Toward the Mott state with Magnetic Cluster Formation in Heavily Cu-Doped NaFe$_{1-x}$Cu$_{x}$As
Recent neutron scattering measurements indicate that NaFe$_{1-x}$Cu$_{x}$As forms an antiferromagnetic stripe phase near $x\approx 0.5$ in a Mott insulating state. This copper concentration is well in excess of that required for superconductivity, $x < 0.04$. We have investigated the development of magnetism in this compound using $^{23}$Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation measurements performed on single crystals ($x$ = 0.13, 0.18, 0.24, and 0.39). We find multiple inequivalent Na sites, each of which is associated with a different number of nearest neighbor Fe sites occupied by a Cu dopant. We show that the distribution of Cu substituted for Fe is random in-plane for low concentrations ($x = 0.13$ and 0.18), but deviates from this with increasing Cu doping. As is characteristic of many pnictide compounds, there is a spin pseudo gap that increases in magnitude with dopant concentration. This is correlated with a corresponding increase in orbital NMR frequency shift indicating a change in valence from Cu$^{2+}$ to a Cu$^{1+}$ state as $x$ exceeds 0.18, concomitant with the change of Fe$^{2+}$ to Fe$^{3+}$ resulting in the formation of magnetic clusters. However, for $x\leq 0.39$ there is no evidence of long-range static magnetic order.