Evidence for low-field crossover in the vortex critical velocity of type-II superconducting thin films

We measure current-voltage characteristics as function of magnetic field and temperature in Nb strips of different thickness and width. The instability voltage of the flux-flow state related to the vortex critical velocity $v^{\ast }$ is studied and compared with the Larkin-Ovchinnikov theory. Beside the usual power-law dependence $v^{\ast }\approx B^{-1/2}$, in the low-field range a new crossover field, $B_{cr1}$, is observed below which $v^{\ast }$ decreases by further lowering the external magnetic field $B$. We ascribe this unexpected crossover to vortex channeling due to a fanlike penetration of the applied magnetic field as confirmed by magneto-optic imaging. The observation of $B_{cr1}$ becomes a direct evidence of a general feature in type-II superconducting films at low fields that is a channel-like vortex motion induced by the inhomogeneous magnetic state caused by the relatively strong pinning.

Figure 1

$I\text{−}V$ curves for different values of $B$ in the low-field range, at $T=4.2\text{K}$, for NbA1 sample. The field values are: $a=0$, $b=0.78$, $c=1.56$, $d=2.08$, $e=2.34$, $f=2.60$, $g=3.90$, $h=5.20$, $i=6.50$, $l=7.80$, $m=9.10$, and $n=10.40\text{mT}$. Inset: full view of the $I\text{−}V$ curves where the transition to the normal state is shown.

Figure 2

(a) Vortex critical velocity $v^{\ast }$ as function of $B$ in the low-field range, at $T=4.2\text{K}$, for the sample NbB5. The arrow marks the crossover field $B_{cr1}$. (b) The $v^{\ast }\left(B\right)$ dependence at $T=4.2\text{K}$ for the sample NbA02 in the low-field range for positive and negative field values.

Figure 3

Critical vortex velocity as function of $B$ in the low-field region, at $T=4.2\text{K}$, for three different strips on the 60-nm-thick Nb film. Open circles refer to NbA1 $\left(w=20\mu \text{m}\right)$, triangles to NbA3 $\left(w=50\mu \text{m}\right)$, and squares to NbA4 $\left(w=100\mu \text{m}\right)$. The arrows mark $B_{cr1}$ for each sample.

Figure 4

Critical vortex velocity as function of $B$ in the low-field region for NbA1, at different $t=T/T_c$. (a) At $t=0.5$ (full circles) and 0.6 (stars). (b) At $t=0.90$ (open circles) and $t=0.99$ (full triangles).

Figure 5

MOI measurements of the sample NbA4 at $T=4.1\text{K}$. After zero-field cooling, a sequence of increasing magnetic field was applied. Dark contrast represents the zero-field Meissner state. The bright line is the sample edge along the strip length. A fanlike penetration pattern clearly develops after vortex nucleation occurred at sample edges.

Figure 6

(a) Flux flow resistance as function of $B$ in the millitesla range for NbA1, at $t=0.67$ (squares) and $t=0.74$ (triangles). The corresponding lines refer to the Bardeen-Stephen prediction $R_{\text{BS}}=R_{n}B/B_{c2}$. Inset: scale factor $L/l$ as function of $B$ at $t=0.67$ (solid line) and $t=0.74$ (dotted line). (b) Vortex critical velocity as function of $B$ at $t=0.67$ for NbA1 corrected by the factor $L/l$ (open circles). The full circles represent the experimental data.