Effects of Rashba spin-orbit coupling on low energy magnetization dynamics of the Hubbard model

Magnetization dynamics is conventionally studied using the Landau-Lifchitz-Gilbert (LLG) equation, which originates from quantum mechanics of electron spins, but can most of the time be used without referring to the electronic degrees of freedom that give rise to the magnetism.
In the presence of strong spin-orbit coupling or magnetic fields, magnetization dynamics may involve nontrivial electronic corrections beyond the LLG equation. To address this problem we consider a microscopic Hubbard model on a 2D square lattice at half filling, which has a Neel antiferromagnetic ground state. The low energy magnetization dynamics can be obtained through perturbation theory based on the mean field ground state in the path integral formalism. We add a Rashba spin-orbit coupling to the standard Hubbard model and examine its modification on the Neel state. We then calculate the low-energy excitations by treating small variations on the order parameters as a perturbation. The study will shed light on effects of competing interactions and spin-orbit coupling on magnetization dynamics.