Doping and the unique role of vacancies in promoting the magnetic ground state in carbon nanotubes and ${\mathrm{C}}_{60}$ polymers

The role of various types of defects in establishing the magnetic properties of the ${\mathrm{C}}_{60}$-based polymers and the single-wall carbon nanotubes is investigated. Comparing the role of carbon vacancies, and that of substitutional impurity atoms $X$ ($X=\mathrm{N}$, B, O, Si, P, and S) in establishing a magnetic ground state it is found that the impurity $X$ atoms promote the spin density delocalization, whereas its localization appears as one of the primary effects of the carbon vacancies.

Figure 1

(Color online) Figure showing “cis” (on the same side) and “trans” (on the opposite sides) configurations of substitutional N on the ${\mathrm{C}}_{60}$ dimer.

Figure 2

(Color online) Results for the spin density (left) and charge distribution (right) in the case of a ${\mathrm{C}}_{60}$ dimer in the presence of defects in the form of; two vacancies (top panel), one vacancy and one substitutional N (middle panel), and two substitutional N atoms (bottom panel). The location of each vacancy is indicated by the dashed circle and the substitutional N atoms are indicated by dashed circles outlined in blue.

Figure 3

(Color online) The calculated charge accumulation around an impurity atom $X=\mathrm{B}$, N, O, Si, P, and S, as a function of its relative electronegativity with respect to that of the C atom obtained using both Mulliken population and NBO analysis.

Figure 4

(Color online) Results for the spin density and charge distribution in the case of SWCN in the presence of defects in the form of two vacancies (top panel), one vacancy, and one substitutional N (middle panel) and two substitutional N atoms (bottom panel). As in Fig. 2, the location of each vacancy is indicated by the dashed circle and the substitutional N atoms are indicated by dashed circles outlined in blue.