Unusual Spin Exchanges Mediated by the Molecular Anion P2S64-: Theoretical Analyses of the Magnetic Ground States, Magnetic Anisotropy and Spin Exchanges of MPS3 (M = Mn, Fe, Co, Ni).

We examined the magnetic ground states, the preferred spin orientations and the spin exchanges of four layered phases MPS3 (M = Mn, Fe, Co, Ni) by first principles density functional theory plus onsite repulsion (DFT + U) calculations. The magnetic ground states predicted for MPS3 by DFT + U calculations using their optimized crystal structures are in agreement with experiment for M = Mn, Co and Ni, but not for FePS3. DFT + U calculations including spin-orbit coupling correctly predict the observed spin orientations for FePS3, CoPS3 and NiPS3, but not for MnPS3. Further analyses suggest that the ||z spin direction observed for the Mn2+ ions of MnPS3 is caused by the magnetic dipole-dipole interaction in its magnetic ground state. Noting that the spin exchanges are determined by the ligand p-orbital tails of magnetic orbitals, we formulated qualitative rules governing spin exchanges as the guidelines for discussing and estimating the spin exchanges of magnetic solids. Use of these rules allowed us to recognize several unusual exchanges of MPS3, which are mediated by the symmetry-adapted group orbitals of P2S64- and exhibit unusual features unknown from other types of spin exchanges.