NMR study of over-doped NaFe$_{1-x}$Cu$_x$As Single Crystals*

We present a preliminary $^{23}$Na and $^{75}$As NMR study of the over-doped NaFe$_{1-x}$Cu$_{x}$As pnictide, which has been demonstrated to be a possible Mott insulator near $x\approx0.5$.[1, 2] Our NMR spectra for three over-doped crystals (x = 0.15, 0.20, and 0.35) indicate that there are two inequivalent $^{23}$Na sites associated with a binomial distribution of Cu dopants. From NMR Knight shift and spin-lattice measurements of $^{23}$Na, we show that NaFe$_{1-x}$Cu$_{x}$As exhibits spin pseudo-gap behavior in the heavily Cu-doped regime. Comparison is made to earlier work on Ba(Fe$_{1-x}$Co$_{x}$)$_2$As. A possible presence of the coupling between charge density and spin density fluctuations is also discussed to account for the origin of the temperature dependence of the quadrupolar frequency. [1] Song, Yu, \textit{et al}., arXiv preprint arXiv:1504.05116 (2015). [2] C.E. Matt \textit{et al}.Phys. Rev. Lett. 117, 097001 (2016) \\