Using scanning susceptibility microscopy, we shed new light on the dynamics of individual superconducting vortices and examine the hypotheses of the phenomenological models traditionally used to explain the macroscopic ac electromagnetic properties o
f superconductors. The measurements, carried out on a 2H-NbSe$_2$ single crystal at relatively high temperature $T=6.8$ K, show a linear amplitude dependence of the global ac-susceptibility for excitation amplitudes between 0.3 and 2.6 Oe. We observe that the low amplitude behavior, typically attributed to the shaking of vortices in a potential well defined by a single, relaxing, Labusch constant, corresponds actually to strongly non-uniform vortex shaking. This is particularly accentuated in the field-cooled disordered phase, which undergoes a dynamic reorganization above 0.8 Oe as evidenced by the healing of lattice defects and a more uniform oscillation of vortices. These observations are corroborated by molecular dynamics simulations when choosing the microscopic input parameters from the experiments. The theoretical simulations allow us to reconstruct the vortex trajectories providing deeper insight in the thermally induced hopping dynamics and the vortex lattice reordering.
We investigated experimentally the frequency dependence of a superconducting vortex ratchet effect by means of electrical transport measurements and modeled it theoretically using the time dependent Ginzburg-Landau formalism. We demonstrate that the
high frequency vortex behavior can be described as a discrete motion of a particle in a periodic potential, i.e. the so called stepper motor behavior. Strikingly, in the more conventional low frequency response a transition takes place from an Abrikosov vortex rectifier to a phase slip line rectifier. This transition is characterized by a strong increase in the rectified voltage and the appearance of a pronounced hysteretic behavior.
The theoretical and experimental results concerning the thermodynamical and low-frequency transport properties of hybrid structures, consisting of spatially-separated conventional low-temperature superconductor (S) and ferromagnet (F), is reviewed. S
ince the superconducting and ferromagnetic parts are assumed to be electrically insulated, no proximity effect is present and thus the interaction between both subsystems is through their respective magnetic stray fields. Depending on the temperature range and the value of the external field H_{ext}, different behavior of such S/F hybrids is anticipated. Rather close to the superconducting phase transition line, when the superconducting state is only weakly developed, the magnetization of the ferromagnet is solely determined by the magnetic history of the system and it is not influenced by the field generated by the supercurrents. In contrast to that, the nonuniform magnetic field pattern, induced by the ferromagnet, strongly affect the nucleation of superconductivity leading to an exotic dependence of the critical temperature T_{c} on H_{ext}. Deeper in the superconducting state the effect of the screening currents cannot be neglected anymore. In this region of the phase diagram various aspects of the interaction between vortices and magnetic inhomogeneities are discussed. In the last section we briefly summarize the physics of S/F hybrids when the magnetization of the ferromagnet is no longer fixed but can change under the influence of the superconducting currents. As a consequence, the superconductor and ferromagnet become truly coupled and the equilibrium configuration of this soft S/F hybrids requires rearrangements of both, superconducting and ferromagnetic characteristics, as compared with hard S/F structures.
We experimentally demonstrate that the origin of multiply reversed rectified vortex motion in an asymmetric pinning landscape is a consequence not only of the vortex-vortex interactions but also essentially depends on the ratio between the characteri
stic interaction distance and the period of the asymmetric pinning potential. Our system consists of an Al film deposited on top of a square array of size-graded magnetic dots with a constant lattice period a=2mu m. Four samples with different periods of the size gradient d were investigated. For large d the dc voltage Vdc recorded under a sinusoidal ac excitation indicates that the average vortex drift is from bigger to smaller dots for all explored positive fields. As d is reduced a series of sign reversals in the dc response are observed as a function of field. We show that the number of sign reversals increases as d decreases. These findings are in agreement with recent computer simulations and illustrate the relevance of the different characteristic lengths for the vortex rectification effects.
