Spin model for the honeycomb NiPS 3

In the Van der Waals material NiPS 3 , Ni atoms have spin S = 1 and realize a honeycomb lattice. Six sulfur atoms surround each Ni and split their d manifold into three filled and two unfilled bands. Aimed to determine the spin Hamiltonian of NiPS 3 , we study its exchange mechanisms using a two-band half-filled Hubbard model. Hopping between d-orbitals is mediated by p orbitals of sulfur and gives rise to bilinear and biquadratic spin couplings in the limit of strong electronic correlations. The microscopic model exposed a ferromagnetic biquadratic spin interaction K 1 , allowing the completion of a minimal J 1 − J 3 − K 1 spin Hamiltonian for NiPS 3 . In bulk, a ferromagnetic first nearest neighbor J 1 and a more significant antiferromagnetic third nearest neighbor spin coupling J 3 agreed with the literature, while in monolayer, J 1 is positive and very small in comparison. Using a variational scheme, we found that a zig-zag antiferromagnetic order is the ground state of bulk samples. The zig-zag pattern is adjacent to commensurate and incommensurate spin spirals, which could hint at the puzzling results reported in NiPS 3 monolayers.