Theory of magnetic short-range order in the t-J model

A spin-rotation-invariant theory of antiferromagnetic short-range order (SRO) in the two-dimensional t-J model is presented based on the Green’s-function projection technique for the dynamic spin susceptibility which is divided into a local and an itinerant contribution. The SRO is incorporated in the local contribution. By a sum-rule-conserving mean-field approximation the two-spin correlation functions of arbitrary range, the staggered magnetization, and the uniform static spin susceptibility are calculated self-consistently over the whole doping and temperature region. A good agreement with available exact diagonalization data at ratios J/t realistic for the cuprates is found. The antiferromagnetic long-range order at T=0 is destroyed at the critical doping δ_c=5.9% (J/t=0.4) in favor of a paramagnetic phase with SRO. The maxima in the doping and temperature dependences of the uniform spin susceptibility found in exact diagonalization studies are explained as an effect of antiferromagnetic SRO. Comparing the theory with magnetic susceptibility experiments on La_2-δSr_δCuO₄, a reasonable agreement in the doping dependence is obtained.