Quartic asymmetric exchange for two-dimensional ferromagnets with trigonal prismatic symmetry

TL;DR

This paper proposes a novel mechanism, distinct from Dzyaloshinskii-Moriya interaction, explaining noncollinear magnetic textures in 2D ferromagnets with trigonal prismatic symmetry, supported by symmetry analysis and experimental relevance.

Contribution

It introduces a fourth-order asymmetric exchange mechanism specific to $D_{3h}$ symmetry, predicting long-range magnetic spirals and bimerons in 2D ferromagnets.

Findings

Predicts conical magnetic spirals dependent on propagation direction

Relates the mechanism to experimental observations in Fe$_3$GeTe$_2$

Suggests stabilization of bimerons in easy-plane materials

Abstract

We suggest a possible origin of noncollinear magnetic textures in ferromagnets (FMs) with the $D_{3h}$ point group symmetry. The suggested mechanism is different from the Dzyaloshinskii-Moriya interaction (DMI) and its straightforward generalizations. The considered symmetry class is important because a large fraction of all single-layer intrinsic FMs should belong to it. In particular, so does a monolayer Fe$_3$GeTe$_2$. At the same time, DMI vanishes identically in materials described by this point group, in the continuous limit. We use symmetry analysis to identify the only possible contribution to the free energy density in two dimensions that is of the fourth order with respect to the local magnetization direction and linear with respect to its spatial derivatives. This contribution predicts long-range conical magnetic spirals with both the average magnetization and the average chirality dependent on the spiral propagation direction. We relate the predicted spirals to a recent experiment on Fe$_3$GeTe$_2$. Finally, we demonstrate that, for easy-plane materials, the same mechanism may stabilize bimerons.