Weyl nodes and magnetostructural instability in antiperovskite Mn$_3$ZnC

The ferromagnetic phase of the cubic antiperovskite Mn$_3$ZnC is suggested from first-principles calculation to be a nodal line Weyl semimetal. Features in the electronic structure that are the hallmark of a nodal line Weyl state, a large density of linear band crossings near the Fermi level, can also be interpreted as signatures of a structural and/or magnetic instability. Indeed, it is known that Mn$_3$ZnC undergoes transitions upon cooling from a paramagnetic to a cubic ferromagnetic state under ambient conditions and then further into a non-collinear ferrimagnetic tetragonal phase at a temperature between 250$,$K and 200$,$K. The existence of Weyl nodes and their destruction via structural and magnetic ordering is likely to be relevant to a range of magnetostructurally coupled materials.