Electronic structure and magnetic interactions in MnN andMn3N2

Electronic structure calculations were performed for MnN and ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ using a full-potential linearized muffin-tin orbital method in the local spin density approximation. Structural relaxation by energy minimization and calculations for various different magnetic configurations were performed. Antiferromagnetic ordering along the [001] direction was found to have the lowest energy in both materials in agreement with experimental neutron diffraction data. The magnetic moments were found to be about $3{\ensuremath{\mu}}_{B}$ in good agreement with experiment. Analysis of the partial densities of states reveals that the magnetic moments arise primarily from the ${t}_{2g}$ orbitals. In ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2},$ the magnetic moment was found to be slightly larger on the ${\mathrm{Mn}}_{1}$ atoms, i.e., the Mn atoms in planes without N than on ${\mathrm{Mn}}_{2}$ atoms. Band structures and densities of states are presented. The energy differences between different magnetic configurations were analyzed in terms of a Heisenberg Hamiltonian. We find strong second-nearest-neighbor ferromagnetic interactions for Mn connected collinearly with N, indicative of a double exchange mechanism and about four times weaker nearest-neighbor antiferromagnetic interactions in MnN. In a perfect rocksalt structure, this situation would lead to a multiply degenerate ground state. However, we find that the $c/a$ reduction of about 2% is due to the AFM coupling (it is absent in FM and nonmagnetic MnN) and leads to stronger inter-(001)-plane exchange interactions than intraplane exchange interaction. In ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2},$ the Mn connected via a vacancy lack the strong ferromagnetic interaction. This would suggest a lower N\'eel temperature for MnN with increasing concentration of N vacancies. However, the nearest-neighbor direct exchange interaction in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ is found to be about two times as large in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ than in MnN which partially compensates for the lack of fewer indirect second-nearest exchange interactions. These changes in the exchange interactions are related to the structural relaxations. Nevertheless, the mean field approximation predicts a slightly lower N\'eel temperature in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ than in MnN in contrast with experiment. Effects beyond mean field are discussed and are deemed not to be able to provide an explanation for this discrepancy. We suggest that the observed phase transition in ${\mathrm{Mn}}_{3}{\mathrm{N}}_{2}$ previously interpreted as the AFM-paramagnetic phase transition may in reality be an order-disorder transition of the N vacancies.