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Thickness uniformity is regarded as an important parameter in designing thin film devices. However, some applications based on films with non-uniform thickness have recently emerged, such as gas sensors and optimized materials based on the gradual change of film composition. This work deals with superconducting Pb thin films with a thickness gradient prepared with the aid of a diffuse stencil mask. Atomic Force Microscopy and Energy-Dispersive X-ray Spectroscopy show variations ranging from 90~nm to 154~nm. Quantitative magneto-optical images reveal interesting features during both the abrupt and the smooth penetration regimes of magnetic flux, as well as the thickness-dependent critical current density ($J_c$). In addition, we observe a gradual superconducting transition as the upper critical field is progressively reached for certain thicknesses. Furthermore, the hysteresis observed for triggering flux avalanches when increasing and decreasing magnetic fields is also accounted for by the $J_c$ profile evolution along the thickness gradient. Numerical simulations based on the Thermomagnetic Model are in fair agreement with the experimental data. These findings demonstrate that wedge-shaped films are a viable approach to investigate, in a continuous fashion, thickness-dependent properties of a superconducting materials.

Graphene is a promising substrate for future spintronics devices owing to its remarkable electronic mobility and low spin-orbit coupling. Hanle precession in spin valve devices is commonly used to evaluate the spin diffusion and spin lifetime properties. In this work, we demonstrate that this method is no longer accurate when the distance between inner and outer electrodes is smaller than six times the spin diffusion length, leading to errors as large as 50% for the calculations of the spin figures of merit of graphene. We suggest simple but efficient approaches to circumvent this limitation by addressing a revised version of the Hanle fit function. Complementarily, we provide clear guidelines for the design of four-terminal spin valves able to yield flawless estimations of the spin lifetime and the spin diffusion coefficient., Comment: 7 pages, 5 figures

Efficient conversion of a spin signal into an electric voltage in mainstream semiconductors is one of the grand challenges of spintronics. This process is commonly achieved via a ferromagnetic tunnel barrier where non-linear electric transport occurs. In this work, we demonstrate that non-linearity may lead to a spin-to-charge conversion efficiency larger than 10 times the spin polarization of the tunnel barrier when the latter is under bias of a few mV. We identify the underlying mechanisms responsible for this remarkably efficient spin detection as the tunnel barrier deformation and the conduction band shift resulting from a change of applied voltage. In addition, we derive an approximate analytical expression for the detector spin sensitivity $P_{\textrm{det}}(V)$. Calculations performed for different barrier shapes show that this enhancement is present in oxide barriers as well as in Schottky tunnel barriers even if the dominant mechanisms differs with the barrier type. Moreover, although the spin signal is reduced at high temperatures, it remains superior to the value predicted by the linear model. Our findings shed light into the interpretation and understanding of electrical spin detection experiments and open new paths to optimize the performance of spin transport devices., Comment: 11 pages, 9 figures

Border indentations in non-linear conductors, such as superconducting thin films in the creep regime, alter the distribution of currents and magnetic fields near and far from the indentation. One of such disturbances are the discontinuity lines, or \textit{d}-lines, a parabolic-like line originating from the indentation where the current density direction changes abruptly. Hodograph series results are obtained for the currents around a triangular indentation and its corresponding $d$-lines in a conducting stripe of finite width and in an infinite half plane, considering two cases: uniform creep exponent and mixed infinite and ohmic exponents. The mixed creep exponent case presents currents distributions resembling the purely ohmic case, with significant current disturbances only near the indentation. For uniform creep exponent, results similar to a planar indentation are obtained, with far ranged currents features and parabolic-like $d$-lines with shapes depending on the creep exponent. In particular, the same $d$-line asymptotic behaviour is obtained for the triangle indentation as that of the planar defect in the critical state, a result obtained here just on continuity considerations of the hodograph expansions. This equivalence is due to identical contributions to the Fourier series of the current stream-function in the hodograph space, obtained from an images method expansion.

We present a detailed quantitative magneto-optical imaging study of several superconductor/ferromagnet hybrid structures, including Nb deposited on top of thermomagnetically patterned NdFeB, and permalloy/niobium with erasable and tailored magnetic landscapes imprinted in the permalloy layer. The magneto-optical imaging data is complemented with and compared to scanning Hall probe microscopy measurements. Comprehensive protocols have been developed for calibrating, testing, and converting Faraday rotation data to magnetic field maps. Applied to the acquired data, they reveal the comparatively weaker magnetic response of the superconductor from the background of larger fields and field gradients generated by the magnetic layer., Comment: 21 pages, including 2 pages of supplementary material

Quantized magnetic vortices driven by electric current determine key electromagnetic properties of superconductors. While the dynamic behavior of slow vortices has been thoroughly investigated, the physics of ultrafast vortices under strong currents remains largely unexplored. Here we use a nanoscale scanning superconducting quantum interference device to image vortices penetrating into a superconducting Pb film at rates of tens of GHz and moving with velocities up to tens of km/s, which are not only much larger than the speed of sound but also exceed the pair-breaking speed limit of superconducting condensate. These experiments reveal formation of mesoscopic vortex channels which undergo cascades of bifurcations as the current and magnetic field increase. Our numerical simulations predict metamorphosis of fast Abrikosov vortices into mixed Abrikosov-Josephson vortices at even higher velocities. This work offers an insight into the fundamental physics of dynamic vortex states of superconductors at high current densities, crucial for many applications.

We study the instability of the superconducting state in a mesoscopic geometry for the low pinning material Mo$_3$Ge characterized by a large Ginzburg-Landau parameter. We observe that in the current driven switching to the normal state from a nonlinear region of the Abrikosov flux flow, the mean critical vortex velocity reaches a limiting maximum velocity as a function of the applied magnetic field. Based on time dependent Ginzburg-Landau simulations we argue that the observed behavior is due to the high velocity vortex dynamics confined on a mesoscopic scale. We build up a general phase diagram which includes all possible dynamic configurations of Abrikosov lattice in a mesoscopic superconductor., Comment: 7 pages, 6 figures

Sudden avalanches of magnetic flux bursting into a superconducting sample undergo deflections of their trajectories when encountering a conductive layer deposited on top of the superconductor. Remarkably, in some cases flux is totally excluded from the area covered by the conductive layer. We present a simple classical model that accounts for this behaviour and considers a magnetic monopole approaching a semi-infinite conductive plane. This model suggests that magnetic braking is an important mechanism responsible for avalanche deflection., Comment: 14 pages, 5 figures

A graded distribution of pinning centers (antidots) in superconducting MoGe thin films has been investigated by magnetization and magneto-optical imaging. The pinning landscape has maximum density at the border, decreasing progressively towards the center. At high temperatures and low fields, where this landscape mimics the vortex distribution predicted by the Bean model, an increase of the critical current is observed. At low temperatures and fields, the superconducting performance of the non-uniform sample is also improved due to suppression of thermomagnetic avalanches. These findings emphasize the relevance of non-uniform pinning landscapes, so far experimentally unexplored, on the enhancement of pinning efficiency., Comment: 5 pages and 3 figures

We investigate the nucleation of superconductivity in a superconducting Al strip under the influence of the magnetic field generated by a current-carrying Nb wire, perpendicularly oriented and located underneath the strip. The inhomogeneous magnetic field, induced by the Nb wire, produces a spatial modulation of the critical temperature T_c, leading to a controllable localization of the superconducting order parameter (OP) wave function. We demonstrate that close to the phase boundary T_c(B_ext) the localized OP solution can be displaced reversibly by either applying an external perpendicular magnetic field B_ext or by changing the amplitude of the inhomogeneous field., Comment: 10 pages, 6 figures

We investigate theoretically and experimentally the transport properties of a plain Al superconducting strip in the presence of a single straight current-carrying wire, oriented perpendicular to the superconducting strip. It is well known that the critical current of the superconducting strip, Ic, in such cryotron--like system can be tuned by changing the current in the control wire, Iw. We demonstrated that the discrete change in the number of the pinned vortices/antivortices inside the narrow and long strip nearby the current-carrying wire results in a peculiar oscillatory dependence of Ic on Iw., Comment: 8 pages, 8 figures

We demonstrate the controlled spatial nucleation of superconductivity in a thin film deposited on periodic arrays of ferromagnetic dots with gradually increasing diameter. The perpendicular magnetization of the dots induces vortex-antivortex molecules in the sample, with the number of (anti)vortices increasing with magnet size. The resulting gradient of antivortex density between the dots predetermines local nucleation of superconductivity in the sample as a function of the applied external field and temperature. In addition, the compensation between the applied magnetic field and the antivortices results in an unprecedented enhancement of the critical temperature.