Structural Reconstruction Induced d-wave Altermagnetism in $\mathrm{V_{2}X_2}$ ($X = \mathrm{S, Se}$) monolayer

Original Abstract

Altermagnetism, featuring momentum-dependent spin splitting without relativistic effects, holds promise for next generation spintronic applications. In this study, we investigate the momentum-dependent spin splitting in the electronic band structure of a reconstructed $V_{2}X_{2}$ ($X=\mathrm{S, Se}$) lattice, achieved by introducing chalcogen cluster vacancies in trigonal $VX_{2}$ ($X=\mathrm{S, Se}$) monolayer. The reconstructed structure forms an inverse Lieb lattice of vanadium atoms, comprising two magnetic sublattices related by $C_{4}$ lattice rotational symmetry and $C_{2}$ magnetic symmetry, resulting in zero net magnetization despite the breaking of time-reversal ($\mathcal{T}$) and combined inversion time-reversal ($\mathcal{PT}$) symmetries. The electronic structure exhibits strongly anisotropic spin splitting on the Fermi surface, pronounced along $Γ\!-\!X$ and $Γ\!-\!Y$ and vanishing near $M$ point, revealing symmetry-enforced nodal features. The spin splitting follows a fourfold angular modulation consistent with $d_{x^{2}-y^{2}}$-type altermagnetism, while the real-space spin density exhibits a corresponding $d$-wave pattern localized on vanadium sites. Our findings demonstrate that vacancy-driven reconstruction provides an effective route realizing two-dimensional d-wave altermagnets, opening a new avenue for advanced spintronic technologies.