Ferrimagnetic Order in Tetragonal Antiperovskite Mn$_3$GeN

Abstract

The crystal and magnetic structures of the nitride antiperovskite Mn$_3$GeN reveals ferrimagnetic order stemming from a distorted kagome-derived lattice of the Mn atoms. Polycrystalline Mn$_3$GeN was synthesized via a solid-state reaction and characterized using neutron powder diffraction, DC magnetometry, and first-principles calculations. Rietveld refinement reveals near-stoichiometric composition (Mn$_3$GeN$_{0.94(1)}$) adopting a tetragonal $I4/mcm$ structure at $T$ = 500 K and below, featuring axially distorted and tilted [NMn$_6$] octahedra that result in a buckled Mn kagome lattice. On heating, the tetragonal distortion and octahedral tilt angle decrease continuously before transitioning to the cubic $Pm\bar{3}m$ antiperovskite phase at $T \approx$ 524 K. Neutron diffraction and magnetometry together reveal noncollinear ferrimagnetic ordering. For 30 K $\le T \le$ 500 K, the magnetic structure is described by a single propagation vector, $k$ = (0, 0, 0), with inequivalent Mn1 and Mn2 sublattices that couple antiferromagnetically to yield a net moment. Density functional theory-based calculations show the different local moments originate from the bandwidths associated with the distinct Mn-N bond lengths. The temperature dependence of the sublattice moments indicates a compensation-like crossover between Mn1- and Mn2-derived magnetization near 380 K. These findings uncover a previously unrecognized subtlety in the magnetic and structural behavior of Mn$_3$GeN, highlighting the interplay between structural distortions, magnetic ordering, and electronic structure in kagome-derived antiperovskite materials.