Recently, Associate Professor Hu Zhixin from Tianjin University collaborated with the research groups of Professor Ji Wei and Associate Researcher Wang Cong from Renmin University of China. Based on first-principles calculations and using both VASP and the domestic first-principles software ABACUS, they revealed the microscopic mechanisms of the changes in the easy magnetization axis and topological properties with the number of layers in MnSe₂. The relevant research results were published in the journal Physical Review B under the title "Interlayer coupling driven rotation of the magnetic easy axis in MnSe₂ monolayers and bilayers" (DOI: 10.1103/PhysRevB.111.054422). The first authors of the paper are Zhang Zhongqin and Wang Cong.
Research Background
Magnetic anisotropy plays a crucial role in maintaining the long-range magnetic order of 2D magnets at finite temperatures and is closely related to the magnetic coercivity (a core parameter determining the hard or soft magnetic behavior of materials). As an effective means of regulating magnetism, interlayer coupling has received extensive attention in 2D materials in recent years. However, research on how interlayer coupling affects magnetic anisotropy remains relatively limited, which has hindered to some extent the in-depth understanding of its physical mechanism and the expansion of its applications in spintronics.
Research Results
1T-MnSe₂ is a 2D van der Waals ferromagnetic metal. In monolayers and bilayers, Mn atoms within the layer or between different layers are ferromagnetically coupled. The calculation results show that the easy magnetization axis of monolayer MnSe₂ is along an inclined direction deviated 67° from the z-axis; in the bilayer, the easy magnetization axis rotates to the z-axis direction.
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.
Figure 2 : (a) Side view of the interlayer differential charge density of bilayer MnSe₂; (b) Contributions of Mn and Se atoms to MAE in monolayer and bilayer MnSe₂; (c - d) Contributions of orbitals of monolayer Se and bilayer Se-interface to MAE.
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.
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.
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.
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.
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.
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.
Conclusion
This study reveals the key role of interlayer coupling in regulating the direction of the easy magnetization axis of 2D magnetic materials. Through the MAE analysis of atomic and orbital decomposition, it is found that non-metal Se atoms, especially the occupation and coupling of their p orbitals, play a core role in the rotation of the easy magnetization axis. These findings not only deepen the understanding of the physical mechanism of magnetic anisotropy in 2D magnets but also provide a theoretical basis and material foundation for the design of future spintronic devices.