Coupling Theory of Emergent Spin Electromagnetic Field and Electromagnetic Field

Abstract

In ferromagnetic metals, an effective electromagnetic field that couples to conduction electron spins is induced by the sd exchange interaction. We investigate how this effective field, namely, the spin electromagnetic field, interacts with the ordinary electromagnetic field by deriving an effective Hamiltonian based on the path integral formalism. It turns out that the dominant coupling term is the product of the electric field and spin gauge field. This term describes the spin-transfer effect, as was pointed out previously. The electric field couples also to the spin electric field, but this contribution is smaller than the spin-transfer contribution in the low frequency regime. The magnetic field couples to the spin magnetic field, and this interaction suggests an intriguing intrinsic mechanism of frustration in very weak metallic ferromagnets under a uniform magnetic field. We also propose a voltage generation mechanism due to a nonlinear effect of non-monochromatic spin-wave excitations.

Spin dynamics with inertia in metallic ferromagnets

“…(the indices α, β, · · · = ± correspond to spin up or down) with 14) where 0 denotes a positive infinitesimal. We define a 2×2 matrix g k,ω by (g k,ω ) αβ ≡ δ αβ g k,ω,α (no summation over α), or,…”

“…To be precise, there emerge other coupling terms between spin and electromagnetic field in addition to the Zeeman coupling, such as in ref [14],. by integrating out conduction electrons.…”

Effective Hamiltonian theory for nonreciprocal light propagation in magnetic Rashba conductor

“…The coupling of the adiabatic spin gauge field to the electromagnetic field was studied based on the effective Hamiltonian study in Refs. [18,19]. It was found that the spin-transfer effect is described using the linear coupling term of the adiabatic spin gauge field and the electric field.…”