Aspects of Magnon Renormalization Near the Transition Temperature

Abstract

The temperature dependence of the magnon energy is studied, together with the magnetization, by a self‐consistent treatment of the model hamiltonian obtained by keeping the Heisenberg hamiltonian up to the diagonal term of fourth order in magnon operators. In this formalism, the dispersion relation appears to have the same form as for free magnons, apart from an important temperature‐dependent factor α(T). The calculations have been carried out for simple cubic ferromagnets and CsCl‐type antiferromagnets, with due account taken of the Brillouin zone boundary effect. It is found that no solution for α(T) exists above a maximum temperature T_M which is compared to the values of the Curie and Néel temperatures calculated by the methods of Kramers‐Opechowski and Bethe‐Peierls‐Weiss. At T_M the magnetization has about 25 percent of its value at absolute zero. The fact that α(T) is independent of k appears to be a property of the cubic geometry to which the following considerations have been limited.