Indirect exchange coupling between magnetic adatoms in carbon nanotubes

The long range character of the exchange coupling between localized magnetic moments indirectly mediated by the conduction electrons of metallic hosts can play a significant role in determining the magnetic order of low-dimensional structures. Here we consider how this indirect coupling influences the magnetic alignment of adatoms attached to the walls of carbon nanotubes. A general expression for the indirect coupling in terms of single-particle Green functions is presented. Contrary to the general property that magnetic moments embedded in a metal display Friedel-like oscillations in their magnetic response, calculated values for the coupling across metallic zigzag nanotubes show monotonic behaviour as a function of the adatom separation. Rather than an intrinsic property, the monotonicity is shown to reflect a commensurability effect in which the coupling oscillates with periods that coincide with the lattice parameter of the nanotube host. Such a commensurability effect does not dominate the coupling across semiconducting zigzag or metallic armchair nanotubes. We argue that such a long-range character in the magnetic interaction can be used in future spintronic devices.