Sudden decay of indirect exchange coupling between magnetic atoms on carbon nanotubes

Indirect exchange coupling plays a central role in determining the magnetic order in systems composed of adsorbed magnetic moments on a metallic host. For low-dimensional metallic structures, such as nanotubes, this interaction is predicted to decay rather slowly. Ab initio calculations have nevertheless been unable to reproduce this prediction. To clarify this matter, we make use of a simple analytical expression for the indirect exchange coupling that, on the one hand, confirms the long ranged nature of this interaction, and, on the other hand, points to situations in which the coupling may display unexpectedly shorter ranges. We show that the interaction range depends rather sensitively on the location of the magnetic moments, which explains the difficulty in probing the long range character of the indirect exchange coupling from standard ab initio calculations.