Hedgehog lattices induced by chiral spin interactions

TL;DR

This paper investigates a classical Heisenberg spin model with chiral interactions, revealing a robust hedgehog lattice phase that undergoes a first-order transition, and relates findings to experimental hedgehog lattices in certain materials.

Contribution

It introduces a model with multiple chiral interactions that stabilizes a hedgehog lattice, connecting theoretical predictions with experimental observations.

Findings

Discovery of a 4Q bipartite hedgehog lattice phase.

Hedgehog density depends non-linearly on Dzyaloshinskii-Moriya interaction.

Hedgehog density varies linearly with chiral interaction, acting as a chemical potential.

Abstract

We analyze a classical Heisenberg spin model on the simple cubic lattice which is invariant under time reversal and contains multiple chiral spin interactions. The modelled dynamics is appropriate either for local moments coupled to itinerant Weyl electrons, or localized electrons with a strong spin-orbit coupling that would produce a Weyl spectrum away from half filling. Using a Monte Carlo method, we find a robust $4Q$ bipartite lattice of hedgehogs and antihedgehogs which melts through a first order phase transition at a critical temperature in certain segments of the phase diagram. The density of hedgehogs is a non-linear function of the Dzyaloshinskii-Moriya interaction, and a linear function of the multiple-spin chiral interaction which plays the fundamental role of a ``magnetic flux'' or a hedgehog chemical potential. These findings are related to the observations of hedgehog lattices in MnGe, MnSi$_{1-x}$Ge$_x$ and SrFeO$_3$, and indirectly support the possible existence of incompressible quantum-disordered hedgehog liquids.