Single Crystal NMR Study of Frustrated Spin-Liquid in S = 1/2 Kagome Lattice $ZnCu_{3}(OD)_{6}Cl_{2}$

Herbertsmithite $ZnCu_{3}(OD)_{6}Cl_{2}$ is one of the most promising examples for a quantum spin liquid state. Despite the remarkable absence of long range magnetic order down to at least 50mK, understanding the magnetic properties of $ZnCu_{3}(OD)_{6}Cl_{2}$ remains a challenge. This is mainly due to the difficulty in locating the defects, and in understanding the possible role of defects in the physical properties of this material. We have investigated the local magnetic and lattice environment of $ZnCu_{3}(OD)_{6}Cl_{2}$ single crystals\footnote{T. H. Han \textit{et al}., Phys. Rev. B {\bf 83}, 100402(R) (2011)} using NMR techniques\footnote{T. Imai \textit{et al}., Phys. Rev. B {\bf 84}, 020411(R) (2011); see also Phys. Rev. Lett. {\bf 100}, 077203 (2008)}. With successful identification of $^{2}D$ NMR signals arising from the nearest neighbors of $Cu^{2+}$ defects substituting Zn, we find that $14(2)\%$ of Zn sites are occupied by these weakly interacting $Cu^{2+}$ defect spins, which contribute to the large Curie-Weiss enhancement of bulk susceptibility at low temperatures. We then discuss the key aspects of nuclear spin-lattice relaxation rate $1/T_{1}$ measured near the defect and intrinsic sites.