Spin Gaps and Bilayer Coupling in YBa2Cu3O7−δ and YBa2Cu4O8

We investigate the relevance to the physics of underdoped YBa2Cu3O6+x and YBa2Cu4O8 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 ω, T coupled-planes regime in which the optic spin excitations are frozen out and a high ω, 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 YBa2Cu4O8 the crossover from the coupled to the decoupled planes regime occurs at T700K or T ∼ 200K. The predicted correlation length is of order 6 lattice constants at T = 200K. Experimental data related to the antiferromagnetic susceptibility of YBa2Cu4O8 may be made consistent with the theory, but available data for the uniform susceptibility