Non-local topological magnetoelectric effect by Coulomb interaction at a topological insulator-ferromagnet interface

TL;DR

This paper investigates how long-range Coulomb interactions induce a non-local topological magnetoelectric effect at a topological insulator-ferromagnet interface, affecting magnetization dynamics over large distances.

Contribution

It introduces a theoretical framework showing Coulomb interactions cause non-local magnetoelectric effects, extending understanding of topological insulator-ferromagnet interfaces.

Findings

Coulomb interactions induce non-local magnetoelectric effects.

Divergences in in-plane magnetization influence large-distance dynamics.

Derived Landau-Lifshitz and Coulomb field equations with one-loop calculations.

Abstract

The interface between a topological insulator and a ferromagnetic insulator exhibits an interesting interplay of topological Dirac electrons and magnetism. As has been shown recently, the breaking of time-reversal invariance by magnetic order generates a Chern-Simons term in the action, that in turn leads to a Berry phase and a magnetoelectric effect of topological origin. Here, we consider the system in the presence of long-range Coulomb interaction between the Dirac electrons, and find that the magnetoelectric effect of the fluctuating electric field becomes non-local. We derive a Landau-Lifshitz equation for the fluctuation-induced magnetization dynamics and the Euler-Lagrange equation of the Coulomb field by explicit one-loop calculations. Via the Coulomb interaction, divergences in the in-plane magnetization affect the magnetization dynamics over large distances in a topologically protected way.