Microscopic investigation of the dopant oxygen distribution using $^{199}$Hg NMR in the high temperature superconductor HgBa$_2$CuO$_{4+\delta}$*

In the high temperature superconductor HgBa$_2$CuO$_{4+\delta}$, it has been determined that the dopant oxygen O$_\delta$ resides in the Hg-plane [1]. The systematic development of the $^{199}$Hg NMR spectrum as a function of O$_\delta$ content is presented. For high O$_\delta$, 4 different resonance peaks are observed. Three of the peaks follow a binomial distribution and correspond to 0, 1, and 2 O$_\delta$ nearest neighbors. The fourth peak persists down to low doping and may be indicative of a Hg vacancy nearest neighbor. This work was supported by the DOE BES under grants No. DE-FG02-05ER46248 and No. DE-SC0006858 and the NHMFL through the NSF and State of Florida. \\[4pt] [1] J. G. Correia \textit{et}. PRB \textbf{64}, 11769 (2000).