# Phenomenology of $^{63}$Cu nuclear relaxation in cuprate superconductors

## TL;DR

This paper develops an empirical phenomenology for planar Cu nuclear relaxation in hole-doped cuprates, revealing a universal, anisotropy-driven relaxation mechanism linked to electronic excitations, with minimal influence from spin fluctuations.

## Contribution

It introduces a unified framework explaining Cu nuclear relaxation across various cuprates, emphasizing anisotropy and electronic excitations over spin fluctuation effects.

## Key findings

- Relaxation rates are mainly affected by temperature-independent anisotropy.
- Above Tc, relaxation rates are doping-independent and follow Fermi liquid behavior.
- Below Tc, relaxation rates scale with reduced temperature T/Tc.

## Abstract

Nuclear relaxation is an important thermodynamic probe of electronic excitations, in particular in conducting and superconducting systems. Here, an empirical phenomenology based on all available literature data for planar Cu in hole-doped cuprates is developed. It is found that most of the seemingly different relaxation rates among the systems are due to a temperature independent anisotropy that affects the mostly measured $1/T_{1\parallel}$, the rate with an external magnetic field along the crystal $c$-axis, while $1/T_{1\perp}$ is largely independent on doping and material above the critical temperature of superconductivity ($T_c$). This includes very strongly overdoped systems that show Fermi liquid behavior and obey the Korringa law. Below $T_c$ the relaxation rates are similar, as well, if plotted against the reduced temperature $T/T_c$. Thus, planar Cu nuclear relaxation is governed by a simple, dominant mechanism that couples the nuclei with varying anisotropy to a rather ubiquitous bath of electronic excitations that appear Fermi liquid-like irrespective of doping and family. In particular, there is no significant enhancement of the relaxation due to electronic spin fluctuations, different from earlier conclusions. Only the La$_{2-x}$Sr$_x$CuO$_4$ family appears to be an outlier as additional relaxation is present, however, the anisotropy remains temperature independent. Also systems with very low doping levels, for which there is a lack of data, may behave differently.