Absence of Static Phase Separation in the High $T_c$ Cuprate ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+y}$

We use ${}^{\mathrm{89}}\mathrm{Y}$ NMR in ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+y}$ in order to evaluate with high sensitivity the distribution of hole content $p$ in the ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ planes. For $y=1$ and $y=0.6$, this hole doping distribution is found narrow with a full width at half maximum smaller than $\Delta p=0.025$. This rules out any large static phase separation between underdoped and optimally doped regions in contrast with the one observed by STM in Bi2212 and by NQR in LaSrCuO. This establishes that static electronic phase separation is not a generic feature of the cuprates.

Figure 1

${}^{\mathrm{89}}\mathrm{Y}$ NMR shift ${}^{89}K$ for $H_{\mathrm{e}\mathrm{x}\mathrm{t}}\perp c$ for different oxygen contents $y$ versus temperature. In the inset, $T_c$ for each sample is plotted versus hole doping with the same symbol as the one used for $K$.

Figure 2

${}^{\mathrm{89}}\mathrm{Y}$ NMR Fourier transform spectra are plotted at different temperatures and dopings in ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+y}$ for $H_{\mathrm{e}\mathrm{x}\mathrm{t}}\perp c$ (solid lines) with arbitrary normalization. In each panel, a doping scale gives the relation between the shift ${}^{89}K$ and hole doping $p$. Dotted lines are simulated spectra (see text). At ${\mathrm{O}}_7$ $T=120\mathrm{K}$, an additional dashed line is plotted, which corresponds to the simulation made using the dotted distribution of the upper panel of Fig. 3.

Figure 3

The solid dots represent $T_c$ versus oxygen content (upper panel) and hole doping (lower panel) for ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{6+y}$. Distributions of oxygen content $P(y)$ and the corresponding distribution of hole content $\mathcal{P}(p)$ were used to fit the spectra for $y=1$ and $y=0.6$ samples (see text). The dark and light gray envelopes are obtained with a minimal distribution of chemical shift and hyperfine coupling within assumptions (i) and (ii), respectively. The dashed distribution and the arrow shown in the lower panel represent the distributions measured in Bi2212 [5] and LaSrCuO [10].