Nodeless energy gaps of single-crystalline Ba0.68K0.32Fe2As2 as seen via 75As NMR

We report ${}^{75}$As nuclear magnetic resonance studies on a very clean hole-doped single-crystal Ba${}_{0.68}$K${}_{0.32}$Fe${}_2$As${}_2$ ($T_{\rm {c}}=38.5$K)\mathrm{.}Thespin-latticerelaxationrate$1/T_{1}$ shows an exponential decrease below $T\simeq 0.45T_{\mathrm{c}}$ down to $T\simeq 0.11T_{\mathrm{c}}$, which indicates a fully opened energy gap. From the ratio $(T_{1}){c} / (T{1})_{a}$,where$a$and$c$ denote the crystal directions, we find that the antiferromagnetic spin fluctuation is anisotropic in the spin space above $T_{\mathrm{c}}$. The anisotropy decreases below $T_{\mathrm{c}}$ and disappears at $T \rightarrow 0$. We argue that the anisotropy stems from spin-orbit coupling whose effect vanishes when spin-singlet electron pairs form with a nodeless gap.