Universality and unconventional enhancement of flux-flow resistivity in $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_2{\mathrm{As}}_2$

Measurements of the current-voltage characteristics ($I-V$) were performed on ${\mathrm{Ba}(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ single crystals with doping level $0.044\le x\le 0.100$. An unconventional increase in the flux-flow resistivity ${\rho }_{\mathrm{ff}}$ with decreasing magnetic field $H$ was observed across this doping range. Such an abnormal field dependence of ${\rho }_{\mathrm{ff}}$ is in contrast with the linear ${\rho }_{\mathrm{ff}}\left(H\right)$ of conventional type-II superconductors, but similar to the behavior recently observed in the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$. A significantly enhanced ${\rho }_{\mathrm{ff}}$ was found for the $x=0.06$ single crystals, implying a strong single-particle energy dissipation around the vortex cores. At different temperatures and fields and for a given doping concentration, the normalized ${\rho }_{\mathrm{ff}}$ scales with normalized field and temperature. The doping level dependence of the scaling parameters strongly suggests that the abnormal upturn in ${\rho }_{\mathrm{ff}}$ is likely related to the enhancement of spin fluctuations around the vortex cores of the samples with $x\approx 0.06$.

Figure 1

Sketch of the temperature-doping $T-x$ phase diagram for ${\mathrm{Ba}(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$. The phases depicted on this phase diagram are: SDW (purple region), coexistence of SC and SDW phases [1] (green region), spin glass phase [7] (hatched green region), and pure SC phase (yellow region). The arrows mark the five doping levels discussed in this paper. Inset: In-plane resistivity normalized to its value at 300 K, $\rho /\rho (300$ K), measured in zero field and for five doping levels.

Figure 2

Schematic drawing of the current-voltage $I-V$ measurement configuration that takes care of Joule heating caused by the large applied current.

Figure 3

(a) Current-voltage $I-V$ curves measured in the mixed state of ${\mathrm{Ba}(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ ($x=0.060$) single crystal at a temperature $T$ of 23.2 K and different magnetic field $H$ values. (b) Plot of the critical current $I_c$ vs $H$. Inset to (b): $H-T$ phase diagram obtained from this work (filled symbols) and from [11] (open symbols). (c) $H$ dependence of the flux-flow resistivity ${\rho }_{\mathrm{ff}}$ (filled circles) and the resistivity ${\rho }_{ab}$ measured with a constant current of 1 mA applied parallel with the $ab$ plane of the single crystal (open squares). (d) ${\rho }_{\mathrm{ff}}$ vs $T$ measured at 2 T on the $x=0.060$ single crystal.

Figure 4

Current-voltage $I-V$ curves measured at different magnetic field $H$ values in the mixed state of ${\mathrm{Ba}(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ with (a) $x=0.044$ at a temperature $T$ of 14.4 K and (b) $x=0.100$ at $T=17.8$ K. Plots of the critical current $I_c$ vs $H$ for (c) $x=0.044$ and (d) $x=0.100$. (c) $H$ dependence of the flux-flow resistivity ${\rho }_{\mathrm{ff}}$ (filled circles) and the resistivity ${\rho }_{ab}$ measured with a constant current of 1 mA applied parallel with the $ab$ plane of the single crystals (open squares) for the (e) the $x=0.044$ and (f) $x=0.100$ samples.

Figure 5

(a) Temperature $T$ dependent magnetoresistivity $\text{MR}\equiv {\rho }_{ab}\left(H\right)/{\rho }_{ab}\left(14\mathrm{T}\right)-1$ curve of the $x=0.044$ single crystal measured in a magnetic field of 0.5 T and with a current of 1 mA. Inset: ${\rho }_{ab}$ vs $T$ measured in zero magnetic field. (b) $T$ dependent MR curve for 1, 4, and 12 T.

Figure 6

Normalized flux-flow resistivity $\mathrm{\Delta }{\rho }_{\mathrm{ff}}/{\rho }_{\mathrm{n}}\equiv {\rho }_{\mathrm{ff}}/{\rho }_{\mathrm{n}}-1$ as a function of reduced magnetic field $H/H_{c2}$ measured at the same reduced temperature $T/T_c=0.94$ for all Co doping values $x$. Inset: $\mathrm{\Delta }{\rho }_{\mathrm{ff}}/{\rho }_n$ vs $x$ measured at $T/T_c=0.94$ and $H/H_{c2}=0.34$ for all the single crystals studied.

Figure 7

Semi-log plots of the normalized free-flux-flow resistivity $\mathrm{\Delta }{\rho }_{\mathrm{ff}}/{\rho }_{\mathrm{n}}$ vs reduced field and temperature ${(\mathrm{\Delta }H/H_{c2})}^m{(\mathrm{\Delta }T/T_{c0})}^n$ for all five doping levels of ${\mathrm{Ba}(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ studied. The straight lines are guides to the eye. Inset: Linear plots of the same data.

Figure 8

Doping dependence of the scaling parameters $m$ and $n$ (top panel), and $A$ (bottom panel).