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 $\lambda$. 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 ${\kappa }^{-1}\sim T^{-1/2}$, we find that the interaction $\lambda$ leads to spin pairing at a temperature $T^{\ast }\sim \lambda$, much higher than the usual BCS result $exp(-J/\lambda )$. We suggest that this is a possible explanation of the spin gap effects observed below $T^{\ast }\sim 150K$ in $YB{a}_{2}C{u}_3{O}_{6.6}$.