Trends in the hyperfine interactions of magnetic adatoms on thin insulating layers

Nuclear spins are among the potential candidates prospected for quantum information technology. A recent breakthrough enabled to atomically resolve their interaction with electron spin, so-called hyperfine interaction, within individual atoms utilizing scanning tunneling microscopy (STM). Intriguingly, this was only realized a few species put on two-layers thick MgO. Here, we systematically quantify from first-principles interactions of whole series 3d transition adatoms deposited various thicknesses MgO, NaF, NaCl, h--BN and Cu$_2$N films. We identify adatom-substrate complexes largest unveil main trends exceptions. reveal core mechanisms at play, such as interplay local bonding geometry chemical nature thin films, which trigger transitions between high- low-spin states accompanied subtle internal rearrangements magnetic electrons. By providing general map interactions, our work has immediate implications in future STM investigations aiming detecting realizing concepts hinging nuclear spins.