Ab initio prediction on ferrotoroidic and electronic properties of olivine Li4MnFeCoNiP4O16

First-principles calculations predict that olivine Li₄MnFeCoNiP₄O₁₆ has a large toroidal moment and ferrimagnetic configuration with a magnetic moment of 1.99μ_B per formula unit. Density functional theory plus U (DFT+U) shows an indirect band gap of 0.65~eV in this hypothetical material. The band gap is not simply related to the electronic conductivity when it is used as cathode material in rechargeable Li-ion batteries. Based on the orbital-resolved density of states for the transition-metal ions in the hypothetical material, Co, Ni and Mn are in the high-spin configuration while Fe is in the low-spin configuration, which leads to a large resulting toroidal moment deriving from the Co and Ni ions. The spin configuration of the transition-metal ions in the system breaks the space- and time-inversion symmetry and leads to the magnetoelectric property simultaneously. The ferrotoroidic domain, the fourth form of ferroic, is observed in this new material, as in the case of LiCoPO_4 reported recently.