${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ NMR evidence for a fermi-liquid behavior in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathrm{x}}$

We report NMR shift ΔK and $T_1$ data of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ taken from 77 to 300 K in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathrm{x}}$ for 0.35<x<1, from the insulating to the metallic state. A Korringa law and therefore a Fermi-liqud picture is found to apply for the spin part $K_s$ of ΔK. The spin contribution ${\chi }_s$(x,T) to ${\chi }_m$ is singled out, as the T variation of ΔK scales linearly with the macroscopic susceptibility ${\chi }_m$. This implies that Cu(3d) and O(2p) holes do not have independent degrees of freedom. Their hybridization, which has a σ character, hardly varies with doping. These results put severe constraints on theoretical models of high-$T_c$ cuprates.