Spin model for the Honeycomb $\mathrm{NiP}{\mathrm{S}}_3$

Abstract

In the Van der Waal material $\mathrm{NiP}{\mathrm{S}}_3$, 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 $\mathrm{NiP}{\mathrm{S}}_3$, 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 ${\mathrm{K}}_1$ allowing the completion of a minimal ${\mathrm{J}}_1-{\mathrm{J}}_3-{\mathrm{K}}_1$ spin Hamiltonian for $\mathrm{NiP}{\mathrm{S}}_3$. In bulk, a ferromagnetic first nearest neighbor ${\mathrm{J}}_1$ and a more significant antiferromagnetic third nearest neighbor spin coupling ${\mathrm{J}}_3$ agreed with the literature, while in monolayer ${\mathrm{J}}_1$ 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 $\mathrm{NiP}{\mathrm{S}}_3$ monolayers.

6 pages, 3 figures, 2 tables