Optical detection of 4-spin chiral interaction in a 2D honeycomb ferrimagnet

Broken inversion symmetry of magnetic lattice is normally described by Lifshitz invariants in micromagnetic energy functional. Three exceptions are the lattices with T$_\textrm{d}$, C$_\textrm{3h}$ and D$_\textrm{3h}$ point group symmetries. The inversion symmetry breaking of the corresponding magnets is described by more complex 4-spin chiral invariants that cannot be related to Dzyaloshinskii-Moriya interaction. Experimental detection of 4-spin chiral interactions is an important task that has yet to be performed. We propose that the 4-spin chiral interaction can be probed by energy selective magnon relaxation in two-dimensional ferromagnet Fe$_{3}$GeTe$_{2}$ that possess D$_\textrm{3h}$ point group symmetry.