Abstract
In insulating rare-earth compounds, unquenched orbital momentum and weak crystal-field (CF) splitting of the atomic J multiplet at rare-earth ions result in a highly ranked (multipolar) exchange interaction between them and a complex low-temperature magnetic order not fully uncovered by experiment. Explicitly correlated ab initio methods proved to be highly efficient for an accurate description of CF multiplets and magnetism of individual rare-earth ions in such materials. Here we extend this ab initio methodology and develop a first-principles microscopic theory of multipolar exchange interaction between J multiplets in f-metal compounds [1]. The key point of the approach is a complete account of Goodenough's exchange mechanism along with traditional Anderson’s superexchange and other contributions, the former being dominant in many rare-earth materials. Application of this methodology to the description of the ground-state order in the neodymium nitride (NdN) with rocksalt structure reveals the multipolar nature of its ferromagnetic order. We found that the primary and secondary order parameters contain non-negligible J-tensorial contributions up to the ninth order. The calculated spin-wave dispersion and magnetic and thermodynamic properties show that they cannot be simulated quantitatively by confining to the ground CF multiplet on the lanthanide sites.