Nonlinear Spin-Wave Theory for Antiferromagnets

The spin-wave interaction in simple antiferromagnets is studied at higher temperatures by a method similar to that of Bloch for ferromagnets. It is shown that the energy spectrum, the sublattice magnetization, and the internal energy of the system depend on a renormalization parameter $\alpha \mathrm{}\left(T\right)\mathrm{}$. This parameter satisfies an implicit equation from which its dependence on the temperature may be determined. It is found that the equation has a solution only up to a temperature $T_{max}$ which is within a few percent of the theoretical values of the Néel temperature. At very low temperatures the theory reduces to the Oguchi theory after all quantities are expanded in powers of the temperature. The parallel and perpendicular susceptibilities are also calculated.