Analysis of the spin exchange interactions and the ordered magnetic structures of lithium transition metal phosphates LiMPO₄ (M = Mn, Fe, Co, Ni) with the olivine structure

The olivine-type compounds LiMPO₄ (M = Mn, Fe, Co, Ni) consist of MO₄ layers made up of corner-sharing MO₆ octahedra of high-spin M²⁺ ions. To gain insight into the magnetic properties of these phosphates, their spin exchange interactions were estimated by spin dimer analysis using tight binding calculations and by electronic band structure analysis using first principles density functional theory calculations. Three spin exchange interactions were found to be important for LiMPO₄, namely, the intralayer superexchange J₁, the intralayer super-superexchange J_b along the b-direction, and the interlayer super-superexchange J₂ along the b-direction. The magnetic ground state of LiMPO₄ was determined in terms of these spin exchange interactions by calculating the total spin exchange interaction energy under the classical spin approximation. In the spin lattice of LiMPO₄, the two-dimensional antiferromagnetic planes defined by the spin exchange J ₁ are antiferromagnetically coupled by the spin exchange J ₂, in agreement with available experimental data.