Transferable mechanism of perpendicular magnetic anisotropy switching by hole doping in V$X_2$ ($X$=Te, Se, S) monolayers

TL;DR

The work reveals a transferable mechanism for switching 2D ferromagnetic VX2 monolayers from in-plane to perpendicular magnetic anisotropy via hole doping. It shows that first-order spin-orbit coupling acting on topmost degenerate valence states with $m_l\neq0$ drives PMA, with the effect being stronger when the valence-band edge hosts degenerate orbitals protected by symmetry. The authors formulate simple criteria and demonstrate band-engineering routes to promote PMA with minimal hole doping, including strain-induced reordering of valence-band edge states. They validate the mechanism across VTe2, VSe2, and VS2, discuss robustness against the Hubbard $U$, and extend the concepts to additional materials (e.g., MnX2), highlighting practical pathways for high-performance spintronic materials. The work thus provides a fundamental, design-principle framework for tunable PMA in 2D magnets via hole doping and band engineering.

Abstract

The ability to tune and switch magnetic anisotropy to a perpendicular orientation is a key challenge for implementing 2D magnets in spintronic devices. H-phase vanadium dichalcogenides V$X_2$ ($X$=Te, Se, S) are promising ferromagnetic semiconductors with large magnetic anisotropy energy (MAE). Recent work has shown that hole doping can switch their easy axis to out-of-plane, though the microscopic origin of this perpendicular magnetic anisotropy (PMA) remains unclear. Using density-functional-theory calculations, we demonstrate that the PMA enhancement arises from first-order spin-orbit coupling (SOC) acting on topmost degenerate valence states with nonzero orbital angular momentum projection ($m_l\ne 0$). In this case, the $\hat{L}_z\hat{S}_z$ term dominates for perpendicular magnetization, while in-plane orientations involve only weaker, second-order SOC contributions. The increased valence bandwidth leads to depletion of higher-energy states upon hole doping, stabilizing PMA. From this mechanism, we identify two transferable design principles for enhancing MAE under weak hole doping: (i) orbital degeneracy at the valence-band edge protected by point-group symmetry and (ii) finite SOC in the degenerate manifold. Notably, we identify multiple magnetic semiconductors that meet these criteria and display enhanced MAE under hole doping. Furthermore, we show that band engineering can strategically place these degenerate orbitals at the valence band edge, significantly boosting PMA when hole-doped. We also examine trends in VTe$_2$, VSe$_2$, and VS$_2$ to determine the influence of crystal-field splitting, exchange interaction, and orbital hybridization on the valence band edges. These results provide both a fundamental understanding of PMA switching upon hole doping and a transferable strategy for tuning magnetic anisotropy, essential for designing high-performance spintronic materials.

Figures (25)

• Figure 1: a) Trigonal prismatic structure of H-VTe2 (blue: V, gray: Te) with the top view in the upper panel and side view in the lower panel. The parallelogram marks the unit cell with lattice constant $a$. Other vanadium dichalcogenide monolayers in the H phase have the same type of structure replacing Te with Se or S. b) The path in the Brillouin zone used in the band structure calculations. Phonon dispersion of H-VTe2. The inset illustrates the path in the Brillouin zone used in the phonon and band structure calculations.
• Figure 2: MAE versus charge carrier doping concentrations $\delta$ for FM H-VTe2. The calculated $E_{MCA}$ corresponds to the MAE since $E_{SA}$ is 15 $\mu$eV for the pristine case, and smaller than 18 $\mu$eV for all doping levels shown in the plot (see Supplementary Section S3). Hole doping corresponds to $\delta>0$ while electron doping $\delta<0$.
• Figure 3: (a) Spin-polarized band structure of H-VTe2; the blue/red bands represent majority/minority spin channels. Fully relativistic spin-projected bands for pristine H-VTe2 with (b) in-plane and (c) out-of-plane magnetization. The energies are referenced to the vacuum level and the dotted line denotes the Fermi level. The bar at the right indicates the color code for the band projection of the spins along $x$ in (b) and along $z$ in (c).
• Figure 4: Fully relativistic band edges of the undoped (top) and the hole-doped (with increasing concentration from $\delta=+0.03$ to $\delta=+0.05$ to $\delta=+0.10$ h/cell towards the bottom panels) H-VTe2 for in-plane (left) and out-of-plane (right) magnetization direction. Energy values are relative to the vacuum potential. The horizontal dashed lines are the Fermi levels.
• Figure 5: (a) MAE versus charge carrier doping concentrations $\delta$ for FM VSe2 and VS2. The calculated $E_{MCA}$ corresponds to the MAE since $E_{SA}$ is negligible (see Supplementary Section S2). Hole doping corresponds to $\delta>0$ while electron doping $\delta<0$. Band structure of pristine (b) VSe2 and (c) VS2 monolayers without (cyan/magenta thick curves for the majority/minority spin bands) and with (thin curves) spin-orbit coupling effect. The bar at the right indicates the color code for the band projection of the spins along the corresponding magnetization direction. Energy values are relative to the corresponding vacuum potential. The horizontal line marks the Fermi level.