Cuprate universal electronic spin response and the pseudogap from NMR

The understanding of high-temperature superconductivity, in particular in the cuprates, is still central to condensed matter physics, and telltale experimental laws for guiding theory are desirable. Here we report on such a universal property concerning the linear response of the electronic matter to a homogeneous static magnetic field. With the new law we can distinguish between two different spin components in all cuprates. One is the expected spin from the hybridized Cu 3d(x^2-y^2) and planar O 2p_σ states. It is material independent in the sense that the metallic density of states is universal, however, a temperature independent, doping dependent pseudogap causes changes of the spin polarization as a function of temperature from excitations across the gap. This pseudogap component shows a steep temperature dependence at condensation, i.e. below the critical temperature, T_c, for overdoped materials, and below the pseudogap temperature, T^*, at lower doping levels. A second spin component originates from symmetric (or anisotropic, ), metallic Cu states that do not involve planar O significantly. The second component is family and doping dependent in the sense that the density of states increases with doping. It can condense at the same or lower temperatures as the pseudogap component, but the slope is significantly different, suggesting different pairing scenarios. Our second component reminds one of the proposed involvement of another Cu axial orbital that relates to the distance or presence of the apical oxygen [1-3] and the charge distribution in the CuO_2 plane [4,5], and finally the maximum T_c.