Evidence of a critical hole concentration in underdoped YBa${}_2$Cu${}_3$O${}_y$ single crystals revealed by ${}^{63}$Cu NMR

We report a ${}^{63}$Cu NMR investigation in detwinned YBa${}_2$Cu${}_3$O${}_y$ single crystals, focusing on the highly underdoped regime (y=6.35-6.6). Measurements of both the spectra and the spin-lattice relaxation rates of ${}^{63}$Cu uncover the emergence of static order at a well-defined onset temperature $T_0$ without a known order parameter as yet. While $T_0$ is rapidly suppressed with increasing hole doping concentration $p$, the spin pseudogap was identified only near and above the doping content at which $T_0\to 0$. Our data indicate the presence of a critical hole doping $p_c\sim 0.1$, which may control both the static order at $p<p_c$ and the spin pseudogap at $p>p_c$.