Optimizing Density Functional Theory for Strain-Dependent Magnetic Properties of Monolayer MnBi$_2$Te$_4$ with Diffusion Monte Carlo

Abstract

Monolayer MnBi$_{2}$Te$_{4}$ (MBT) is an intrinsically magnetic topological insulator whose magnetic response is strongly affected by strain and electron correlation. In density functional theory with an on-site Hubbard correction (DFT+$U$), however, predictions vary substantially with the choice of Hubbard $U$, making it difficult to establish a reliable strain-dependent picture of magnetism in this system. Here we use diffusion Monte Carlo (DMC) to benchmark DFT+$U$ for monolayer MBT and to determine an effective $U$ as a function of strain. We find that the predicted magnetic phase diagram depends strongly on $U$, indicating that a single fixed value is not sufficient across the strain range considered. DMC nodal optimization further shows that the optimal $U$ increases with strain magnitude and is well captured by a simple quadratic form. When this DMC-informed strain-dependent $U$ is used in PBE+$U$, the calculated Mn local moments are brought into close agreement with DMC and are improved relative to commonly used fixed-$U$ choices. These results show that, for monolayer MBT, correlation strength itself should be treated as strain dependent, and they provide a practical many-body-guided strategy for improving strain-dependent DFT+$U$ descriptions of magnetic van der Waals materials.

Figures (6)

• Figure 1: Magnetic configurations of the monolayer MBT considered in this study: FM (a), AFM-stripy (b), AFM-zigzag 1 (c), and (d) AFM-zigzag 2. The stable magnetic phases among these four magnetic states depending on the in-plane strain, x and y, up to 10% of the tensile and compressive strains. The magnetic phase diagram changes drastically depending on the choice of exchange-correlation functional and Hubbard $U$ values: (e) PBE+$U$ = 3 eV, (f) LDA+$U$ = 4 eV, and (g) PBE+$U_{DMC}$, DMC optimized $U$ depending on strain.
• Figure 2: Magnetic moments of the Mn atoms in the pristine (unstrained) monolayer MBT based on the calculations with a) GGA+$U$ and b) LDA+$U$.
• Figure 3: Energy difference versus different choices of the $U$ parameter for a) GGA+$U$ and b) LDA+$U$ exchange correlation functionals. The energy difference is defined as the difference between the different magnetic states and the ferromagnetic state.
• Figure 4: Sensitivity analysis to guide optimal determination of Hubbard U via DMC. In (a) the absolute difference in $J_1$ exchange parameter between LDA+$U$ = 4.4 eV and PBE+$U$ = 3 eV is used to indicate the spin model sensitivity to U. Strain regions showing high sensitivity (large absolute $J_1$ difference) are used to select $x$ and $y$ strain points (circled in green) for subsequent determination of optimal $U$ via DMC. In (b) the DMC optimized $U$ (for PBE+$U$) is determined by the variational principle at zero strain. The distribution of minima resulting from resampled quadratic fits are shown in color.
• Figure 5: Variation in DMC optimized U vs strain. Panel (a) shows the near isotropic strain model for U supported by the DMC data collected at multiple strains ($U_{\mathrm{DMC}}(S)=U_0+\Delta U S^2$), with $S$ being the absolute magnitude of total strain. Panel (b) shows the same model for U, but as contours over the x/y strain field of the monolayer MBT.