The magnetism of 1T-MX₂ (M = Zr, Hf; X = S, Se) monolayers by hole doping

The magnetism of hole doped 1T-MX₂ (M = Zr, Hf; X = S, Se) monolayers is systematically studied by using first principles density functional calculations. The pristine 1T-MX₂ monolayers are semiconductors with nonmagnetic ground states, which can be transformed to ferromagnetic states by the approach of hole doping. For the unstrained monolayers, the spontaneous magnetization appears once above the critical hole density (10¹⁴ cm^-2), where the p orbital of S or Se atoms contributes the most of the magnetic moment. As the tensile strains exceed 4%, the magnetic moments per hole of ZrS₂ and HfS₂ monolayers increase sharply to a saturated value with increasing hole density, implying obvious advantages over the unstrained monolayers. The phonon dispersion calculations for the strained ZrS₂ and HfS₂ monolayers indicate that they can keep the dynamical stability by hole doping. Furthermore, we propose that the fluorine atom modified ZrS₂ monolayer could obtain stable ferromagnetism. The magnetism in hole doped 1T-MX₂ (M = Zr, Hf; X = S, Se) monolayers has great potential for developing spintronic devices with desirable applications.