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We present a systematic study of the electronic and magnetic properties oftwo-dimensional ordered alloys, consisting of two representative hosts(MnPS$_3$ and NiPS$_3$) of transition metal phosphorus trichalcogenides dopedwith $3d$ elements. For both hosts our DFT+U calculations are able toqualitatively reproduce the ratios and signs of all experimentally observedmagnetic couplings. The relative strength of all antiferromagnetic exchangecouplings, both in MnPS$_3$ as well as in NiPS$_3$, can successfully beexplained using an effective direct exchange model: they reveal that thethird-neighbor exchange dominates in NiPS$_3$ due to the filling of the$t_{2g}$ subshell, whereas for MnPS$_3$ the first neighbor exchange isprevailed owing to the presence of the $t_{2g}$ magnetism. On the other hand,the nearest neighbor ferromagnetic coupling in NiPS$_3$ can only be explainedusing a more complex superexchange model and is (also) largely triggered by theabsence of the $t_{2g}$ magnetism. For the doped systems, the DFT+Ucalculations revealed that magnetic impurities do not affect the magneticordering observed in the pure phases and thus in general in these systemsferromagnetism may not be easily induced by such a kind of elemental doping.However, unlike for the hosts, the first and second (dopant-host) exchangecouplings are of similar order of magnitude. This leads to frustration in caseof antiferromagnetic coupling and may be one of the reasons of the observedlower magnetic ordering temperature of the doped systems.

Limited ferromagnetic interactions in monolayers of MPS$_3$ (M=Mn, Ni)