Direct visualization of the Campbell regime in superconducting stripes

Abstract

A combination of scanning Hall microscopy and scanning ac-susceptibility measurements in superconducting stripes ͑ribbons͒ of width w Ͻ 10 m was used to observe the dimensional phase transitions of the vortex lattice and its stability under alternating fields. At low dc magnetic fields applied perpendicularly to the plane of the stripes, vortices form a one-dimensional chain at the center of the stripes. Above a certain field H ‫ء‬ ͑w͒, the vortex chain splits in two parallel rows displaced laterally in such a way that a zigzag vortex pattern is observed. By shaking the vortices with an external magnetic ac field and detecting their in-phase motion locally, we can identify the degree of mobility of each individual vortex. This technique allows us ͑i͒ to directly visualize the transition from intravalley ͑Campbell regime͒ to intervalley vortex motion as the amplitude of the ac modulation is increased and ͑ii͒ to accurately determine the temperature at which the vortex lattice freezes in a field-cooling experiment. The hallmark of type II superconductivity is the presence of quantized magnetic flux encircled by a rotating condensate of paired electrons when a sufficiently strong magnetic field is applied. The free motion of these fluxons leads to dissipation thus destroying the perfect conductivity of the system. The ever growing electricity demand has motivated for several decades a fierce strive for understanding, improving, and optimizing the mechanisms to prevent the fluxon's motion by introducing a rich diversity of pinning centers. 1Among the most powerful experimental methods used to determine the efficiency of pinning sites is the ac-susceptibility technique which consist of shaking the flux-line lattice with a small alternating magnetic field while recording its in-phase magnetic response.2 Pioneering theoretical works by Campbell and co-workers substantially contributed to comprehend and interpret the ac response of a superconducting system. 3,4 In the most simple version, two different regimes with distinctive ac responses can be identified. For a gentle ac shacking, flux lines oscillate inside the pinning potential following a reversible and low dissipative motion ͑Campbell regime͒. By increasing the strength of the ac excitation, the intravalley vortex motion first senses the anharmonicities of the potential well and eventually switches to an intervalley motion where vortices can hop from one pinning site to another. 5So far, all the experimental and theoretical reports are focused on global ac-susceptibility investigations where the recorded signal represents an average over millions of flux lines each of which trapped in a different pinning potential and subjected to a different environment. [6][7][8] In this paper, we introduce a local vortex imaging technique with singlevortex resolution which allows us to directly visualize the oscillatory motion of individual vortices submitted to harmonic ac excitations. The system to investigate consists of superconducting ribbons which, due to the proximity o...

Imaging the Statics and Dynamics of Superconducting Vortices and Antivortices Induced by Magnetic Microdisks

“…For instance, for one single vortex-antivortex pair, the high degeneracy in the position of the antivortex makes it more susceptible to small excitation forces than the vortex pinned by the disk. This hypothesis can be experimentally demonstrated by using a scanning ac-susceptibility technique, which reveals the points of maximum amplitude of oscillation of each individual vortex when submitted to an external ac field [30]. In Fig.…”

Closer look at the low-frequency dynamics of vortex matter using scanning susceptibility microscopy

“…In previous works [26][27][28], we have demonstrated that the SSM technique is capable of extracting useful information of individual vortex dynamics with single-vortex resolution. Here we benefit from the MD simulation to analyze the vortex trajectories at much smaller scales.…”

Probing the low-frequency vortex dynamics in a nanostructured superconducting strip

“…The incapacity to resolve the ac-response of a single vortex and the indirect relation between the vortex dynamics and the integrated response can be circumvented by the scanning ac-susceptibility microscopy (SSM) technique, [6][7][8] which allows to probe the in-and out-of-phase response to an applied ac magnetic field or current with single-vortex resolution. 3,8,9 In contrast to standard susceptibility measurements, in SSM the periodic change in flux due to vortex motion and screening currents is measured locally by scanning a submicron-sized Hall probe over the surface, thereby revealing the microscopic vortex response.…”

“…3,8,9 In contrast to standard susceptibility measurements, in SSM the periodic change in flux due to vortex motion and screening currents is measured locally by scanning a submicron-sized Hall probe over the surface, thereby revealing the microscopic vortex response. Moreover, the screening current response imaged close to the border, also probed in classical macroscopic ac-susceptibility experiments, can be cross-correlated with the present vortex physics and the theoretical models describing them.…”

“…1, we present the profiles of the local magnetic permeability b ac (x)/h ac of a superconducting strip, which is the typical quantity accessed in ac susceptibility imaging experiments, using either scanning Hall probes or SQUIDs. 3,8,9,33 This quantity was calculated for different values of Λ and Λ v , covering 0.05a ≤ |Λ ac | ≤ 2.5a, at a height z 0 = 0.005a above the plane of the strip. This value for z 0 is close to the typical probe height used in our experiments.…”