On the theory of the spin gap in bilayer cuprates

Abstract

We formulate and solve a model of two planes of antiferromagnetically correlated electrons coupled together by a weak antiferromagnetic interaction of strength $λ$. We show that in-plane antiferromagnetic correlations dramatically enhance the pairing effect of the interplane interaction. For the case where the in-plane correlation length $κ^{-1} \sim T^{-1/2}$, we find that the interaction $λ$ leads to spin pairing at a temperature $T^{*} \sim λ$, much higher than the usual BCS result $exp(-J/λ)$. We suggest that this is a possible explanation of the spin gap effects observed below $T^{*} \sim 150K$ in $YBa_2Cu_3O_{6.6}$.