Fast Dynamics of Guided Magnetic Flux Quanta

The dynamics of Abrikosov vortices in superconductors is usually limited to vortex velocities $v\approx 1$ km/s, above which samples abruptly transit into the normal state. In the Larkin-Ovchinnikov framework, near the critical temperature, this transition is because of a flux-flow instability triggered by the reduction of the viscous drag coefficient due to the quasiparticles leaving the vortex cores. While the existing instability theories rely upon a uniform spatial distribution of vortex velocities, the measured (mean) value of $v$ is always smaller than the maximal possible one, since the distribution of $v$ never reaches the $\delta$-functional shape. Here, by guiding magnetic flux quanta at a tilt angle of ${15}^{\circ }$ with respect to a $\mathrm{Co}$ nanostripe array, we speed up vortices to 3–6 km/s. These exceed $v$ in the reference as-grown $\mathrm{Nb}$ films by almost an order of magnitude and are only a factor of about 3 smaller than the maximal vortex velocities observed in superconductors so far. We argue that such high $v$ values appear in consequence of a collective dynamic ordering when all vortices move in the channels with the same pinning strength and exhibit a very narrow distribution of $v$. Our findings render the well-known vortex guiding effect to open prospects for investigations of ultrafast vortex dynamics.

Figure 1

(a) Experimental geometry. The transport current $\mathbf{I}$ in a superconducting film exerts the Lorentz force ${\mathbf{F}}_L=\mathbf{I}\times \mathbf{B}$ on Abrikosov vortices. The $\mathrm{Co}$ stripes deposited on top of the $\mathrm{Nb}$ film under a tilt angle $\alpha$ with respect to $\mathbf{I}$ induce pinning channels for vortices and make them move with the velocity $\mathbf{v}\nparallel {\mathbf{F}}_L$ due to the vortex guiding effect. Longitudinal $V_{\parallel }^{+}=V_2^{-}-V_2^{+}$ and transverse $V_{\perp }^{+}=V_2^{+}-V_1^{+}$ voltages are measured as a function of the current value. Atomic force microscopy images are shown for a $\mathrm{Nb}$ film decorated with $\mathrm{Co}$ stripes (b), an as-grown $\mathrm{Nb}$ film (c), and a continuous $\mathrm{Co}$ layer (d) deposited on top of a $\mathrm{Nb}$ film.

Figure 2

The $I$-$V$ curves for the longitudinal (a) and perpendicular (b) voltage components. The curves $1$ and $2$ are acquired for the positive and negative current polarity, respectively. (c) The enlarged longitudinal $I$-$V$ curve with the definition of the depinning currents $I_d^i$ and $I_d^a$, the instability current $I^{\ast }$, and the instability voltage $V^{\ast }$. (d) Reference measurement demonstrating the absence of $V_{\perp }^{+}$ in the as-grown $\mathrm{Nb}$ film and in the $\mathrm{Nb}$/$\mathrm{Co}$ bilayer.

Figure 3

$I$-$V$ curves for the as-grown $\mathrm{Nb}$ film (a) and the $\mathrm{Nb}$ film decorated with $\mathrm{Co}$ stripes (c) with $\alpha ={75}^{\circ }$ at $T=0.975T_c$ for a series of magnetic field values, as indicated. The respective differential resistances are shown in panels (b) and (d).

Figure 4

Instability $I^{\ast }$ and depinning $I_d^a$ currents, instability velocity $v^{\ast }$, and the relaxation time ${\tau }_{\mathrm{qp}}$ (c) deduced using Eq. (1) as a function of the guiding angle $\alpha$ at $B=10$ mT. The dashed lines in (b),(c) depict the respective values for the $\mathrm{Nb}$/$\mathrm{Co}$ bilayer and the as-grown $\mathrm{Nb}$ film. Dependences of the instability current density $j^{\ast }$ (d) and the instability velocity $v^{\ast }$ (e) on the magnetic field value. In panels (a)–(e), $T=0.975T_c$. (f) Temperature dependence of the relaxation time at $B=10$ mT. The solid line is a fit ${\tau }_{\mathrm{qp}}^{\mathrm{Nb}}\propto \exp [2\mathrm{\Delta }(T)/k_{B}T]$ with $\mathrm{\Delta }(0)\approx 1.85k_B{T}_c$. The dashed lines are guides for the eye.