to the ideal Meissner screening. b -- Schematic illustration depicting the magnetostatic interaction between an extended magnetic probe and pinned Pearl vortex/antivortex. Red and blue arrows illustrate the configurations of the magnetic field ${\bf B}({\bf r})$ above a Pearl vortex (on the left) and a Pearl antivortex (on the right). Interestingly, that the ${\bf B}({\bf r})$ distributions resemble the structure of the electric field ${\bf E}({\bf r})$ induced by positive and negative monopoles. This qualitatively explains why the MFM probe attracts to the pinned vortex and repels from the pinned antivortex. The resulting profile of the phase shift $\delta \varphi(x)$ for a superconducting film with pinned vortices should combine both components (uniform and nonuniform), illustrated by thick black lines in the lower parts of panels a and b (see figure \ref{['Fig03-V-and-AV']}).
• Figure 4: a, b, c -- The typical dependences of the normalized dc-resistance $R$ on temperature $T$ for the Nb films of different thicknesses: 50 nm (panel a), 100 nm (panel b), and 240 nm (panel c). Three curves in each panel show the $R(T)$ dependences in the presence of the external magnetic field: zero field (rightmost curves), 100 Oe (middle curves), and 200 Oe (leftmost curve). The critical temperatures, defined at the point corresponding to half of the normal-state resistance are the following: 8.99 K for 50-nm-thick film, 9.11 K for 100-nm-thick film, and 9.23 K for 240-nm-thick film.
• Figure 5: a, b -- Spatial distributions of the phase shift $\delta\varphi(x,y)$ in 240-nm-thick Nb film at low temperatures showing ensembles of the vortices and antivortices trapped in 240-nm thick Nb film after cooling down in the presence of the external magnetic field of $+10\,$Oe and $-10\,$Oe, respectively (image size $5\times 5\,\mu$m$^2$, $T=4.06\,$K, scanning height 80 nm, regime of the constant frequency 66.941 kHz). c -- Profiles of the phase shifts $\delta\varphi(x,y)$ along the $A-B$ line (panel a) and the $C-D$ line (panel b).