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 Jb 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 J1 are antiferromagnetically coupled by the spin exchange J2, in agreement with available experimental data.