Defect engineering of two-dimensional materials routinely produces local magnetic moments, yet itinerant half-metallic ferromagnetism remains elusive—experiments frequently yield paramagnetic insulators. We resolve this paradox for vacancy-doped monolayer $1T\text{−}{\mathrm{TiS}}_2$ by demonstrating that the insulator-to-half-metal transition is governed by universal geometric percolation of the defect network, extending the percolation framework established for three-dimensional diluted magnetic semiconductors into the 2D vacancy-doped regime. Half-metallicity emerges via a two-step mechanism: Crystal-field symmetry breaking ($O_h\to C_{4v}$) selectively stabilizes the Ti $3d_{z^2}$ orbital, generating robust local moments ($0.94{\mu }_B$), but spin-polarized transport requires these moments to form a spanning cluster. At critical vacancy concentration $x_c\approx 12.5\%$, a percolation transition drives the majority-spin impurity band from flat, localized levels ($W<0.1\mathrm{eV}$) to a dispersive 1.5-eV wide band with 100% spin polarization and a minority-spin gap of 1.0 eV. Finite-size scaling yields a Fisher exponent $\tau =2.09\pm 0.03$, confirmed by fractal scaling of ab initio charge densities (${\tau }_{\text{eff}}^{\text{DFT}}=1.87\pm 0.26$), placing the transition in the 2D percolation universality class. The percolation mechanism is independently corroborated by a striking supercell-size effect: at identical concentration, $2\times 2$ cells yield antiferromagnetic order while $4\times 4$ cells mandate ferromagnetism, reflecting the presence or absence of a spanning cluster. We estimate a Curie temperature exceeding 300 K from the exchange coupling, and identify a geometric jamming instability at $x>20\%$ that fragments the network. These results define a narrow functional window ($11\%<x<15\%$) for half-metallic operation and establish geometric connectivity as a quantitative design principle for defect-engineered 2D spintronics.

Close

PrevNext

View figure in article

• Vacancies
• Half-metals
• Density functional theory