Evidence for Atomic-Scale Inhomogeneity in Superconducting Cuprate NMR

Abstract

In 1990, the Millis, Monien, and Pines (MMP) model and its improvement, the Zha, Barzykin, and Pines (ZBP) model in 1996, emerged as a realistic explanation of the cuprate NMR. These two models assume a single electronic component, translational symmetry, and that the electrons simultaneously have aspects of localized antiferromagnetic (AF) spins and delocalized Cu $d_{x^2-y^2}$ band states. NMR experiments were routinely fit to these models in the 1990s and early 2000s until they finally failed as NMR experiments developed further. It appears that cuprate theorists have given up on explaining the NMR and the NMR data is forgotten. Here, we assume a two-component model of electrons where the electrons reside in two regions, one metallic with delocalized band states, and the other antiferromagnetic with localized spins. This model breaks translational symmetry. We show that the normal state spin relaxation for the planar Cu, O, and Y atoms in $\mathrm{YBa_2Cu_3O_{7-\delta}}$ and their Knight shifts are explained by this two-component model. The temperature dependence of the Cu spin relaxation rate anisotropy in the superconducting state is also explained qualitatively.