Theory of Magnon Spintronics: Non-Abelian Gauge Theory of Electron Spintronics

TL;DR

This paper develops a non-Abelian gauge theory for magnon spintronics, modeling electron spin interactions with novel topological objects and mixing phenomena, advancing the theoretical understanding of spin-based electronic systems.

Contribution

It introduces a non-Abelian SU(2)xU(1) gauge framework for magnon spintronics, incorporating photon-magnon mixing and topological excitations, which is a novel approach in the field.

Findings

Photon-magnon mixing leads to massless and massive gauge bosons.

The theory predicts non-Abelian topological objects like vortices and monopoles.

Distinct penetration lengths are associated with different gauge boson masses.

Abstract

Treating the electron as a charged spinon we propose a theory of magnon spintronics, a non-Abelian gauge theory of SU(2)xU(1), which could be viewed as an effective theory of electron spintronics. Just like QED the theory has the U(1) electromagnetic interaction, but the new ingredient is the non-Abelian SU(2) gauge interaction of the magnon with the spinon. A remarkable feature of the theory is the photon-magnon mixing, the mixing between the electromagnetic U(1) gauge boson and the diagonal part of the SU(2) magnon gauge boson. After the mixing we have the massless Abelian magnon and a massive photon, and the doubly charged massive off-diagonal non-Abelian magnons which induce the spin-flip interaction to the spinon. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different penetration lengths, the one fixed by the mass of the photon which generates the well known Meissner effect and the other fixed by the mass of the off-diagonal magnons which generates the non-Abelian Meissner effect. The non-Abelian structure of the theory naturally accommodates new topological objects, the non-Abrikosov quantized magnonic vortex and non-Abelian magnonic monopole of the Cho-Maison type, as well as the well known Abrikosov vortex. We discuss the physical implications of the non-Abelian gauge theory of the magnon spintronics.