Cuprate universal electronic spin response and the pseudogap from NMR

It is shown that three independently measured NMR shifts in the cuprates in their whole temperature dependence are linearly related to each other with a doping and family dependent, but temperature independent constant. It is the Cu shift anisotropy that changes in proportion to the planar O shift for all materials found in the literature, independent of sample origin or details of the measurements. Such a relation involving three shifts rules out a single spin component description of the cuprates. It is argued that the relation is so robust since it depends for Cu on ($A_perp-A_parallel$), the hyperfine coefficient $A_alpha$ for the Cu $3d(x^2-y^2)$ hole, and not on the isotropic Cu term $B$ from transferred spin. The Cu $3d(x^2-y^2)$ spin together with a second spin that determines the planar O shift can explain the data.

For overdoped metallic samples, both become temperature dependent only at the critical temperature of superconductivity, $T_mathrm{c}$, where both begin to decrease. However, the Cu spin component turns increasingly negative until the second spin has disappeared. In the presence of a small pseudogap the onset temperature of this process coincides with the onset of the temperature dependence of the shifts, which is now above $T_mathrm{c}$. As the pseudogap increases further, the behavior does not change even as $T_mathrm{c}$ begins to decrease again. The temperature independent constant in the linear relationship describing the negative spin is related to the size of the uncoupled spin components and depends on the planar oxygen hole content that is known to correlate with the maximum $T_mathrm{c}$. The Cu spin component does not appear to carry significant entropy as the nuclear relaxation ceases in the condensed state.