  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.
