Precise spin-wave model for one-, two-, and three-dimensional Heisenberg antiferromagnets inclusive of dipolar interactions

Abstract

A spin-wave formalism has been developed for Heisenberg antiferromagnets with combined exchange and dipolar interactions. Magnon-magnon interactions, represented by higher-order contributions to the spin Hamiltonian, are included to have the magnon energies renormalized with temperature. Distinct from conventional perturbation theory, these contributions are random-phase decoupled prior to diagonalization. This allows incorporation in the coefficients of the lowest-order Hamiltonian, which is diagonalized by a standard Bogoliubov transformation. In this way, all higher-order terms taken into account fully contribute to the corrections of both the magnon modes and their energies, whereas in conventional perturbation theory only the energies are corrected by a selection of higher-order terms written in the diagonal representation of the unperturbed zero-order Hamiltonian. Excellent agreement with experiment is found for the temperature dependence of the sublattice magnetization in representative one-, two-, and three-dimensional antiferromagnets up to at least 80% of the Néel temperature. This is a marked improvement over the classical perturbation approach to incorporate magnon-magnon interactions. It is thereby essential to allow for phase differences between spin waves in all spatial directions, irrespective of the dimensionality of the exchange interactions. The formalism includes faithful renormalization of the magnon modes and their energies by the model itself, rather than letting the energy gap fall with temperature in a semiempirical way. This leaves only the zero-temperature spin-wave parameters as inputs.