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 $T_0$ with an as yet unknown order parameter. 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 $p>p_c$.

Figure 1

${}^{63}$Cu NMR spectra in YBCO${}_y$ at 7 T along the $c$ axis for $y=6.35$ (left panel) and 6.45 (right panel). Cu(1) denotes the Cu sites in the CuO chains, where the subscripts 0 and 2 represent the number of neighboring oxygen ions along the chain, and Cu(2) (dotted lines) denotes the planar Cu sites (Ref. 17). An emerging Cu spectral feature sp0 consisting of two resonance lines indicated by two dashed lines is clearly visible for $y=6.35$. The horizontal bar indicates the region that was irradiated during a $T_1$ measurement. See Supplemental Material for details and for other doping levels (Ref. 14).

Figure 2

Recovery of the (normalized) nuclear magnetization $m\left(t\right)$ as a function of time $t$ for $y=6.35$ (a) and $y=6.45$ (b). In (a), $m\left(t\right)$ deviates progressively from a single $T_1$ process with decreasing $T$, revealing the long $T_{1\ell }$ process which overwhelms the short one at low $T$. Note that the short $T_{1s}$ component is no longer detectable at 30 K. In (b), the $T_{1\ell }$ process is strongly suppressed, i.e., it appears below $\sim$150 K and a large portion of the $T_{1s}$ process remains down to 30 K. The solid lines are fits to Eq. (1).

Figure 3

(a) Nuclear spin-lattice relaxation rates divided by $T$, ${\left(T_{1}T\right)}^{-1}$ vs $T$ for the short $T_{1s}$. The opening of the PG at $T^{*}$ (denoted by arrows) was detected only for $y\ge 6.5$, whereas there are no signatures of the PG for $y\le 6.45$. In (b), ${\left(T_{1\ell }T\right)}^{-1}$ data are presented, together with ${\left(T_{1s}T\right)}^{-1}$, for comparison. In YBCO${}_{6.35}$, ${\left(T_{1\ell }T\right)}^{-1}$ forms a local maximum at $T_g\sim 11$ K, indicating a SG transition. This behavior is significantly suppressed for $y=6.45$. (c) $T$ dependence of the volume fraction $w$. The onset temperature $T_0$ is defined from the values at which $w\to 0$ (down arrows).

Figure 4

Phase diagram of underdoped YBCO${}_y$ in terms of hole concentration $p$. $y$ values are shown on the top axis for convenience. The antiferromagnetic (AFM) transition is from Ref. 13 and the dotted line drawn for $T^{*}$ is estimated from previously known NMR results (Refs. 11 and 18).