The dynamics of local magnetic moments induced by itinerant Weyl electrons

TL;DR

This paper develops a theory for how Weyl electrons mediate complex, long-range magnetic interactions in topological semimetals, leading to potential skyrmion and chiral spin liquid states.

Contribution

It introduces a comprehensive model of Weyl electron-mediated spin interactions, including Heisenberg, Kitaev, Dzyaloshinskii-Moriya, and chiral three-spin couplings, with implications for magnetic dynamics.

Findings

Weyl electrons induce oscillatory, long-range magnetic interactions.

The Dzyaloshinskii-Moriya vector aligns with the spin displacement.

Chiral three-spin interactions can stabilize skyrmion lattices.

Abstract

We derive the effective interactions between local magnetic moments which are mediated by Weyl electrons in magnetic topological semimetals. The resulting spin dynamics is governed by the induced Heisenberg, Kitaev and Dzyaloshinskii-Moriya (DM) interactions with extended range and oscillatory dependence on the distance between the spins. These interactions are realized in multiple competing channels shaped by the multitude of Weyl nodes in the electron spectrum. Microscopic spins need to be spatially modulated with a channel-dependent wavevector in order to take advantage of the interactions. The DM vector is parallel to the displacement between the two interacting spins, and requires the presence of Weyl electron Fermi surfaces. We also derive the Weyl-induced chiral three-spin interaction in the presence of an external magnetic field. This interaction has an extended range as well, and acts upon the spatially modulated spins in various channels. Its tendency is to produce a skyrmion lattice or a chiral spin liquid which exhibits topological Hall effect. Ultimately, the theory developed here addresses magnetic dynamics in relativistic metals even when chiral magnetism is microscopically precluded. We discuss insights into the ordered state of the magnetic Weyl semimetal NdAlSi.