The broken inversion symmetry of the magnetic lattice is normally described by Lifshitz invariants in a micromagnetic energy functional. Three exceptions are the lattices with $T_d, C_{3h}$, and $D_{3h}$ point group symmetries. For such lattices all Lifshitz invariants are forbidden despite broken inversion symmetry. In these cases the inversion symmetry breaking of the corresponding magnets is reflected by four-spin chiral invariants that are not related to the Dzyaloshinskii-Moriya interaction. The experimental detection of four-spin chiral interactions is an important task that has yet to be performed. We propose that the four-spin chiral interaction can be probed by energy-selective magnon relaxation in the two-dimensional ferromagnet ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ that possesses $D_{3h}$ point group symmetry.

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• Magnetization dynamics
• Magneto-optics
• Magnons
• Spin dynamics
• Ultrafast magnetic effects
• Ferrimagnets
• Magnetic systems
• Noncollinear magnets