Evidence of unconventional low-frequency dynamics in the normal phase of Ba(Fe${}_{1-x}$Rh${}_x$)${}_2$As${}_2$ iron-based superconductors

This work presents ${}^{75}$As NMR spin-echo decay rate ($1/T_2$) measurements in Ba(Fe${}_{1-x}$Rh${}_x$)${}_2$As${}_2$ superconductors, for $0.041⩽x⩽0.094$. It is shown that $1/T_2$ increases upon cooling, in the normal phase, suggesting the onset of an unconventional very low-frequency activated dynamic. The correlation times of the fluctuations and their energy barriers are derived. The motion is favored at large Rh content, while it is hindered by the application of a magnetic field perpendicular to the FeAs layers. The same dynamic is observed in the spin-lattice relaxation rate, in a quantitatively consistent manner. These results are discussed in the light of nematic fluctuations involving domain wall motion. The analogies with the behavior observed in the cuprates are also outlined.

Figure 1

The exponential (black half-filled squares) and Gaussian (blue half-filled circles) $1/T_2$ measured by Hahn echo at 11 T $\parallel c$ of the $x=6.8\%$ sample. The red solid line shows the best fit to fast motion equation (see Eq. (2)). (Inset) The spin-echo amplitude decay at different T, for $x=9.4\%$, at ${\mathbf{H}}_{\mathbf{0}}=11$ T $\parallel c$ axis, corrected by the $T_1$ contribution.

Figure 2

(a) $1/T_{2\text{exp}}$ measured at $H_0=$ 6.4 T $\parallel c$, for $x=9.4\%$. The red solid line shows the best fit according to the fast motion equation (see Eq. (2)). The blue circles show $1/T_{2\text{exp}}$ measured at $H_0=$ 6.4 T $\perp c$. (b) The $T$ dependence of the FWHM of ${}^{75}$As central line: The width increases with decreasing $T$ down to $T^{*}$ (red dashed line), where it starts to decrease. Finally the linewidth increases again at the vortex freezing temperature $T_m$ (green dashed-dotted line). The blue line marks $T_c$ at 6.4 T. The inset displays an example of the ${}^{75}$As NMR spectrum, showing a clear asymmetry.

Figure 3

The HE $1/T_{2\text{exp}}$ is shown for the overdoped sample, at 11 T $\parallel c$ (green half-filled squares). The red half-filled circles show the $1/T_{2\mathrm{CPMG}}$ at 11 T $\parallel c$. The green solid line is the best fit according to the fast motion equation, while the dashed line is a guide to the eye. The dashed vertical line indicates $T_c$. The inset displays $1/T_1$ data collected at 6.4 T $\parallel$ (blue circles) and $\perp$ (purple squares) to the $c$ axis. The solid lines are $1/T_1$ best fits according to a power law (blue line) or to the sum of a BPP and a power law (purple line).

Figure 4

(a) Energy barriers estimated from $1/T_{2\text{exp}}$ according to the fast motion equation at different doping levels. (b) The field dependence of the amplitude of the longitudinal field fluctuations at different Rh contents. The inset shows a sketch where columnar antiferromagnetic regions are separated by an antiphase domain wall: the blue/red arrows stand, respectively, for the down/up spins, while the gray circles indicate the electronic charges which may favor the domain formation.