Magnetism in the layered transition-metal thiophosphates<i>M</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">PS</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>(<i>M</i>=Mn, Fe, and Ni)

Anisotropic magnetic susceptibilities of single crystals of the layered transition-metal thiophosphates ${\mathrm{MnPS}}_{3}$, ${\mathrm{FePS}}_{3}$, and ${\mathrm{NiPS}}_{3}$ have been measured as a function of temperature. The materials order antiferromagnetically at low temperatures, the N\'eel temperatures being 78, 123, and 155 K, respectively. In the ordered state, the magnetization axis lies perpendicular to the layers for ${\mathrm{MnPS}}_{3}$ and ${\mathrm{FePS}}_{3}$, while for ${\mathrm{NiPS}}_{3}$ it lies in the layer. In the paramagnetic regime, the anisotropies of these compounds are different; while the susceptibility for ${\mathrm{MnPS}}_{3}$ is isotropic and that for ${\mathrm{NiPS}}_{3}$ shows only a weak ansiotropy, ${\mathrm{FePS}}_{3}$ exhibits highly anisotropic susceptibility. The anisotropic susceptibilities have been analyzed to obtain information on the state of the magnetic ions and the nature of magnetic interactions between them. The results show that ${\mathrm{MnPS}}_{3}$, ${\mathrm{FePS}}_{3}$, and ${\mathrm{NiPS}}_{3}$ form a unique class of compounds. Although all three compounds are isostructural with the magnetic lattice being the two-dimensional honeycomb, the spin dimensionalities for the three are different. While ${\mathrm{MnPS}}_{3}$ is best described by the isotropic Heisenberg Hamiltonian, ${\mathrm{FePS}}_{3}$ is most effectively treated by the Ising model and ${\mathrm{NiPS}}_{3}$ by the anisotropic Heisenberg Hamiltonian. The origin of the anisotropy in these compounds has been discussed, and it is shown how it arises from a combination of spin-orbit coupling and the trigonal distortion of the M${\mathrm{S}}_{6}$ octahedra. The magnetic exchange constant, J and the zero-field splitting energies of the ground state of the transition-metal ion have been evaluated from the anisotropic paramagnetic susceptibilities.