Torus*

The giant single-molecule magnet Mn₈₄ has a shape of torus of eighty-four Mn³⁺ ions (S=2). As the manganese atoms in Mn₈₄ are all bridged by O^2- or MeO^- groups, strong pairwise exchange interactions between these manganese atoms are expected. Even though the magnetic susceptibility of this system has been measured experimentally, its electronic-magnetic structure and spin-spin couplings remain unknown. In this work, we investigate these interactions using first-principles calculations, from which a Heisenberg model is developed. The exchange coupling constants are extracted by fitting to the total energies of different spin configurations of Mn₈₄. In addition, we compute the magnetic anisotropy energy by including spin-orbital couplings.