Spin Gaps and Bilayer Coupling in YBa$_2$Cu$_3$O$_{7-\delta}$ and YBa$_2$Cu$_4$O$_8$

TL;DR

This paper models the spin dynamics and interlayer coupling in underdoped YBa2Cu3O7−δ and YBa2Cu4O8 using a Schwinger boson mean field approach, revealing a crossover between coupled and decoupled planes affecting magnetic properties.

Contribution

It introduces a theoretical framework to analyze the quantum critical point and interlayer coupling effects in cuprate superconductors using a Schwinger boson mean field theory.

Findings

Identification of a crossover temperature between coupled and decoupled planes regimes.

Prediction of a correlation length of about 6 lattice constants at 200K.

Experimental data partially supports the theory, but some discrepancies remain.

Abstract

We investigate the relevance to the physics of underdoped YBa$_2$Cu$_3$O$_{\rm 6+x}$ and YBa$_2$Cu$_4$O$_8$ of the quantum critical point which occurs in a model of two antiferromagnetically coupled planes of antiferromagnetically correlated spins. We use a Schwinger boson mean field theory and a scaling analysis to obtain the phase diagram of the model and the temperature and frequency dependence of various susceptibilities and relaxation rates. We distinguish between a low $\omega ,T$ coupled-planes regime in which the optic spin excitations are frozen out and a high $\omega ,T$ decoupled-planes regime in which the two planes fluctuate independently. In the coupled-planes regime the yttrium nuclear relaxation rate at low temperatures is larger relative to the copper and oxygen rates than would be naively expected in a model of uncorrelated planes. Available data suggest that in YBa$_2$Cu$_4$O$_8$ the crossover from the coupled to the decoupled planes regime occurs at $T 700K$ or $T \sim 200K$. The predicted correlation length is of order 6 lattice constants at $T=200K$. Experimental data related to the antiferromagnetic susceptibility of YBa$_2$Cu$_4$O$_8$ may be made consistent with the theory, but available data for the uniform susceptibility are inconsistent with the theory.