Quest for nuclear quadrupole relaxation in HgCa$_{2}$Ba$_{2}$Cu$_{3}$O$_{8+\delta}$

TL;DR

This paper develops a simplified model for analyzing nuclear quadrupole relaxation in complex superconductors and applies it to estimate magnetic and quadrupolar relaxation rates in a high-temperature superconductor.

Contribution

It introduces a reduced analytical form for the nuclear spin-lattice relaxation function applicable to quadrupole-split NMR spectra, extending its use to inhomogeneous relaxation effects.

Findings

Estimated magnetic relaxation rate $^{63}W_M$ in HgBa$_2$Ca$_2$Cu$_3$O$_{8+eta}$

Determined upper limit of quadrupolar relaxation rate $^{63}W_Q$

Validated the reduced relaxation model with experimental data

Abstract

We derived a simple reduced form from the exact solution of the mixed magnetic and quadrupolar nuclear spin--lattice relaxation function at the central transition line of a quadrupole-split NMR spectrum for the nuclear spin $I$ = 3/2. The reduced form of the exact solution could be extended to include inhomogeneous relaxation effects. From the application of the reduced form to the $^{63}$Cu nuclear spin--lattice relaxation curves in the high-$T_\mathrm{c}$ superconductors of $^{63}$Cu-enriched triple-layer HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$, we estimated the predominant magnetic relaxation rate $^{63}W_M$ and the upper limit of a weak nuclear electric quadrupole spin--lattice relaxation rate $^{63}W_Q$.