Quantum fluctuations and magnon-magnon interactions in antiferromagnets

Abstract

We derive relaxation times for magnon-magnon interactions in antiferromagnetic spin configurations with easy-axis anisotropy and an external magnetic field. We apply the Holstein-Primakoff transformation to the Heisenberg exchange Hamiltonian to calculate the ground state energy. It turns out that the antiferromagnetic configuration is not an eigenstate of the Heisenberg exchange Hamiltonian. We go on to describe quantum fluctuations in antiferromagnetic spin configurations with easy-axis anisotropy in an external magnetic field. Also we derive spin wave dispersion using Landau-Lifshitz-Gilbert phenomenology. We calculate the scattering amplitudes of magnon-magnon interactions and derive the scale of relaxation times of out-of-equilibrium antiferromagnetic configurations, from which we find that the relaxation rate is proportional to T^2. Thermal magnons have a relaxation rate proportional to T. For Gilbert damping it is found that the relaxation rate is proportional to T.