Exchange and Dzyaloshinskii-Moriya interactions in bulk FeGe: Effects of atomic vacancies

We examine the effects of atomic vacancies on the (1) spin interaction, and (2) electronic character in the cubic B20 chiral magnet FeGe. For the former, Heisenberg exchange and Dzyaloshinskii-Moriya (DM) interactions are studied. The latter is done via a particular Wannier flavor of the Hamiltonian in the form of maximally-localized Wannier functions (MLWFs). Using first-principles calculations based on full-potential linearized augmented plane-wave (FLAPW)-based density functional theory (DFT), the spin order of bulk FeGe, in its pristine form, and with a Fe (Fe75%Ge100%) or Ge vacancy (Fe100%Ge75%) is investigated. Despite the presence of vacancies, the ground state of FeGe remains helimagnetic, i.e. spin spirals in FeGe are fairly robust. The energetic stability of FeGe increases in the presence of the vacancies. The spiral size is increased by approximately 40%, suggesting that vacancies can be introduced to manipulate the chiral order. The vacancies lift the band degeneracy in the valence manifold of the Wannier-interpolated band structures. Only the spin-down Fermi surfaces are substantially different between the pristine and defective FeGe; it is electron-like in the pristine case, but largely hole-like in the defective ones. The Ge vacancy splits the Fermi surface more than the Fe vacancy. The Heisenberg exchange between nearest Fe pairs is ferromagnetic in pristine FeGe. This Fe-Fe interaction remains ferromagnetic, albeit a slight decrease in strength, in the presence of a Fe vacancy. In contrast, a Ge vacancy in FeGe induces anti-ferromagnetism between nearest Fe pairs. By including spin-orbit coupling effects, we find that the DM interaction of defective FeGe is reversed in sign, and it is more uniform in strength along the three highly symmetric directions, relative to that in pristine FeGe. All in all, the versatility of FeGe makes it an excellent functional material, especially in data storage and spintronics applications. (C) 2017 Author(s).