Momentum Transport in Ferromagnetic–Plasmon Heterostructures Within the Keldysh Formalism

We investigate momentum transport in ferromagnetic–plasmon heterostructures using Keldysh field theory and energy–momentum tensor formalism. A three-layer model reveals that plasmon frequency shifts generate a non-zero expectation value for the xz-component of the energy–momentum tensor ⟨Txz⟩ through magnon–plasmon coupling. The momentum transport exhibits linear velocity dependence, with temperature behavior transitioning from exponential suppression at low temperatures to linear growth at high temperatures, governed by the magnon energy gap. Spatial oscillations follow sin(2nπz/h) patterns within the ferromagnetic layer. This framework provides fundamental insights into quantum momentum transport mechanisms in magnetic systems.