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We examined the magnetic ground states, the preferred spin orientations and the spin exchanges of four layered phases MPS 3 (M = Mn, Fe, Co, Ni) by first principles density functional theory plus onsite repulsion (DFT + U) calculations. The magnetic ground states predicted for MPS 3 by DFT + U calculations using their optimized crystal structures are in agreement with experiment for M = Mn, Co and Ni, but not for FePS 3 . DFT + U calculations including spin-orbit coupling correctly predict the observed spin orientations for FePS 3 , CoPS 3 and NiPS 3 , but not for MnPS 3 . Further analyses suggest that the ||z spin direction observed for the Mn 2+ ions of MnPS 3 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 MPS 3 , which are mediated by the symmetry-adapted group orbitals of P 2 S 6  4- and exhibit unusual features unknown from other types of spin exchanges.

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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)