Spin orientation -- a subtle interplay between strain and multipole Coulomb interactions

We address the technologically important issue of the spin orientation on a correlated magnetic surface and how to manipulate it. We consider a prototypical strongly correlated system, NiO, and show that a single particle approach with anisotropic hoppings, or even a many-electron model with a scalar Hubbard $U$ and Hund's $J$ fails to explain the strain driven spin reorientation transition (SRT). We set up a model treating both anisotropic single particle effects and orbital-dependent, full multipole electron-electron interaction effects at the same footing. Within this model, predictive power to explain the observed SRT is regained and the results indicate the novel possibility of using an electric field to control SRT in magnetic films grown on piezoelectric substrates.