Spin Model for Nontrivial Magnetic Orders in the Inverse-Perovskite Antiferromagnets

Nontrivial magnetic orders in the inverse-perovskite manganese nitrides are theoretically studied by constructing a classical spin model describing the magnetic anisotropy and frustrated exchange interactions inherent in specific crystal and electronic structures of these materials. With a replica-exchange Monte-Carlo technique, a theoretical analysis of this model reproduces the experimentally observed triangular \Gamma^{5g} and \Gamma^{4g} spin ordered patterns and the systematic evolution of magnetic orders. Our work solves a 40-year-old problem of nontrivial magnetism for the inverse-perovskite manganese nitrides and provides a firm basis for clarifying the magnetism-driven negative thermal expansion phenomenon discovered in this class of materials.