Ab initio prediction on ferrotoroidic and electronic properties of olivine Li4MnFeCoNiP4O16

First-principles calculations predict that olivineLi₄MnFeCoNiP₄O₁₆ has a large toroidal moment andferrimagnetic 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 conductivitywhen it is used as cathode material in rechargeable Li-ionbatteries. Based on the orbital-resolved density of states for thetransition-metal ions in the hypothetical material, Co, Ni and Mnare in the high-spin configuration while Fe is in the low-spinconfiguration, which leads to a large resulting toroidal momentderiving from the Co and Ni ions. The spin configuration of thetransition-metal ions in the system breaks the space- andtime-inversion symmetry and leads to the magnetoelectric propertysimultaneously. The ferrotoroidic domain, the fourth form offerroic, is observed in this new material, as in the case ofLiCoPO_4 reported recently.