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Non-reciprocal magnons in a two dimensional crystal with off-plane magnetization

Non reciprocal spin waves have a chiral asymmetry so that their energy is different for two opposite wave vectors. They are found in atomically thin ferromagnetic overlayers with in plane magnetization and are linked to the anti-symmetric Dzyaloshinskii-Moriya surface exchange. We use an itinerant fermion theory based on first principles calculations to predict that non-reciprocal magnons can occur in Fe$_3$GeTe$_2$, the first stand alone metallic two dimensional crystal with off-plane magnetization. We find that both the energy and lifetime of magnons are non-reciprocal and we predict that acoustic magnons can have lifetimes up to hundreds of picoseconds, orders of magnitude larger than in other conducting magnets.