Critical-doping universality for cuprate superconductors: Oxygen nuclear-magnetic-resonance investigation of Ca(x)La(1-x)Ba(1.75-x)La(0.25+x)Cu(3)O(y)

The critical doping levels in cuprates, where the ground state changes its nature (from an antiferromagnet to a spin glass to superconductor to metal), are not universal. We investigate the origin of these critical doping variations by measuring the in-plane oxygen $p_{\sigma}$ hole density in the CuO$_{2}$ layers as a function of the oxygen density $y$ in (Ca$_{x}$ La$_{1-x}$)(Ba$_{1.75-x}$La$_{0.25+x}$)Cu$_{3}$O$_{y}$. This is done using the oxygen 17 nuclear quadrupole resonance parameter $\nu_{Q}$. We compare compounds with $x=0.1$ and 0.4 which have significant critical $y$ variations and find that these variations can be explained by a change in the efficiency of hole injection into the $p_{\sigma}$ orbital. This allows us to generate a unified phase diagram for the CLBLCO system across the entire doping range, with no adjustable parameters.