# Contrasting Phenomenology of NMR Shifts in Cuprate Superconductors

## TL;DR

This paper reviews NMR shift data in cuprate superconductors, challenges the traditional single-fluid interpretation, and proposes a new phenomenological model emphasizing orbital localization and revised temperature dependence rules.

## Contribution

It introduces a contrasting NMR shift phenomenology that departs from earlier models and aligns with all published data, highlighting the inadequacy of the hyperfine scenario.

## Key findings

- Large isotropic shift component discovered
- Temperature dependence rules identified
- Substantial spin shift at low temperatures in CuO$_2$ plane

## Abstract

Nuclear magnetic resonance (NMR) shifts, if stripped off their uncertainties, must hold key information about the electronic fluid in the cuprates. The early shift interpretation that favored a single-fluid scenario will be reviewed, as well as recent experiments that reported its failure. Thereafter, based on literature shift data for planar Cu a contrasting shift phenomenology for cuprate superconductors is developed, which is very different from the early view while being in agreement with all published data. For example, it will be shown that the hitherto used hyperfine scenario is inadequate as a large isotropic shift component is discovered. Furthermore, the changes of the temperature dependences of the shifts above and below the superconducting transitions temperature proceed according to a few rules that were not discussed before. It appears that there can be substantial spin shift at the lowest temperature if the magnetic field lies in the CuO$_2$ plane, which points to a localization of spin in the $3d(x^2-y^2)$ orbital. A simple model is presented based on the most fundamental findings. The analysis must have new consequences for theory of the cuprates.