Packing fraction related distortion of Mn${}_6$C octahedra and its effect on the first order magnetic transition in Mn based antiperovskites

In this paper, we attempt to understand the cause of magnetostructural transformation in Mn-based antiperovskites by calculating EXAFS at the K edges of constituent metal atoms in three antiperovskite compounds, Mn${}_3$GaC, Mn${}_3$SnC and Mn${}_3$InC. These three compounds have very different magnetic ground states despite the similar cubic structure. Our calculations show that the distortions of Mn${}_6$C octahedra, which are responsible for the first-order magnetic transition to antiferromagnetic state, depends on the packing fraction of the lattice.