Quartic asymmetric exchange for monolayer Fe$_3$GeTe$_2$ and other two-dimensional ferromagnets with trigonal prismatic symmetry

Abstract

We suggest a possible origin of noncollinear magnetic textures in ferromagnets (FMs) with the D 3h point group symmetry. Suggested mechanism is different from the Dzyaloshinskii-Moriya interaction (DMI). 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 Fe3GeTe2. At the same time, DMI vanishes identically in materials described by this point group, in the continuous limit. We use symmetry analysis to derive all possible contributions to the free energy density that are of the fourth order with respect to the unit vector n of the local magnetization direction and linear with respect to spatial derivatives of n. There are precisely seven such contributions. However, up to boundary terms, only two of them can be considered as independent. Moreover, for a twodimensional system, one of these two necessarily vanishes! We investigate whether the remaining contribution can serve as a source of spin spirals and skyrmions recently observed in Fe3GeTe2. We also address a possible stabilization of bimerons by the same contribution.

Imaging current control of magnetization in Fe$_3$GeTe$_2$ with a widefield nitrogen-vacancy microscope

“…However, the existence of a spin torque does not guarantee domain wall motion [14], and the exact mechanism driving CIDM in our experiments remains unclear. Using symmetry arguments based on the D 3h point group of monolayer FGT [49,50] [see SI, Sec. X], it is found the chiral spin spirals typically associated with SOT-driven domain-wall motion are not stabilized, suggesting there may be additional unexplored mechanisms contributing to the observed behaviour.…”

Signatures of quartic asymmetric exchange in a class of two dimensional magnets

“…It has been shown, however, that for lattices with D 3h , C 3h , and T d point group symmetries the DMI cannot induce linearin-gradient terms in micromagnetic energy [20] and, moreover, such terms are generally forbidden in quadratic order with respect to magnetization. Consequently, in the corresponding materials the role of DMI (and any other long-range two-spin antiymmetric exchange) must be negligible for the formation of non-collinear magnetic textures that are smooth on atomic scales [21][22][23].…”

“…The quartic asymmetric exchange is known to stabilize conical magnetic spirals [23,30,31]. The aim of this paper is to investigate how this interaction can be detected and quantified in 2D ferromagnetic monolayer of D 3h point group.…”

“…Quartic asymmetric exchange for 2D ferromagnets with trigonal prismatic symmetry has been first introduced in Ref. [23]. Independently of its microscopic origin it is represented by a unique term in the energy density of a magnet,…”

“…For m directed along x axis (ϕ = 0), the spiral propagates along y axis, hence k and m are perpendicular vectors. For m directed along the zigzag direction of the honeycomb lattice (ϕ = π/6), the vectors k and m are parallel to each other [23].…”