Abstract

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-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 ($W < 0.1$ 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 \textit{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, $2\times2$ cells yield antiferromagnetic order while $4\times4$ 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.

Shrestha Dutta

Research Scholar

Computational screening of 2D MXenes for hydrogen evolution catalysis using DFT to identify noble-metal-free alternatives for water splitting.

Rudra Banerjee

Assistant Professor, Computational Condensed Matter

Designing next-generation magnetic, catalytic, and quantum materials from first principles — bridging atomic-scale disorder to device-relevant function.