Shearing transition in a superconducting vortex lattice subject to periodic pinning

We have studied the shearing forces in a superconducting vortex system with artificial pinning sites using the Corbino geometry. Current was injected into the center of a Nb disc and propagated radially outward to produce a force in the azimuthal direction on the vortices, with strength proportional to 1/$r$. We investigated the magnetoresistance properties of the vortex lattice as a function of temperature, current, and pinning lattice configuration. The measurements show steps instead of minima at the matching field positions, indicating an unexpected influence of the pinning array on the motion of the vortex lattice. The results imply that these steps are due to a shearing transition of the vortices.

Figure 1

Geometries used for the fabrication of the Corbino system. (a) SEM image of a square array of Co pinning sites. (b) A schematic of the outer Au contacts (red) connected to the Nb Corbino disc (blue). (c) A schematic of the Corbino disc. Current enters through the center (I${}_{+}$) and leaves from the edges (I${}_{-}$). The voltage taps are placed at positions V${}_1$ and V${}_2$ at radii 17.5 μm and 31.5 μm, respectively, allowing measurements of the middle ring and the inner region of the disc (dashed lines are added as a guide to the eye).

Figure 2

Magnetoresistance of a square array of pinning sites with I $=$ 10 μA in different configurations. (a) Measurements of the middle ring of the Corbino disc. Voltage was measured between the V${}_1$ and V${}_2$ leads. (b) Measurements of the inner region of the Corbino disc. Voltage was measured between the I${}_{+}$ and V${}_1$ leads. The insets show the resistance versus temperature at zero magnetic field.

Figure 3

Temperature and current dependencies of the steps. (a) The height of the steps as a function of temperature for a triangular pinning lattice with $T_C$ $=$ 8.1 K. Symbols correspond to different matching fields (MF), as indicated by the legend. (b) Voltage as a function of magnetic field for different currents in a square pinning lattice at $T$ $=$ 7.5 K. The curves have been shifted along the $y$ axis for clarity.

Figure 4

(a) Resistance as a function of time for different magnetic fields. The black lines are a guide to the eye. (b) The field on the sample at the different times. The black line at $H$ $=$ 264.5 Oe is a guide to the eye to denote the approximate transition field. (c) Histogram of the number of counts for each resistance and field. In the above graphs, for fields above 265 Oe, the points are shown in green, below 264 Oe the points are shown in blue, and for fields between 264 and 265 the points are shown in red.