Research project involving Dzyaloshinskii-Moriya-Interaction (DMI) in magnetic materials using Landau-Lifshitz-Gilbert-Bazily (LLGB) formalism.
The generalized continuity equation for diffusive spin current has a torque contribution over the magnetization dynamics M in a ferromagnet. Such dynamics is described by LLGB equation,
Where is the effective magnetic field given by
The torque contribution is represented by the following equation,
where the parameters and
are proportional to de electric current Je.
As first approach, given a magnetic field such as , the system could be written as,
with operator L defined by:
The propagator of this equation takes the following form,
with