Low-energy antiferromagnetic spin fluctuations limit the coherent superconducting gap in cuprates

TL;DR

This study investigates low-energy spin fluctuations in cuprates near a critical doping level, finding that spin gaps are equal to or less than the superconducting gap, suggesting spin fluctuations limit superconductivity.

Contribution

It provides empirical evidence linking spin gap and superconducting gap in cuprates, challenging the quantum critical point hypothesis and suggesting spin fluctuations constrain superconducting coherence.

Findings

Peak in spin-fluctuation weight at ~20 meV for x=0.17 and 0.21

Spin gap equals the coherent superconducting gap in cuprates

Spin gap is less than or equal to the superconducting gap across cuprates

Abstract

Motivated by recent attention to a potential antiferromagnetic quantum critical point at $x_c\sim 0.19$, we have used inelastic neutron scattering to investigate the low-energy spin excitations in crystals of La$_{2-x}$Sr$_x$CuO$_4$ bracketing $x_c$. We observe a peak in the normal-state spin-fluctuation weight at $\sim20$~meV for both $x=0.21$ and 0.17, inconsistent with quantum critical behavior. The presence of the peak raises the question of whether low-energy spin fluctuations limit the onset of superconducting order. Empirically evaluating the spin gap $\Delta_{\rm spin}$ in the superconducting state, we find that $\Delta_{\rm spin}$ is equal to the coherent superconducting gap $\Delta_c$ determined by electronic spectroscopies. To test whether this is a general result for other cuprate families, we have checked through the literature and find that $\Delta_c\le\Delta_{\rm spin}$ for cuprates with uniform $d$-wave superconductivity. We discuss the implications of this result.