High magnetic field ultrasound study of spin freezing in La$_{1.88}$Sr$_{0.12}$CuO$_4$

TL;DR

This study investigates how high magnetic fields influence the coupling between lattice vibrations and spin freezing in La$_{1.88}$Sr$_{0.12}$CuO$_4$, revealing a nematic character of spin fluctuations and their competition with superconductivity.

Contribution

It provides the first detailed analysis of ultrasound anomalies at this doping level under high magnetic fields, confirming the lattice-spin glass coupling and modeling it with a phenomenological approach.

Findings

Sound velocity and attenuation anomalies are linked to spin glass coupling.

High magnetic fields reveal competition between superconductivity and spin freezing.

Spin fluctuations exhibit nematic characteristics.

Abstract

High-$T_{\rm{c}}$ cuprate superconductors host spin, charge and lattice instabilities. In particular, in the antiferromagnetic glass phase, over a large doping range, lanthanum based cuprates display a glass-like spin freezing with antiferromagnetic correlations. Previously, sound velocity anomalies in La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) for hole doping $p\geq 0.145$ were reported and interpreted as arising from a coupling of the lattice to the magnetic glass [Frachet, Vinograd et al., Nat. Phys. 16, 1064-1068 (2020)]. Here we report both sound velocity and attenuation in LSCO $p=0.12$, i.e. at a doping level for which the spin freezing temperature is the highest. Using high magnetic fields and comparing with nuclear magnetic resonance (NMR) measurements, we confirm that the anomalies in the low temperature ultrasound properties of LSCO are produced by a coupling between the lattice and the spin glass. Moreover, we show that both sound velocity and attenuation can be simultaneously accounted for by a simple phenomenological model originally developed for canonical spin glasses. Our results point towards a strong competition between superconductivity and spin freezing, tuned by the magnetic field. A comparison of different acoustic modes suggests that the slow spin fluctuations have a nematic character.