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Recently topological aspects of magnon band structure have attracted muchinterest, and especially, the Dirac magnons in Cu3TeO6 have been observedexperimentally. In this work, we calculate the magnetic exchange interactionsJ's using the first-principles linear-response approach and find that these J'sare short-range and negligible for the Cu-Cu atomic pair apart by longer than 7Angstrom. Moreover there are only 5 sizable magnetic exchange interactions, andaccording to their signs and strengths, modest magnetic frustration isexpected. Based on the obtained magnetic exchange couplings, we successfullyreproduce the experimental spin-wave dispersions. The calculated neutronscattering cross section also agrees very well with the experiments. We alsocalculate Dzyaloshinskii-Moriya interactions (DMIs) and estimate the cantingangle (about 1.3{\deg}) of the magnetic non-collinearity based on thecompetition between DMIs and J's, which is consistent with the experiment. Thesmall canting angle agrees with that the current experiments cannot distinguishthe DMI induced nodal line from a Dirac point in the spin-wave spectrum.Finally we analytically prove that the "sum rule" conjectured in [Nat. Phys.14, 1011 (2018)] holds but only up to the 11th nearest neighbour.

Calculated magnetic exchange interactions in Dirac magnon material Cu3TeO6