Toward a unified magnetic phase diagram of the cuprate superconductors

We propose a unified magnetic phase diagram of the cuprate superconductors. A new feature of this phase diagram is a broad intermediate doping region of quantum-critical, z=1, behavior, characterized by temperature independent T₁T/T2G and linear T₁T, where the high energy spin waves are not overdamped. The spin gap in the moderately doped materials is related to the suppression of the spectral weight for frequencies smaller than Δ_ξ=c/{ξ} in the quantum disordered, z=1, regime. The crossover to the z=2 regime, where T₁T/T2G²{}const, occurs only in the fully doped materials.