Estimation of the Doping Dependence of Antiferromagnetism in the Copper Oxide Material

Within the t-J model, we study the doping dependence of antiferromagnetism in the copper oxide materials by considering quantum fluctuations of spinons in the random-phase-approximation. The staggered magnetization vanishes around doping δ = 5% for a reasonable parameter value t/J = 5, which is in agreement with the experiments on copper oxide materials. 1 Since the discovery that the copper oxide sheets in the High Tc superconductors show strong antiferromagnetic (AF) spin correlations [?], there has been increased interest in studying magnetic properties of these systems. This followed from the argument, made by Anderson and many other researchers [?], that the essential physics of the copper oxide superconductors is contained in doped antiferromagnets, where a central issue is the relationship between the hole doping and AF spin correlations [?,?]. In particular, the phase diagrams of these materials as functions of hole doping have been established by neutron scattering, muon spin rotation, and magnetic resonance measurements [?]. When the hole doping concentration exceeds some critical value (about 5%), AF long-range order (AFLRO) disappears and the materials are converted into nonmagnetic metals. It is believed [?] that the physics of these materials may be effectively described by a 2D, large U Hubbard model or its equivalent, the t-J model. In an attempt to understand the relationship between the hole doping and AF spin correlations , many authors have studied holes moving in the background of the spin resonating valence bond state [?], spin flux phase [?], and spiral spin phase [?]. A hole in the AF background has a very large effective mass because of frustrations [?]. Numerical simula