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 ${\mathit{T}}_1$T/${\mathit{T}}_{2\mathit{G}}$ and linear ${\mathit{T}}_1$T, 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 ${\mathrm{\Delta }}_{\xi }$=c/ξ in the quantum disordered, z=1, regime. The crossover to the z=2 regime, where ${\mathit{T}}_1$T/${\mathit{T}}_{2\mathit{G}}^2$≃const, occurs only in the fully doped materials.