diff --git a/source/_posts/ABACUS_16_04_2025.md b/source/_posts/ABACUS_16_04_2025.md index b6dc0f3..f2a2d2f 100644 --- a/source/_posts/ABACUS_16_04_2025.md +++ b/source/_posts/ABACUS_16_04_2025.md @@ -23,7 +23,7 @@ Magnetic anisotropy plays a crucial role in maintaining the long-range magnetic *Figure 1 : (a) Top and side views of monolayer MnSe₂; (b - c) Side and oblique views of AA-stacked bilayer MnSe₂; (d) Definition of polar angle θ and azimuthal angle φ in the spherical coordinate system; (e - f) Energies of magnetic moments of monolayer (e) and bilayer (f) MnSe₂ along different directions.* -The calculation results of the interlayer differential charge density (Figure 2a) indicate that MnSe₂ has a strong interlayer coupling. The researchers further decomposed the contribution of the magnetic anisotropy energy (MAE) to atoms (Figure 2b) and orbitals (Figure 2c - d), and found that the interaction between the $`p_y`$ and $`p_z`$ orbitals of interface Se atoms plays a key role in the transformation of the easy magnetization axis. +The calculation results of the interlayer differential charge density (Figure 2a) indicate that MnSe₂ has a strong interlayer coupling. The researchers further decomposed the contribution of the magnetic anisotropy energy (MAE) to atoms (Figure 2b) and orbitals (Figure 2c - d), and found that the interaction between the py and pz orbitals of interface Se atoms plays a key role in the transformation of the easy magnetization axis.
@@ -33,10 +33,13 @@ The calculation results of the interlayer differential charge density (Figure 2a According to the second-order perturbation theory, the contribution of electron states to MAE can be expressed by the following formula: +
+ +
-where o and u represent the occupied and unoccupied states, respectively. Since the energy difference $`E_{o}-E_{u}`$ between the occupied and unoccupied states appears in the denominator, the states closer to the Fermi level have a greater impact on MAE, while the states far from the Fermi level contribute relatively less. +where o and u represent the occupied and unoccupied states, respectively. Since the energy difference Eo - Eu between the occupied and unoccupied states appears in the denominator, the states closer to the Fermi level have a greater impact on MAE, while the states far from the Fermi level contribute relatively less. -Combined with the electronic structure analysis, the researchers found that in monolayer MnSe₂, the p_z orbital of Se atoms is far from the Fermi level (Figure 3a, 3c), so the coupling between $`p_z`$ and $`p_y`$ is weak; in the bilayer structure, the interlayer coupling causes the $`p_z`$ orbitals of interface Se atoms to hybridize, forming bonding and antibonding states (Figure 3d). The antibonding states split and approach the Fermi level, thus enhancing the coupling between the $`p_y`$ and $`p_z`$ orbitals and making the easy magnetization axis of bilayer MnSe₂ out-of-plane. +Combined with the electronic structure analysis, the researchers found that in monolayer MnSe₂, the p_z orbital of Se atoms is far from the Fermi level (Figure 3a, 3c), so the coupling between pz and py is weak; in the bilayer structure, the interlayer coupling causes the pz orbitals of interface Se atoms to hybridize, forming bonding and antibonding states (Figure 3d). The antibonding states split and approach the Fermi level, thus enhancing the coupling between the py and pz orbitals and making the easy magnetization axis of bilayer MnSe₂ out-of-plane. In addition, MnSe₂ also exhibits topological properties that change with the number of layers, including the evolution of the Chern number and surface states (Figure 3e - f). The layer evolution of the above electronic structure and topological properties was calculated and verified using the domestic first-principles software ABACUS. @@ -44,7 +47,7 @@ In addition, MnSe₂ also exhibits topological properties that change with the n
-*Figure 3 here: (a - b) Spin-down band structures of monolayer and bilayer MnSe₂; (c) Projected density of states of $`p_y`$ and $`p_z`$ orbitals of (interface) Se at the Gamma point in monolayer and bilayer; (d) Charge densities of the marked states in (a - c); (e - f) Surface states of monolayer and bilayer MnSe₂.* +*Figure 3 here: (a - b) Spin-down band structures of monolayer and bilayer MnSe₂; (c) Projected density of states of py and pz orbitals of (interface) Se at the Gamma point in monolayer and bilayer; (d) Charge densities of the marked states in (a - c); (e - f) Surface states of monolayer and bilayer MnSe₂.* Some external regulation methods can also affect the occupation state of the p orbitals of Se atoms, and thus are expected to achieve the regulation of the direction of the easy magnetization axis of the material. Based on this, the researchers systematically studied a variety of external regulation methods. The results show that by changing the interlayer stacking mode (Figure 4a - b), applying charge doping (Figure 4c), introducing biaxial strain (Figure 4d), and replacing non-metal atoms, the direction of the easy magnetization axis of MnSe₂ can be effectively regulated, providing new ideas for realizing the controllable regulation of magnetic anisotropy in 2D magnets. @@ -52,7 +55,7 @@ Some external regulation methods can also affect the occupation state of the p o -*Figure 4 here: (a) Top and side views of AB-stacked bilayer MnSe₂; (b) Atom-decomposed MAE of AA and AB stackings; (c - d) Contributions of different atoms to MAE in monolayer MnSe₂ and the changes of $`E_{X}-E_{ea}`$ with doping concentration and in-plane biaxial strain.* +*Figure 4 here: (a) Top and side views of AB-stacked bilayer MnSe₂; (b) Atom-decomposed MAE of AA and AB stackings; (c - d) Contributions of different atoms to MAE in monolayer MnSe₂ and the changes of EX - Eea with doping concentration and in-plane biaxial strain.* ## Conclusion