Critical cation-anion radius ratio and two-dimensional antiferromagnetism in van der Waals TMPS₃ (TM = Mn, Fe, Ni)

Two-dimensional TMPS₃ antiferromagnets, transition metal (TM) = Mn, Fe, Ni, are studied by high-energy x-ray diffraction and atomic pair distribution analysis over a broad temperature range. Results show that the compounds exhibit common average but distinct local atomic structure, including distinct distortions of the constituent TM-S octahedra, magnitude and direction of atomic displacements, TM-TM distances and TM-S-TM bond angles. The differences in the local structure may be rationalized in terms of the Pauling's rule for the critical ratio of TM²⁺ cation and S^2- anion radii for octahedral coordination. We argue that the observed differences in the local structure are behind the differences in the antiferromagnetic properties of TMPS₃ compounds, including different magnetic anisotropy and Neel temperature.