Bilayers composed of two ferromagnetic Chern-insulating ${\mathrm{V}}_2{\mathrm{WS}}_4$ monolayers coupled antiferromagnetically between the layers have recently been identified as a promising platform for realizing an altermagnetic state characterized by a $d$-wave spin texture. In this work, we investigate the impact of spin-orbit coupling (SOC) on the altermagnetic spin texture in bilayer ${\mathrm{V}}_2{\mathrm{WS}}_4$ using first-principles calculations. In the absence of SOC, our nonrelativistic calculations reproduce a distinct altermagnetic state characterized by a $d$-wave spin texture, with a strictly vanishing net magnetization and a momentum-dependent altermagnetic spin polarization. Upon inclusion of SOC, however, the characteristic nonrelativistic $d$-wave spin texture undergoes a continuous SOC-driven reconstruction into a relativistic noncollinear momentum-space spin texture. Our fully relativistic calculations reveal that, although the net magnetization remains exactly zero and the momentum-dependent spin polarization persists, owing to the underlying antiunitary symmetries, the spin texture becomes noncollinear with finite $S_x$ and $S_y$ components beyond the nonrelativistic $d$-wave form. These results demonstrate that, while the symmetry-protected altermagnetic characteristics in bilayer ${\mathrm{V}}_2{\mathrm{WS}}_4$ are robust against SOC, the specific nonrelativistic $d$-wave spin texture is reconstructed by relativistic effects. Our study therefore provides a material-specific first-principles analysis of the SOC-driven reconstruction of the altermagnetic spin texture in bilayer ${\mathrm{V}}_2{\mathrm{WS}}_4$ and highlights how relativistic effects modify its electronic and spin structures.

Close

PrevNext

View figure in article

• Altermagnetism
• Spin-orbit coupling
• van der Waals interaction
• Density functional calculations
• First-principles calculations