Theory of Temperature-Dependent Magnon Energies in Antiferromagnets

A theory of the temperature-dependent magnon energies in antiferromagnets is developed. In this theory, which is based on the Holstein-Primakoff formalism for the Hamiltonian, the dynamical interaction between two spin waves is taken into account in the sense of the random-phase approximation. The kinematical interaction is neglected. The present result, which is different from that of Oguchi and Honma, agrees with that of the Kanamori-Tachiki theory in the spin-wave temperature region. The magnon energies are computed in a self-consistent manner for the system which includes the exchange and the uniaxial anisotropy energies. The maximum temperature at which the energy of a magnon with infinite wavelength becomes zero is calculated. It is found that the maximum temperature which is obtained in this theory is different from that obtained previously by Bloch.