First-order antiferromagnetic transition in CrN

The antiferromagnetic structure of CrN is known to belong to the so-called IV-type cubic antiferromagnets. We discuss the transformation properties of the order parameter and have found that it belongs to a 12-dimensional irreducible representation of the $\mathrm{Fm}3m$ group. We construct the corresponding Landau-Ginzburg model and study the phase transition by examining the fixed points of the renormalization-group transformations to the second order in $\epsilon$ expansion. The renormalization-group equations have no stable fixed points and therefore the transition should be of the first order, which is in agreement with experiment. Other materials of the same symmetry are reviewed and some new physical systems are added to the list of "the physical realizations of $n\ge 4$ component vector models."