Speaker
Description
Two-dimensional van der Waals (vdW) magnets such as the chromium trihalides CrX₃ (X = Cl, Br, I) suit spintronic and magneto-optical heterostructures. First-principles methods struggle to describe them: strong intralayer covalent bonding coexists with weak interlayer dispersion, semi-local functionals overestimate interlayer spacing and underestimate exfoliation energy, and localized Cr 3d states need a Hubbard correction. We benchmark 17 exchange-correlation functionals spanning semi-local GGA (PBE, PBEsol) and their D3(BJ)-corrected variants [1], nonlocal vdW functionals (vdW-DF, vdW-DF2, optPBE-vdW, optB88-vdW, optB86b-vdW, rev-vdW-DF2, vdW-DF-cx [2], rVV10, PBE+rVV10L), and meta-GGA nonlocal functionals (SCAN+rVV10, r²SCAN+rVV10) [3], for bulk, monolayer, and bilayer CrX₃, using DFT+U (Liechtenstein) [4] in VASP [5].
All functionals match the experimental in-plane lattice constant a to within about 5%, so covalent Cr–X bonding is captured even semi-locally. The out-of-plane constant c is far more sensitive: dispersion-free functionals overestimate it by up to 16%, while nonlocal vdW functionals and dispersion corrections cut that to a few percent. Only PBE+D3BJ, optB86b-vdW, and vdW-DF-cx [6] keep errors below 1% for a and below 2% for c across all three compounds, with vdW-DF-cx giving the lowest average error (Figure 1).
Exfoliation energies are near zero or slightly negative for PBE/PBEsol and rise once dispersion is included, following CrCl₃ < CrBr₃ < CrI₃ as halogen polarizability grows. PBE+rVV10L binds noticeably more strongly than other nonlocal functionals, which otherwise resemble the simpler D3BJ correction.
Band gaps (CrCl₃: 2.4–3.7 eV; CrBr₃: 1.8–2.9 eV; CrI₃: 1.0–2.0 eV, bulk to monolayer) are consistently underestimated by semi-local and D3(BJ)-corrected GGA functionals. SCAN+rVV10 overshoots the experimental gaps considerably, while r²SCAN+rVV10 gives a better estimate at lower cost. Both capture the widening from bulk to monolayer and decrease from CrCl₃ to CrI₃.
Except for PBE+rVV10L in CrCl₃, every functional predicts a ferromagnetic monolayer with an out-of-plane easy axis, matching experiment. The MAE is small for CrCl₃ (−0.01 to −0.03 meV/Cr) and grows with halogen spin–orbit coupling, reaching about −0.5 meV/Cr for CrI₃ (Table 1). The exchange constant J is positive for all halides except under PBE+rVV10L and rises from CrCl₃ to CrI₃, pointing to stronger Cr–X–Cr superexchange as halogen polarizability grows. CrCl₃ sits closest to the ferromagnetic–antiferromagnetic crossover, so its J is most sensitive to the functional used.
Exfoliation energy, band gaps, and MAE depend strongly on the functional, but structural and magnetic trends across CrX₃ hold regardless. PBE+D3BJ matches the accuracy of the costlier nonlocal vdW functionals at lower cost, while vdW-DF-cx and optB86b-vdW remain most reliable for higher structural precision.
References
[1] S. Grimme, S. Ehrlich, and L. Goerigk, Journal of Computational Chemistry 32, 1456 (2011).
[2] K. Berland and P. Hyldgaard, Phys. Rev. B - Condens. Matter Mater. Phys. 89, 1 (2014).
[3] J. Ning et al., Phys. Rev. B 075422, 1 (2022).
[4] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B 52, 5467 (1995).
[5] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
[6] J. Klimeš, D. R. Bowler, and A. Michaelides, Phys. Rev. B - Condens. Matter Mater. Phys. 83, (2011).