Long-range order produced by the interaction between spin waves in classical fcc Heisenberg models.

Abstract

Previous linear spin-wave calculations as well as Green's-function theories predict disorder at $Tg0$ for certain Heisenberg models in disagreement with the in-principle exact Monte Carlo simulations. In order to resolve this contradiction we extended the spin-wave theory beyond the usual Bloch's nonlinear approximation, including leading off-diagonal terms. We investigate the classical Heisenberg model on an fcc lattice for three pairs of coupling constants (${J}_{1}$, ${J}_{2}$) which result in an infinite degeneracy for the magnetic ordering vector in the mean-field (MF) theory. We study in detail how the interaction between spin waves selects the ordering vector at the critical field between antiferromagnetic and paramagnetic phases. We find that the usually ignored nonlinear terms generate soft modes which are consistent with the order found by Monte Carlo simulations at zero field. We demonstrate the importance of these nonlinear effects by investigating antiferromagnetic models with a one- or two-dimensional degenerate MF manifold for the ordering vector. The model with the two-dimensional manifold seems ideal for a Monte Carlo study of domain growth in a first-order phase transition. Finally, we show that even when Bloch's nonlinear spin-wave theory gives qualitatively correct results, it can lead to a factor-of-three overestimate for the critical temperature of ferromagnetism. We find that this failure can be understood by considering the higher-order effects included in our extended spin-wave theory.