NMR study of nematic spin fluctuations in a detwinned single crystal of underdoped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

We report the experimental details of how mechanical detwinning can be implemented in tandem with high sensitivity nuclear magnetic resonance measurements and use this setup to measure the in-plane anisotropy of the spin-lattice relaxation rate in underdoped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ with $x=0.048$. The anisotropy reaches a maximum of 30% at $T_N$, and the recovery data reveal that the glassy behavior of the spin fluctuations present in the twinned state persist in the fully detwinned crystal. A theoretical model is presented to describe the spin-lattice relaxation rate in terms of anisotropic nematic spin fluctuations.