NMR investigation of vortex dynamics in the Ba(Fe${}_{0.93}$Rh${}_{0.07}$)${}_2$As${}_2$ superconductor

${}^{75}$As NMR spin-lattice relaxation ($1/T_1$) and spin-echo decay ($1/T_2$) rate measurements were performed in a single crystal of Ba(Fe${}_{0.93}$Rh${}_{0.07}$)${}_2$As${}_2$ superconductor. Below the superconducting transition temperature $T_c$, when the magnetic field $\mathbf{H}$ is applied along the $c$ axes, a peak in both relaxation rates is observed. Remarkably that peak is suppressed for $\mathbf{H}\perp c$. Those maxima in $1/T_1$ and $1/T_2$ have been ascribed to the flux lines lattice motions and the corresponding correlation times and pinning energy barriers have been derived on the basis of a heuristic model. Further information on the flux lines motion was derived from the narrowing of ${}^{75}$As NMR linewidth below $T_c$ and found to be consistent with that obtained from $1/T_2$ measurements. All the experimental results are described in the framework of thermally activated vortices motions.

Figure 1

The irreversibility temperature measured with a dc SQUID magnetometer (open circle) is compared with that derived from the detuning of the NMR probe (blue stars). The red circles refer to the temperature of the peaks in $1/T_1$. The dotted lines are a guide to the eye.

Figure 2

The recovery curves for three different temperatures are shown, for $\mathbf{H}\parallel c$, at 7 T. The blue squares refers to the 15-K data, while the pink circles are taken at 17.7 K, in correspondence with the peak in $1/T_1$, and the black triangles refer to 18.7 K. The dotted colored lines are the best fits according to Eq. (1).

Figure 3

The spin-lattice relaxation rate, measured at 7 T (open squares) and 3 T (blue circles), for $\mathbf{H}\parallel c$ is reported. The inset shows the $1/T_{1}T$ data at 7 T both in the superconducting and normal phase. The arrows show the temperature of the detuning of the NMR probe at the two fields: the blue arrow stands for 3 T and the black arrow for 7 T.

Figure 4

The spin-lattice relaxation rate, measured at 7 T, in $\mathbf{H}\parallel c$ geometry (black diamonds) and $\mathbf{H}\perp c$ geometry (blue circles) is shown. A neat difference for the two field orientations is found in the 16–19-K range. Data, in $\mathbf{H}\perp c$ geometry, have been normalized by a value 1.55 to match the value of $1/T_1$ for $\mathbf{H}\parallel c$, at $T_c$ thus revealing an anisotropy of the hyperfine tensor.

Figure 5

The figure shows two echo decays as a function of 2$\tau$: the black squares refer to 24 K and the blue circles refer to 15 K, below the superconducting transition where the FLL is still dynamic. From the figure one can notice that the echo decay functional form changes while the temperature decreases. The red curves are the best fits according to Eqs. (10) and (11).

Figure 6

The figure shows the spin-echo decay rate measured at 7 T. A peak around 12 K is found for $\mathbf{H}\parallel c$ (black diamonds) while it strongly decreases, for $\mathbf{H}\perp c$ (blue squares), and shifts toward higher temperatures. The red arrow indicates the ab initio value for $1/T_2$ given by the dipolar sums. The inset shows the spin-echo decay rate for $\mathbf{H}\parallel c$ up to room temperature.

Figure 7

The two figures show the full width at half maximum of the central line at 7 T, for $\mathbf{H}\parallel c$ (top) and $\mathbf{H}\perp c$ (bottom), with the Curie-Weiss fit (red solid line) giving the impurity contribution [see Eq. (3) in the text]. In the insets the extra broadening due to the FLL, obtained as described by Eq. (2), is shown. The blue solid lines show the behavior expected according to a two-fluid model. For $\mathbf{H}\parallel c$ one can observe a strong deviation at high temperatures which is not seen for the other orientation. We notice that, at variance with what was reported by Oh et al. (Ref. 28) in the 7.4$\%$ Co-doped compound, here we do not observe any decrease in the linewidth below $T_c$.

Figure 8

The figure shows the Knight shift at 7 T, for $\mathbf{H}\parallel c$ with an Arrhenius-like fitting curve (solid line) in the normal phase.

Figure 9

The figure at the top shows the spin-lattice relaxation rate at 7 T for $\mathbf{H}\parallel c$, while the one at the bottom shows the spin-lattice relaxation rate at 3 T in the same geometry. The fitting curves are given by the 2D uncorrelated pancakes model, deriving from the correlation function $g_1\left(t\right)$ (dash-dotted line) and the correlated vortices model, deriving from the correlation function $g_2\left(t\right)$ (solid line). In both cases the second model shows the best agreement with the experimental data.

Figure 10

The temperature dependence of the correlation time ${\tau }_L$ given by echo decay time (black squares) is compared with the one derived by the linewidth analysis (blue circles) in the assumption of fast motions [see Eq. (12)]. The red curves are the fitting of the correlation time, according to an activated law.