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.