Flux quanta driven by high-density currents in low-impurity ${\text{V}}_3\text{Si}$ and ${\text{LuNi}}_2{\text{B}}_2\text{C}$: Free flux flow and fluxon-core size effect

High-density direct currents are used to drive flux quanta via the Lorentz force toward a highly ordered “free flux flow” (FFF) dynamic state, made possible by the weak-pinning environment of high-quality, single-crystal samples of two low-$T_c$ superconducting compounds, ${\text{V}}_3\text{Si}$ and ${\text{LuNi}}_2{\text{B}}_2\text{C}$. We report the effect of the magnetic field-dependent fluxon-core size on flux flow resistivity ${\rho }_f$. Much progress has been made in minimizing the technical challenges associated with the use of high currents. Attainment of a FFF phase is indicated by the saturation at highest currents of flux flow dissipation levels that are well below the normal-state resistance and have field-dependent values. The field dependence of the corresponding ${\rho }_f$ is shown to be consistent with a prediction based on a model for the decrease of fluxon-core size at higher fields in weak-coupling BCS $s$-wave materials.

Figure 1

Temperature dependence of resistivity for the two compounds, showing critical temperatures $T_c$ (insets), and high RRR that indicate low-impurity levels. The inset graphs show closeups of the transition temperatures and are described in the discussion of results in the text.

Figure 2

Representative curves for the dissipation level, $V/I$, versus current for (a) ${\text{LuNi}}_2{\text{B}}_2\text{C}$ at fields $H=1.2$, 1.5, 1.8, 2.0, 2.2, 2.5, 2.8, and 3.0 T; and (b) ${\text{V}}_3\text{Si}$ at $H=5.0,5.5,\dots ,7.5,8.0\text{T}$. Curves are plotted on semilogarithmic axes to show saturation at highest currents and at field-dependent levels well below the normal-state dissipation level $R_n$ measured at $T=4.2\text{K}$, $H=H_{c2}$ (values indicated by dashed line). Insets: Nonmonotonic “peak effect” in the field dependence of critical current density $J_c$ at $T=4.2\text{K}$, due to re-entrant weak pinning near $H_{c2}$; vertical line indicates upper bound for possibility of FFF, see text.

Figure 3

Temperature dependence of resistivity $\rho \left(T\right)$ measured at fields $H=0$, 1, 3, 4, 5, 6, 7, 8, and 9 T, plotted versus $T^2$. Martensitic transformation, MT, is marked, along with the measured ${\rho }_n$ $\left(T=4.2\text{K},H=H_{c2}=18.3\text{T}\right)=1.56\mu \Omega$. Open circles at $T=4.2\text{K}$ indicate magnetoresistivities obtained by extending the $T^2$ fits, which are then fitted with a Kohler rule form in the inset. See text for discussion.

Figure 4

Comparison of normalized flux-flow resistivity ${\rho }_f/{\rho }_n$ with predicted field dependence based on the KZ model for $t=T/T_c=0$ and 0.5, along with traditional BSFF model. At $t=\left(4.2\text{K}\right)/T_c$, the data falls within these two curves. For ${\text{V}}_3\text{Si}$, black triangles show results after correcting ${\rho }_n\left(H\right)$ values for magnetoresistive effects; while uncorrected data using as-measured ${\rho }_n\left(H_{c2}\right)$ for all fields are shown as open circles; see text.