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 behavior 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.