Enhanced superconducting vortex pinning with disordered nanomagnetic arrays

We studied the effect of disorder on superconducting vortex pinning produced by arrays of artificial pinning sites. The magnetoresistance of samples with pinning configurations varying from a triangular array to an almost random distribution of pinning sites provides a controlled system for such studies. Interestingly even small degrees of order are sufficient to produce enhanced pinning at well-defined magnetic fields. These effects increase with increasing order and evolve toward the expected matching minima for a triangular array. Surprisingly, the position of the first matching minimum decreases with increasing disorder. Furthermore, additional matching minima appear at higher field values which do not coincide with commonly observed triangular pinning lattice matching minima.

Figure 1

(Color online) (a) $R$ vs $T$ curve for sample $D=225\text{nm}$ at $2\text{kA}/{\text{cm}}^2$. Below: $4\times 4\mu {\text{m}}^2$ SEM images of the (b) $D=370\text{nm}$ and (c) $D=280\text{nm}$ samples, respectively. Small (yellow) circles in (b) are a guide to the eyes showing an area where the pinning sites have triangular lattice symmetry.

Figure 2

(Color online) The PCF for the different samples arranged from the most ordered (top, blue) to the most disordered (bottom, light gray). The dashed horizontal line denotes the PCF for a disorder system. The radius at which the PCF of a sample decays to this line is the sample's RLO. The vertical thick black lines denote the PCF for the triangular lattice (a series of delta function peaks).

Figure 3

(Color online) Magnetoresistance (log scale) as a function of field for the different samples. (a) Triangular lattice and (c) $D=335\text{nm}$ samples at a constant current density of $I=2.0\text{kA}/{\text{cm}}^2$. The triangular lattice has $T/T_{\text{c}}=.995$, .994, .993, and .992, and $D=335\text{nm}$ has $T/T_{\text{c}}=.987$, .983, .980, and .978. The different $T_{\text{c}}$’s were chosen because the disordered samples have a transition width about double that of the triangular lattice. (b) Sample $D=370\text{nm}$, the least disordered sample, at constant $T/T_{\text{c}}=.973$ with currents $I=2.0–14\text{kA}/{\text{cm}}^2$. (d) Sample $D=225\text{nm}$, the most disordered sample, at a constant $T/T_{\text{c}}=.972$ with currents $I=1.4–20\text{kA}/{\text{cm}}^2$. There is no change in the matching minima positions as a function of either temperature or current.

Figure 4

(Color online) (a) Magnetoresistance as a function of field for different samples with backgrounds subtracted and heights shifted for clarity. The measurements were done at $T/T_{\text{c}}=0.97–0.98$ and at currents of $1.4–2.0\text{kA}/{\text{cm}}^2$. (b) The position of the first matching minimum for different samples plotted against the RLO. The dotted line is the theoretical first minimum position of a triangular lattice.