Effective Field Theory of a Noncollinear Altermagnet

TL;DR

This paper develops an effective field theory for noncollinear altermagnets, revealing their phase diagram, symmetry properties, magnon excitations, and potential topological solitons, advancing understanding of complex magnetic phases.

Contribution

It introduces a novel effective field theory for noncollinear altermagnets, characterizing their phases, symmetries, and excitations, including topological features.

Findings

Identified a noncollinear phase with full spin rotational symmetry breaking.

Derived an SO(3) sigma model describing magnon excitations with anisotropic dispersion.

Discussed the existence of topological solitons such as Z2 vortices.

Abstract

We derive an effective field theory for a noncollinear altermagnet and magnons on top of the noncollinear ground state from an altermagnetic Heisenberg model. We obtain the ground-state phase diagram, revealing a noncollinear phase and four distinct collinear phases. The ground state of the noncollinear phase fully breaks the spin rotational symmetry, while the ground state of the collinear phases possesses unbroken $\mathrm{SO}(2)$ symmetry. The resulting effective field theory for the noncollinear phase is an $\mathrm{SO}(3)$ sigma model in which the magnonic excitation has three independent degrees of freedom and exhibits the $d$-wave-like anisotropic linear dispersion. We also discuss possible topological solitons, including $\mathbb{Z}_2$ vortices.