Spin pseudo-gap and z=1 pseudo-scaling in cuprate superconductors

We determine the magnetic phase diagram for the YBa2Cu3O6+x and La2-xSrxCuO4 systems from nuclear magnetic resonance (NMR) experiments. We show that there is an extensive temperature regime in metallic underdoped cuprates in which the behaviour of the dynamic magnetic response function is qualitatively similar to the z = 1 quantum critical scaling for the insulator, where the characteristic energy scale is set by temperature, and the correlation length xi proportional to 1/T. Quantitatively, however, the universal ratios predicted from the z = 1 scaling theory turn out to be non-universal in experiment, so that what is being measured is perhaps best described as z = 1 pseudo-scaling. We discuss a possible interpretation of the observed temperature dependences of the NMR relaxation rates in terms of the nearly antiferromagnetic Fermi-liquid model.