Density functional study of the electronic structure of the non-collinear helical magnet Ba₃NbFe₃Si₂O₁₄ (Langasite): Magnetic exchange and Dzyaloshinskii-Moriya interactions

Ba₃NbFe₃Si₂O₁₄ is an iron based compound, which consists of a Fe trimer in the ab-plane with a large spin moment ≈ 5 μ_B /Fe. The spins of Fe trimer form a 120⁰ non-collinear antiferromagnetic structure in the ab-plane followed by a helical structure with a propagation vector q = (0,0,1/7). We study the electronic band structure using density functional theory (DFT), which shows an insulating gap due to the exchange splitting of the 3d bands. The features of the computed optical spectra are discussed in terms of the band structure. In addition, we study the magnetic exchange parameters by mapping the density functional total energy to exchange models. The absence of inversion symmetry in conjunction with the spin-orbit interaction leads to the Dzyaloshinskii-Moriya interaction (DMI) of the type D.S₁ x S₂, which is necessary to explain the observed spin-wave energies. We study the DMI from a model extracted from the DFT in order to gain insight into the magnetic interactions in the system.