Magnon-Magnon Interactions in O(3) Ferromagnets and Equations of Motion for Spin Operators

TL;DR

This paper systematically analyzes magnon-magnon interactions in O(3) ferromagnets using equations of motion, clarifying different approximation methods and their treatment of magnon interactions derived from the effective Lagrangian.

Contribution

It provides a unified framework for understanding various approximations in ferromagnet spin dynamics through perturbation theory and symmetry considerations.

Findings

Different approximations handle magnon interactions distinctly.

The second order approximation relates to perturbation theory for type A magnons.

Physical insights into magnon-magnon interactions and model symmetries are clarified.

Abstract

The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon-magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnon-magnon interactions arising from the Wess-Zumino term are treated, from where specific features and limitations of each of them can be deduced.