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

We have carried out simulations of the magnetic properties of undoped La₂{CuO}₄$, using a classical Heisenberg model for the Cu spin with a strong antiferromagnetic coupling ${J}₀$ 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 (N\'eel temperature) depends only on the difference of these two interactions, {Δ}J. For {Δ}J>0.1{}J₀{}, TN depends nearly linearly on {Δ}J. 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 {Δ}J{}0.025{}J₀{}. The relation between TN and {Δ}J of a three-dimensional simple cubic lattice with in-plane antiferromagnetic interaction J₀ and interplane coupling {Δ}J 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.