Universal Magnetic Properties of $La_{2-δ} Sr_δ Cu O_4$ at Intermediate Temperatures

Abstract

We present the theory of two-dimensional, clean quantum antiferromagnets with a small, positive, zero temperature ($T$) stiffness $ρ_s$, but with the ratio $k_B T / ρ_s $ arbitrary. Universal scaling forms for the uniform susceptibility ($χ_u$), correlation length($ξ$), and NMR relaxation rate ($1/T_1$) are proposed and computed in a $1/N$ expansion and by Monté-Carlo simulations. For large $k_B T/ρ_s$, $χ_u (T)/T$ and $Tξ(T)$ asymptote to universal values, while $1/T_{1}(T)$ is nearly $T$-independent. We find good quantitative agreement with experiments and some numerical studies on $La_{2-δ} Sr_δ Cu O_4$.