Toward a unified magnetic phase diagram of the cuprate superconductors

Abstract

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