Real-Space Green's Function Calculation of Ti–Ti Exchange Anisotropy on MgO Measured by ESR-STM

Recent ESR-STM measurements on Ti atoms deposited on few-layer MgO reveal a strong dependence of the exchange splitting on dimer orientation, suggesting a substrate-mediated superexchange mechanism through MgO hole states. We model this system by solving the Dyson equation for pairs of Ti dimers in real space. The homogeneous Green’s functions are obtained from a realistic electronic dispersion derived from a multiband VASP + Wannier90 tight-binding model. The Ti adatoms are treated as localized perturbations that couple to the two-dimensional MgO substrate via hybridization between surface oxygen p-states and Ti d-orbitals. The exchange anisotropy is evaluated from the difference in integrated local density of states between ferromagnetic and antiferromagnetic Ti-dimer configurations as a function of orientation [1]. We find that the anisotropic exchange arises naturally from the directionally dependent MgO surface Green’s functions, which enhance coupling along $\langle100\rangle$ directions.

[1] D. Kitchen et al., Nature 442, 436 (2006)