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Cuprates phase diagram deduced from magnetic susceptibility: what is the `true' pseudogap line?

Two contradictory phase diagrams have dominated the literature of high-$T_c$ cuprate superconductors. Does the pseudogap line cross the superconducting $T_c$-dome or not? To answer, we have revisited the experimental magnetic susceptibility and knight shift of four different compounds, La$_{1-x}$Sr$_x$CuO$_4$, Bi$_2$Sr$_2$Ca$_{1-x}$Y$_x$Cu$_2$O$_8$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$, and YBa$_2$Cu$_3$O$_{6+y}$, as a function of temperature and doping. The susceptibility can be described by the same function for all materials, having a magnetic and an electronic contributions. The former is the 2D antiferromagnetic (AF) square lattice response, with a characteristic temperature of magnetic correlations $T_{max}$. The latter is the `Pauli' term, revealing the gap opening in the electronic density of states at the pseudogap temperature $T^*$. From precise fits of the data, we find that $T_{max}(p)$ decreases linearly as a function of doping ($p$) over a wide range, but saturates abruptly in the overdoped regime. Concomitantly, $T^*(p)$ is {\it linear and tangent} to the dome, either crossing or approaching $T_{max}(p)$ at the top of the dome, indicating a qualitative change of behavior from underdoped to overdoped regimes. Contrary to the idea that the pseudogap terminates just above optimal doping, our analysis suggests that the gap exists throughout the phase diagram. It is consistent with a pseudogap due to hole pairs, or `pairons', above $T_c$. We conclude that $T_{max}$, reflecting the AF magnetic correlations, has often been misinterpreted as the pseudogap temperature $T^*$.