Current-induced quasiparticle magnetic multipole moments

TL;DR

This paper develops a gauge-invariant theory for magnetic multipole moments in quasiparticles, demonstrating how electric currents can induce and manipulate higher-order magnetic moments like octupoles in materials such as phosphorene.

Contribution

It introduces a general theoretical framework for magnetic multipole moments and their currents, including a concrete example involving quasiparticle magnetic octupoles in phosphorene.

Findings

Quasiparticles in phosphorene can host magnetic octupole moments.

Electric currents can induce and reveal these higher-order moments.

Nonlinear responses can generate currents carrying octupole moments.

Abstract

Magnetic ordering beyond the standard dipolar order has attracted significant attention in recent years, but it remains an open question how to effectively manipulate such nontrivial order parameters using external perturbations. In this context, we present a theory for Cartesian magnetic multipole moments and their currents created by electric currents based on a general gauge-invariant formula for arbitrary-order spin magnetic multipole moments of Bloch wave packets. As a concrete example, we point out that the low-energy quasiparticles in phosphorene subject to a perpendicular electric field have a valley structure that hosts magnetic octupole moments. The quasiparticle magnetic octupole moments can be exhibited by an in-plane electric current and lead to accumulation of staggered spin densities at the corners of a rectangular-shaped sample. A current carrying the octupole moments can further be induced through nonlinear response. Our work paves the way to systematically searching for and utilizing quasiparticles with higher-order magnetic multipole moments in crystal materials.