Coexistence of Cluster Spin Glass and Superconductivity in $\mathrm{Ba}({\mathrm{Fe}}_{1\mathbf{-}x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ for $0.060\mathbf{\le }x\mathbf{\le }0.071$

We present ${}^{75}\mathrm{As}$ nuclear magnetic resonance data from measurements of a series of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ crystals with $0.00\le x\le 0.075$ that reveals the coexistence of frozen antiferromagnetic domains and superconductivity for $0.060\le x\le 0.071$. Although bulk probes reveal no long range antiferromagnetic order beyond $x=0.06$, we find that the local spin dynamics reveal no qualitative change across this transition. The characteristic domain sizes vary by more than an order of magnitude, reaching a maximum variation at $x=0.06$. This inhomogeneous glassy dynamics may be an intrinsic response to the competition between superconductivity and antiferromagnetism in this system.

Figure 1

The signal intensity ($N_0$, upper row), stretching exponent ($\beta$, middle row), and $(T_{1}T{)}^{-1}$ (lower row) vs temperature for several different dopings for $H_0\perp c$ (data for $H_0\parallel c$ is provided in the Supplemental Material [28]). ${\chi }_{\mathrm{ac}}$ (diamond, upper row) and $T_2^{-1}$ (upward triangle, lower row) are shown on the right hand axes. All the data were acquired in 11.7 T except for the $x=0.022$ sample, where the paramagnetic-state data were acquired in 8.75 T and the antiferromagnetic-state data were acquired in 8.5 T. Blue (yellow) shading indicates bulk antiferromagnetism (superconductivity), green indicates bulk coexistence, and the hatched pattern indicates the frozen cluster glass regime. The solid lines in the middle and lower rows are fits to $\beta$ and $(T_{1}T{)}^{-1}$ vs temperature, and in the upper row the solid lines are simulations of $N_0$ as discussed in the text. The dotted vertical lines indicate $\theta$.

Figure 2

(a) $T_1^{-1}$ vs $T^{-1}$; arrows indicate $T_c$. (b) Phase diagram for $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$: solid black lines are polynomial fits to the bulk phase diagram in zero field [37, 53, 54] indicating antiferromagnetic order (blue), orthorhombic structure (gray), superconductivity (yellow), coexisting superconductivity and antiferromagnetism (green), and cluster glass (hatched pattern). The data points are $\theta$ (filled square), $T_{\max }$ (filled circle), $T_c$ (filled upward triangle) at 11.7 T, and $1-\beta (T_{\max })$ (filled downward triangle, right axis). The dashed black line is a linear fit to $\theta$ and the dashed orange line is a guide to the eye for $1-\beta (T_{\max })$, which is a measure of the degree of inhomogeneity.