Stabilization of zigzag order in NiPS${}_3$ via positive biquadratic interaction

Despite extensive research, the precise spin Hamiltonian of the van der Waals antiferromagnet NiPS${}_3$ – which hosts a zigzag-ordered ground state – remains debated. While consensus has emerged on ferromagnetic nearest-neighbor ($J_1$) and antiferromagnetic third-nearest-neighbor ($J_3$) Heisenberg interactions, recent studies suggest a biquadratic ($B$) exchange term may also play a role, though its estimated magnitude varies widely. To address this controversy, we perform density functional theory calculations and extract a positive biquadratic interaction with $B\mathrm{/}{J}_3\approx 0.44$. Within the minimal $J_1$-$J_3$-$B$ model, we show that these parameters naturally stabilize zigzag ordering using minimally augmented spin-wave theory. Density-matrix renormalization group calculations further validate our extracted parameters as a reasonable description of the ground state. Although fully resolving the spin Hamiltonian of NiPS${}_3$ requires further investigation, our findings provide new insights into its biquadratic interaction.