Temperature and time scaling of the peak-effect vortex configuration in FeTe${}_{0.7}$Se${}_{0.3}$

An extensive study of the magnetic properties of FeTe${}_{0.7}$Se${}_{0.3}$ crystals in the superconducting state is presented. We show that weak collective pinning, originating from spatial variations of the charge carrier mean free path ($\delta l$ pinning), rules in this superconductor. Our results are compatible with the nanoscale phase separation observed on this compound and indicate that in spite of the chemical inhomogeneity, spatial fluctuations of the critical temperature are not important for pinning. A power-law dependence of the magnetization vs time, generally interpreted as the signature of a single-vortex creep regime, is observed in magnetic fields up to 8 T. For magnetic fields applied along the $c$ axis of the crystal, the magnetization curves exhibit a clear peak effect whose position shifts when varying the temperature, following the same dependence as observed in YBa${}_2$Cu${}_3$O${}_{7-\delta }$. The time and temperature dependence of the peak position has been investigated. We observe that the occurrence of the peak at a given magnetic field determines a specific vortex configuration that is independent on the temperature. This result indicates that the influence of the temperature on the vortex-vortex and vortex-defect interactions leading to the peak effect in FeTe${}_{0.7}$Se${}_{0.3}$ is negligible in the explored range of temperatures.

Figure 1

Temperature dependence of the DC volume susceptibility (demagnetization corrected) for the investigated samples.

Figure 2

Magnetic moment vs external field curves obtained at different temperatures in sample A for (a) $H\parallel c$ and (b) $H\perp c$. The insets show the results obtained in sample B at $T=4.25$ and $T=7$ K.

Figure 3

Temperature dependence of the magnetic field value at which the peak effect occurs, for the two measured samples. Continuous lines are the best fit curves obtained supposing the same $T$ dependence observed in YBa${}_2$Cu${}_3$O${}_{7-\delta }$.

Figure 4

Field dependence of the critical current density at different temperatures and for $H\parallel c$ in sample A. The inset shows the results obtained at $T=4.25$ K and for $H\parallel c$ for the sample B.

Figure 5

Kramer plot (right axis) and $J_c^{1/2}$ vs $H$ (left axis) curves obtained at $T=6$ and $T=8$ K for samples (a) A and (b) B, as described in the text.

Figure 6

Normalized pinning force density curves as a function of the reduced field, $H/H_{irr}^{Kr}$, for samples (a) A and (b) B. $H_{irr}^{Kr}$ indicates that the irreversibilty field has been deduced by a linear extrapolation in the Kramer plot. The inset in (b) shows the results obtained in sample B, scaled by using the irreversibility field $H_{irr}^J$, deduced by the $J_c^{1/2}$ vs $H$ curves.

Figure 7

Normalized critical current density data, as a function of the reduced temperature $\tau$, obtained at ${\mu }_{0}H=0.5$ and ${\mu }_{0}H=1$ T for $H\parallel c$. The continuous lines are the theoretical curves expected in the case of $\delta l$ and $\delta T_c$ pinning.

Figure 8

Plot of the magnetization vs time (on a log-log scale) at $T=4.25$ K for different values of the magnetic field. The inset shows the field dependence of the relaxation rate $S=|$$d$ $\log M/$$d$ $\log t|$.

Figure 9

Magnetization dependence of the pinning potential energy barrier height calculated in the frame of the Maley model, scaling the data at different temperatures as described in the text.

Figure 10

Time evolution of the second peak position investigated by magnetization measurements performed by the VSM at different $\dot{H}s$, by the SQUID, as well as by magnetic relaxation measurements.

Figure 11

Pairs of values ($H_{\mathrm{peak}}$,$m_{\mathrm{peak}}$) that identify the second peak position in the $m\left(H\right)$ curve at different temperatures and characteristic times. Labels 1, 2, and 3 indicate the measurements performed by the VSM with $\dot{H}=2$, 1, and 0.05 T/min, respectively; label 4 indicates the measurements performed by the SQUID. The continuous line is the best fit curve obtained as described in the text. The inset at the bottom right shows the couples of values ($B_{\mathrm{peak}}$,$m_{\mathrm{peak}}$) corresponding to the peak effect. The inset at the top left is an imaginary drawing of the vortex energy landscape, the line indicating the relaxation path of the vortex configuration associated with the peak effect.