We perform first-principles calculation to investigate the possible magnetism on the Si(111)-$$\sqrt 3 \times \sqrt 3 $$3×3surface, which is stabilized for highly boron-doped samples. When the silicon adatom on top of a boron atom is removed to form a defect structure, three silicon dangling bonds are exposed, generating half-filled doubly degenerate energy levels in the band gap, which stabilizes a local magnetic moment of 2 μB. When many such defect structures are adjacent to one another, they are found to align antiferromagnetically. However, we demonstrate that the ferromagnetism can be stabilized by adjusting the number of electrons in the defects, suggesting a possibility towards spintronic applications for this unique silicon surface structure.