Spin ordering in RKKY nanowires: Controllable phases in 13C nanotubes

Detailed study of nuclear spin order in semiconducting C-13 nanotubes reveals subtle interplay of the chemical potential, length, diameter, and chirality, resulting in the complex four-dimensional phase diagram of the helical ground states. Increase of the chemical potential causes abrupt transitions between different helical spin orderings of three regimes which are interpolated by a smooth change of helical angle within each regime: in the middle one the helimagnet is a deviation from the commensurate order and fully characterizes the geometry of the nanotube, while outside it the ground state is an incommensurate helical deviation from the ferromagnet. This behavior of the C-13 nanotubes manifests the long-range of the RKKY interaction and quasi-one-dimensional geometry, thus being universal for all RKKY interaction governed nanowires. Short enough nanotubes are ferromagnetic; the critical length when frustration arises decreases with the chemical potential but increases with diameter and chiral angle. The results, verified numerically, show that with nanotubes of the different but realistic lengths, various scenarios of the helical order response to the gate voltage can be achieved.