MAGNETIC-PROPERTIES OF THE HUBBARD SIGMA-MODEL WITH 3-DIMENSIONALITY

It has been broadly accepted that the magnetism may play an important role in the high-T(c) superconductivity in the lamellar CuO2 materials. In this paper we give a quantitative study of the magnetic properties in and around the Neel ordered state of three-dimensional quantum antiferromagnets such as La2CuO4 with and without small hole doping. The study is based on the model we call the Hubbard-sigma-model. It is a (3 + 1)-dimensional CP1 or S2 nonlinear-sigma-model derived as an effective field theory describing the low-energy spin dynamics of the three-dimensional Hubbard t-J model with a weak interlayer coupling. The effect of hole dyanics is taken into account in the leading approximation by substituting the CP1 coupling and the spin-wave velocity with "effective" ones including the tree and one-loop corrections by hole fermions. Stationary-phase equations for the one-loop effective potential of the S2 model are analyzed. Based on them, various magnetic properties of the system, such as Neel temperature, spin-correlation length, staggered magnetization, specific heat, and susceptibility as functions of anisotropic parameters, temperature, etc., are investigated in detail. The results show that our anisotropic field-theory model with certain values of parameters gives a good description of the magnetic properties indicated by experiments on La2CuO4 in both the ordered and the disordered phases. These results are supported in part by the renormalization-group analysis. In the doped case it is observed that the hopping effect of holes is very large and reduces the Neel temperature significantly.