Modulated Ferromagnetism and Electric Polarization Induced by Surface Vacancy in MX₂Monolayers

Vacancies are inevitable in present manufacturing due to technical limitations, which inspired us to explore feasible approaches to modulate physical properties via vacancies. A recent tentative exploration was applied in CrX₃(X = F, Cl, Br, I) systems to induce ferroelectricity in 2D magnets by introducing surface anion vacancies, which proved feasible to generate multiferroic behavior. Moreover, vacancies are expected to affect magnetism in multiple aspects other than multiferroicity. This inspired us to explore the comprehensive impact of vacancies in 2D magnetic systems and their underlying mechanisms. We began research on monolayer MX₂transition metal compounds including MnS₂, VS₂, and MSe₂(M = V, Cr, Mn, and Nb) via first-principles calculations. It is demonstrated that the vacancy can induce remarkable multiferroic behavior, varying among system compositions, which is consistent with the theoretical expectation. In addition, we discovered the modulation effect of vacancy on multiple magnetic parameters, including the magnetic moment, the exchange integral, the magnetic anisotropy energy, and Curie temperature. Further theoretical investigation reveals that the vacancy modulates the super exchange interaction via the distortion of lattice and thus affects the ferromagnetic coupling. Variations of other parameters are also verified to be closely related to vacancies. Our research confirms the existence of multiferroics induced by the anion vacancy in low-dimensional ferromagnets and enlightened by the underlying fundamental principle mechanisms of their magnetism.