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Using first-principles electronic structure calculations, we show thatferromagnetic Heusler compounds Co$_2$MnX (X= Si, Ge, Sn) present non-trivialtopological characteristics and belong to the category of Weyl semimetals.These materials exhibit two topologically interesting band crossings near theFermi level. These band crossings have complex 3D geometries in the Brillouinzone and are characterized by non-trivial topology as Hopf links and chain-likenodal lines, that are protected by the perpendicular mirror planes. Thespin-orbit interaction split these nodal lines into several zero-dimensionalWeyl band crossings. Unlike previously known topologically non-trivial Heuslermaterials, these majority-spin band crossings lie in the band gap of minorityspin bands, potentially facilitating its experimental realization.

Electronic properties of the Weyl semimetals Co$_2$MnX (X=Si, Ge, Sn)