Nonlocal vdW-DF2 Study of Electronic and Magnetic Phase Engineering in Half-Functionalized Germanene

Phase engineering of two-dimensional Dirac materials via selective chemical functionalization offers a promising route toward controlling electronic and magnetic properties for nanoscale device integration. Using first-principles density functional theory calculations within the generalized gradient approximation complemented by van der Waals corrections (vdW-DF2), we present a systematic investigation of the energetic, structural, electronic, and magnetic properties of germanene monolayers half-functionalized with hydrogen ( GeH ) and fluorine ( GeF ). Both half-passivated configurations are thermodynamically stable with exothermic formation energies, maintaining robust in-plane covalent \(\mathrm{Ge}-\mathrm{Ge}\) bonding despite significant out-of-plane orbital hybridization \(\left(s p^2 \rightarrow s p^3\right)\). Bader charge analysis and real-space charge density distributions reveal strong out-of-plane polarizations along the adatom-germanium axis, driven by Pauling electronegativity contrasts, alongside negligible in-plane charge transfer across the basal plane. Crucially, single-sublattice passivation breaks the inversion symmetry of the host lattice and unquenches localized \(4 p_z\) orbitals on the unpassivated germanium sites. This leads to distinct electronic and magnetic ground states dictated by the adatom species. Half-hydrogenation (GeH) converts germanene into a ferromagnetic half-metal featuring a 0.32 eV direct bandgap in the majority (spin-up) channel-identical in magnitude to its non-spin-polarized gap-while the minority (spin-down) channel crosses the Fermi level, whereas half-fluorination (GeF) stabilizes an antiferromagnetic semi-metallic state with continuous spin-channel degeneracy across the Brillouin zone. Mean-field estimations based on an \(S=1 / 2\) localized Heisenberg model yield a Curie temperature of \(T_{\mathrm{C}}=30.6 \mathrm{~K}\) for the FM GeH monolayer. Projected density of states (PDOS) analyses confirm that the Fermi-level states in GeH are governed almost exclusively by the unpassivated germanium \(4 p\) orbitals, whereas the magnetic behavior in GeF originates from strong hybridization between host \(4 p\) and fluorine \(2 p\) states. These findings establish single-sided functionalization as an effective, non-destructive strategy for tailoring spin-dependent transport channels in group-IV Dirac monolayers for 2D spintronic and magnetoelectronic applications.