\emph{Ab initio} study of (100) diamond surface spins

Unpaired electronic spins at diamond surfaces are ubiquitous and can lead to excess magnetic noise. They have been observed in several studies to date, but their exact chemical nature is still unknown. We propose a simple model to explain the existence and chemical stability of surface spins associated with the $sp^3$ dangling bond on the (100) diamond surface using density functional theory. We find that the (111) facet, which is naturally generated at a step edge of (100) crystalline diamond surface, can sterically protect a spinful defect. Our study reveals a mechanism for annihilation of these surface spins upon annealing, consistent with recent experimental results. We also demonstrate that the Fermi-contact term in the hyperfine coupling is not negligible between the surface spins and the surrounding nuclear spins, and thus \textit{ab initio} simulation can be used to devise a sensing protocol where the surface spins act as reporter spins to sense nuclear spins on the surface.