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

Abstract

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 $B/J_3 \approx 0.44$. 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.

Figures (8)

• Figure 1: (a) Crystal structure of NiPS$_3$. The red, green, and blue arrows denote the Heisenberg interactions of the first three neighbors, respectively. (b) Sketch of the honeycomb lattice with the first three nearest-neighbor vectors, $\boldsymbol{\delta}_{\gamma}$, $\boldsymbol{\delta}_{\gamma}^{(2)}$, and $\boldsymbol{\delta}_{\gamma}^{(3)}$. (c) Brillouin zones of the magnetic primitive cell and the supercell. The dashed outline indicates the Brillouin zone of the zigzag supercell. The high-symmetry points along $\boldsymbol{\Gamma}$-$\textbf{X}$-$\textbf{M}'$-$\textbf{C}$-$\textbf{M}$ define the $K$-path for the band structure. $\textbf{b}_1$ and $\textbf{b}_2$, and $\textbf{b}_1'$ and $\textbf{b}_2'$ are the reciprocal lattice vectors of the primitive cell and the supercell, respectively.
• Figure 2: (a) Electronic structure and (b) DOS of monolayer NiPS$_3$ calculated by DS-PAW software. The high-symmetry points in the reciprocal space are indicated in Fig. \ref{['FIG-NiPS3']}(c). The horizontal dotted lines at zero energy are guides to the eye.
• Figure 3: Estimates of the exchange parameters $J_1$, $J_2$, $J_3$, and $B$ obtained from different sets of magnetic configurations. The optimal fits (red) are derived using all six linear and nonlinear configurations, while the mean values and error bars (black) are obtained from a statistical analysis of selected subsets.
• Figure 4: (a) Classical phase diagram of the $J_1$-$J_2$-$J_3$ model in the ($J_1/J_3$, $J_2/J_3$) parameter space with $J_3 = 1$. This phase diagram was mapped out by the energy comparison of three collinear phases (FM, AFM, and zigzag) and two proposed noncollinear spiral phases. Parameters specific to NiPS$_3$ are highlighted with a pentagram ($\star$). (b) Spin configurations of the FM, AFM, and zigzag phases, from the left to right.
• Figure 5: Classical energy per site $\mathcal{E}_{cl} = E_{cl}/N$ as a function of $J_1/J_3$ in the $J_1$-$J_3$ model, obtained from Monte Carlo simulations on $2\times L \times L$ clusters with $L = 12$ (red circles), 18 (green triangles), and 24 (blue squares). Solid lines represent the exact energy expressions for the FM, spiral-I, and zigzag phases. Inset: Classical phase diagram extracted from Fig. \ref{['FIG-J1J2J3CPD']}.