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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). The spin-lattice relaxation rate $1/T_{1}$ shows an exponential decrease below $T \simeq 0.45 T_{\rm c}$ down to $T \simeq 0.11 T_{\rm c}$, 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 $T_{\rm c}$. The anisotropy decreases below $T_{\rm c}$ 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.