Helical phase in two-dimensional magnets due to four-spin interactions

We demonstrate that in ferromagnets with the D3h point group of symmetry a possible origin of phase transition from a collinear ferromagnetic state to a non-collinear state can be the fourth order contributions to the free energy density that are allowed by this point group of symmetry. At the same time, Dzyaloshinskii-Moria interaction vanishes in such materials. Via symmetry analysis we derive seven possible fourth order contributions to the free energy density with respect to the unit vector of the local magnetization direction but only two of them can be considered as independent. Moreover, for two-dimensional systems only one survives. Considered symmetry class is essential because a large group of two-dimensional intrinsic ferromagnets belongs to it, for example a monolayer Fe3GeTe2. The four-spin chiral exchange does also manifest itself in peculiar magnon spectra and favors spin waves.