Probing dynamics and pinning of single vortices in superconductors at nanometer scales (original) (raw)

The dynamics of quantized magnetic vortices and their pinning by materials defects determine electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a multi-scale potential of the actual materials defects is still not well understood, mostly due to the scarcity of appropriate experimental tools capable of tracing vortex trajectories on nanometer scales. Using a novel scanning superconducting quantum interference microscope we report here an investigation of controlled dynamics of vortices in lead films with sub-Angstrom spatial resolution and unprecedented sensitivity. We measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the importance of thermal fluctuations even at 4.2 K and of the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors. T he ability to carry non-dissipative electric currents in strong magnetic fields is one of the fundamental features of type-II superconductors crucial for many applications 1–10. The current, however, exerts a transverse Lorentz force on vortices, leading to their dissipative motion and to finite resistance unless materials defects immobilize (pin) vortices at current densities below some critical value J c. Pinning potential wells U(r) produced by defects are the key building blocks that determine collective pinning phenomena, in which a flexible vortex line is pinned by multiple defects. The global electromagnetic response of the vortex matter is thus governed by a complex interplay of individual pinning centers, interaction between vortices, and thermal fluctuations 11. Recent advances in materials science have enabled several groups to controllably produce nano-structures of nonsuperconducting precipitates to optimize the pinning of vortices in superconductors and to achieve J c up to 10–30% of the fundamental depairing current density J d at which the current breaks Cooper pairs 2–10. In artificially-engineered pinning structures, the shape of U(r) can also be made asymmetric to produce the intriguing vortex ratchet and rectification phenomena 12–17. Local studies of individual vortices using scanning probe techniques 18–20 based on STM, MFM, Hall probes and SQUIDs have allowed controllable manipulation of single vortices 21 and have revealed phase transitions 22–24 , vortex dynamics and pinning at grain boundaries 25,26 , collective creep of a vortex lattice 27,28 , and collective motion 29,30 and dissipative hopping of individual vortices in response to an ac magnetic field 31. Even so, the intrinsic structure of a single pinning potential well U(r), which determines the fundamental interaction of vortices with pinning centers, has not yet been measured directly. Difficulties with the measurement of U(r) arise from the necessity of deconvoluting the effect of multiple pinning defects along the elastic vortex line, and from the lack of experimental techniques for extracting U(r) on the scale of the superconducting coherence length j (ranging from 2 to 100 nm for different materials) that quantifies the size of the Cooper pair. To avoid the complexity of the situation in which the vortex line behaves like an elastic string pinned by multiple defects 21 , the vortex length should to be of the order of j. This situation can be achieved in thin superconducting films of thickness d%j in a perpendicular magnetic field. Moreover, in order to simplify the interpretation of experimental data, it is desirable to choose a film in which the three basic length