Quantitative assessment of pinning forces and the superconducting gap in NbN thin films from complementary magnetic force microscopy and transport measurements

Epitaxial niobium-nitride thin films with a critical temperature of Tc=16K and a thickness of 100nm 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 3mT at various temperatures. 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 Delta(0) = 2.9 meV = 2.1*kB*Tc, in perfect agreement with previous reports. The pinning force has been independently estimated from local depinning of individual vortices by 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 << Hc2, 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.Comment: 6 pages, 6 figures, 2 table

Thermally induced magnetic relaxation in square artificial spin ice

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice - we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.Comment: 15 pages, 5 figure

In situ magnetic force microscope studies of magnetization reversal of interaction domains in hot deformed Nd-Fe-B magnets

A hot-deformed Nd-Fe-B sample has been chosen for the investigation of interaction domains by means of magnetic force microscopy. During the imaging process, a magnetic field of up to 6 T was applied in situ along the easy axis of magnetization. The thermally demagnetized state presents a regular pattern of interaction domains with an average width of about 1 μm but with a much larger length scale. Starting from the thermally demagnetized state, magnetization along the initial magnetization curve occurs via sequential switching of neighboring grain columns at the peripheries of the interaction domains. Demagnetization of a saturated sample takes place through the nucleation and expansion of a patchy domain pattern with a much larger extension and a substructure in the lateral range of the underlying grain size. Reversal processes under an applied magnetic field also take place at the borders of the domains