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We investigate the electronic structure of graphene on a series of 2Dhexagonal nitride insulators hXN, X = B, Al, and Ga, with DFT calculations. Asymmetry-based model Hamiltonian is employed to extract orbital parameters andspin-orbit coupling (SOC) from the low-energy Dirac bands of proximitizedgraphene. While commensurate hBN induces a staggered potential of about 10 meVinto the Dirac bands, less lattice-matched hAlN and hGaN disrupt the Diracpoint much less, giving a staggered gap below 100 $\mu$eV. Proximitizedintrinsic SOC surprisingly does not increase much above the pristine graphenevalue of 12 $\mu$eV; it stays in the window of (1-16) $\mu$eV, dependingstrongly on stacking. However, Rashba SOC increases sharply when increasing theatomic number of the boron group, with calculated maximal values of 8, 15, and65 $\mu$eV for B, Al, and Ga-based nitrides, respectively. The individualRashba couplings also depend strongly on stacking, vanishing insymmetrically-sandwiched structures, and can be tuned by a transverse electricfield. The extracted spin-orbit parameters were used as input for spintransport simulations based on Chebyshev expansion of the time-evolution of thespin expectation values, yielding interesting predictions for the electron spinrelaxation. Spin lifetime magnitudes and anisotropies depend strongly on thespecific (hXN)/graphene/hXN system, and they can be efficiently tuned by anapplied external electric field as well as the carrier density in the graphenelayer. A particularly interesting case for experiments is graphene/hGaN, inwhich the giant Rashba coupling is predicted to induce spin lifetimes of 1-10ns, short enough to dominate over other mechanisms, and lead to the same spinrelaxation anisotropy as observed in conventional semiconductorheterostructures: 50\%, meaning that out-of-plane spins relax twice as fast asin-plane spins.

Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties