$^{139}$La NMR investigation of the interplay between the lattice, charge, and spin dynamics in charge ordered high $T_c$ cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$

TL;DR

This study uses $^{139}$La NMR and inverse Laplace transform analysis to explore how lattice, charge, and spin dynamics interact in charge ordered high $T_c$ cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$, revealing detailed fluctuations and their impact on superconductivity.

Contribution

It introduces ILTT$_{1}$ analysis to extract the distribution of relaxation rates, providing deeper insight into the interplay of charge, spin, and lattice fluctuations in charge ordered cuprates.

Findings

Divergent increase of $1/T_1^{lm}$ near charge and spin ordering temperatures.

Asymmetric broadening of the relaxation rate distribution below charge order.

Contrast in behavior of La sites explaining differences in superconductivity suppression.

Abstract

We investigate the interplay between the lattice, charge, and spin dynamics in charge ordered high $T_c$ cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ ($T_{c} =4$~K) based on the inverse Laplace transform (ILT) analysis of the $^{139}$La nuclear spin-lattice relaxation rate $1/T_1$ (dubbed ILTT$_{1}$ analysis here after). A major thrust of the ILTT$_{1}$ analysis is that one can deduce the probability density function $P(1/T_1)$ of distributed $1/T_1$. We demonstrate that $1/T_{1}^{lm}$, defined as the log-mean (i.e. the center of gravity on a logarithmic scale) of $P(1/T_1)$, can be well approximated by $1/T_{1}^{str}$ deduced from the phenomenological stretched fit, however, $P(1/T_1)$ can provide much richer insight into how the lattice, charge, and spin fluctuations and their distribution develop near and below the long range charge order at $T_{charge} \sim 54$~K. Upon entering the charge ordered state, a divergent increase of $1/T_{1}^{lm}$ toward the spin ordering at $T_{spin}^{\mu SR} \simeq 35$~K is accompanied by an asymmetric broadening of $P(1/T_1)$. Even deep inside the charge ordered state, $1/T_{1}$ at a gradually diminishing fraction of $^{139}$La sites continues to slow down as temperature is lowered, as expected for canonical superconducting CuO$_2$ planes without enhanced spin fluctuations. The fraction of such canonical $^{139}$La sites almost disappears by $\simeq 40$~K. In contrast, nearly a half of the $^{139}$La sites in La$_{1.885}$Sr$_{0.115}$CuO$_{4}$ ($T_{charge} \simeq 80$~K) still exhibits the canonical behavior without enhanced spin fluctuations even near its $T_{c} = 31$~K. These contrasting behaviors explain why superconductivity in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ is more strongly suppressed than in La$_{1.885}$Sr$_{0.115}$CuO$_{4}$ despite the lower onset temperature of the charge order.