Figure 76.

Slater-Pauling or volcano plot for 2D magnets. (a) High-throughput screening undertook over several crystal structures and elements of the periodic table including formulas MX′₂, MX, MX′₃, MPX₃, MX₂, and CrFTe₃ with M = Sc–Zn, La, Y; X′=Cl, Br, I; X=O, S, Se, Te; F=Si, Ge. The simulations included mainly transition metals with 3d electrons, but some with 4d and 5d were included for comparison. (b) Variation of the local magnetic moment M(μ_B) at the metal atom as function of its valence Z(e^–). Bader charge analysis was used to extract Z for each metal atom at the compound. The solid lines show a fit to the data set on two different regimes according to the filling of the valence. The positive slope (weak magnets) can be fairly well fitted using M⁺ = 0.84Z – 1.15 (with a linear regression coefficient R² = 0.96) and the negative (strong magnets) with M^– = −0.87Z + 9.27 (R² = 0.90). An electron counting argument can be used to explain both regimes as discussed in the text. (c) Spin resolved density of states (DOS) for monolayer MPTe₃ (M = V, Cr, Mn, Fe, Co, Ni) as function of the energy ε displaying the spin up density n^up (faint gray) and spin down n^down (faint brown) at opposite sides. The energy is shifted to the Fermi energy ε_F at zero. (d) Variation of the model predicted magnetization versus DFT + U calculated magnetization for the compounds showed in (a). Calculations were performed using the VASP code⁸⁸⁴ using a 21 × 21 × 1 k-sampling grid, the Dudarev (GGA+U) scheme⁸⁸⁵ with Hubbard U values following those in ref (341). The energy cutoff is set to 600 eV, the convergence criteria for energy to 10^–7 eV and for the forces to 0.01 eV/Å. In order to avoid interactions between the layers, we applied periodic boundary conditions with a vacuum space of 25 Å. We used the projector augmented wave (PAW)⁸⁸⁶ methods with a plane wave basis. The Vosko–Wilk–Nusair modification scheme⁸⁸⁷ is applied for the spin-polarized calculations. All images in this figure are original, and no permissions are required.