NMR evidence for coexistence of cluster spin glass and superconductivity in Ba(Fe$_{1-\mathrm{x}}$Co$_{\mathrm{x}}$)$_2$As$_2$*

We present $^{75}$As nuclear magnetic resonance data from measurements of a series of Ba(Fe$_{1-\mathrm{x}}$Co$_{\mathrm{x}}$)$_2$As$_2$ crystals with $0 \leq \mathrm{x} \leq 0.075$. Spectral wipeout and the onset of stretched exponential spin-lattice relaxation as a function of decreasing temperature reveal the coexistence of frozen antiferromagnetic domains and superconductivity for $0.060 \leq \mathrm{x} \leq 0.071$. Although bulk probes reveal no long range antiferromagnetic order beyond $\mathrm{x} = 0.06$, we find that the local spin dynamics reveal no qualitative change across this transition. Domain sizes vary by more than an order of magnitude, reaching a maximum variation at $\mathrm{x} = 0.06$. This inhomogeneous glassy dynamics may be an intrinsic response to the competition between superconductivity and antiferromagnetism in this system. We also present field-dependent spin-lattice relaxation studies from 3.5 T to 30.4 T to further probe the glassy dynamics.