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Recently, two monolayer magnetic materials, i.e., FePS3 and NiPS3, have beensuccessfully fabricated. Despite that they have the same atomic structure, thetwo monolayers exhibit distinct magnetic properties. FePS3 holds anout-of-plane zigzag antiferromagnetic (AFM-ZZ) structure, while NiPS3 exhibitsan in-plane AFM-ZZ structure. However, there is no theoretical model which canproperly describe its magnetic ground state due to the lack of a fullunderstanding of its magnetic interactions. Here, by combining thefirst-principles calculations and the newly developed machine learning method,we construct an exact spin Hamiltonian of the two magnetic materials. Differentfrom the previous studies which failed to fully consider the spin-orbitcoupling effect, we find that the AFM-ZZ ground state in FePS3 is stabilized bycompeting ferromagnetic nearest-neighbor and antiferromagnetic thirdnearest-neighbor exchange interactions, and combining single-ion anisotropy.Whereas, the often ignored nearest-neighbor biquadratic exchange is responsiblefor the in-plane AFM-ZZ ground state in NiPS3. We additionally calculatespin-wave spectrum of AFM-ZZ structure in the two monolayers based on the exactspin Hamiltonian, which can be directly verified by the experimentalinvestigation. Our work provides a theoretical framework for the origin ofAFM-ZZ ground state in two-dimensional materials.

Origin of zigzag antiferromagnetic orders in XPS3 (X= Fe, Ni) monolayers