Monte Carlo and mean-field study of antiferromagnetic ordering in cupric oxides

We have carried out simulations of the magnetic properties of undoped La2CuO4, using a classical Heisenberg model for the Cu spin with a strong antiferromagnetic coupling J0 in the a-c plane and weak interplane couplings. In the orthorhombic state, the coupling between nearest-neighbor spins in the b-c and a-b planes are not equal. We found that the antiferromagnetic-to- paramagnetic transition temperature (Néel temperature) depends only on the difference of these two interactions, ΔJ. For ΔJ>0.1J0, TN depends nearly linearly on ΔJ. When compared with the results of ordinary mean-field as well as a renormalized mean-field theory, our Monte Carlo simulation gives a substantially lower TN for ΔJ0.025J0. The relation between TN and ΔJ of a three-dimensional simple cubic lattice with in-plane antiferromagnetic interaction J0 and interplane coupling ΔJ is also calculated using low-temperature spin-wave theory. The spin-wave calculation gives a better estimate of TN compared with our simulation results than the two mean-field-theory results.