Magnetic force microscopy studies of mesoscopic superconducting structures

The superconducting state of matter enables one to observe quantum effects on the macroscopic scale and hosts many fascinating phenomena. Topological defects of the superconducting order parameter, such as vortices and fluxoid states in multiply connected structures, are often the key ingredients of these phenomena. This dissertation describes a new mode of magnetic force microscopy (Φ0-MFM) for investigating vortex and fluxoid sates in mesoscopic superconducting (SC) structures. The technique relies on the magneto-mechanical coupling of a MFM cantilever to the motion of fluxons. The novelty of the technique is that a magnetic particle attached to the cantilever is used not only to sense the state of a SC structure, but also as a primary source of the inhomogeneous magnetic field which induces that state. Φ0-MFM enables us to map the transitions between tip-induced states during a scan: at the positions of the tip, where the two lowest energy states become degenerate, small oscillations of the tip drive the transitions between these states, which causes a significant shift in the resonant frequency and dissipation of the cantilever. For narrow-wall aluminum rings, the mapped fluxoid transitions form concentric contours on a scan. We show that the changes in the cantilever resonant frequency and dissipation are well-described by a stochastic resonance (SR) of cantilever-driven thermally activated phase slips (TAPS). The SR model allows us to experimentally determine the rate of TAPS and compare it to the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory for TAPS in 1D superconducting structures. Further, we use the SR model to qualitatively study the effects of a locally applied magnetic field on the phase slip rate in rings containing constrictions. The states with multiple vortices or winding numbers could be useful for the development of novel superconducting devices, or the study of vortex interactions and interference effects. Using Φ0-MFM allows us to induce, probe and control fluxoid states in thin wall structures comprised of multiple loops. We show that Φ0-MFM images of the fluxoid transitions allow us to identify the underlying states and to investigate their energetics and dynamics even in complicated structures.