Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

TL;DR

This paper derives an unambiguous effective action for quantum Hall ferromagnets, including a topological Hopf term, and studies their electromagnetic interactions, clarifying the nature of skyrmions and spin excitations.

Contribution

It provides a rigorous derivation of the effective action with the Hopf term and analyzes electromagnetic effects on spin excitations in quantum Hall ferromagnets.

Findings

Derived the effective action including the Hopf term unambiguously.

Obtained an explicit expression for electromagnetic coupling of spin excitations.

Clarified the fermionic nature of skyrmions in the system.

Abstract

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.