Thorough investigation of nanoobjects, such as metal [1] and carbon [2] clusters, is essential because their characteristics are unlike bulk materials [3,4]. Carbon fullerenes and nanotubes have been paid immense attention to since they were discovered in 1985 and 1991 [5,6]. Tiny space inside a fullerene or a carbon nanotube (CNT) may be considered as a unique place for atomic clusters. The endohedral fullerenes and CNTs show many remarkable physical and chemical features [7-12].

I reported recently on computational results on magnetic properties of putative Co_n@C_m (n = 5, 13; m = 60, 70 and 80) endohedral metallofullerenes [13,14]. Instead of fullerenes, single-walled nanotubes (SWNTs) may be preferable, because ends of nanotube are open allowing entering the tube [15-17]. In this paper, I use the same computational approach as done in [13,14] to study the magnetism of SWNTs with various chirality which were filled by the icosahedral magnetic Co₁₃ cluster in alternative orientations to the nanotube’s channel.

CoNTub 1.0 program [18,19] was used to determine atomic coordinates of SWNTs with chiral vector (n,m). The diameter of nanotubes was calculated from (n,m) indices as follows:

where a = 0.246 nm. Obtained nanotubes were filled by Co₁₃ cluster using SPDB viewer 4.1 [20]. Magnetic moments of the endohedral nanotubes were calculated on the basis of density functional theory (DFT) [21] within OpenMX 3.5 software [22-25]. Two density functionals, such as the local spin density approximation of CeperleyAlder (LSDA-CA) [26] or the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA-PBE) [27], both with the active spin polarization, were used to compare outputs. Energy convergence was performed by the generalized divide-conquer optimization technique using parameters fitted to d-orbitals of Co-atoms. The self consisted field (SCF) criterion corresponded to 6 × 10⁻⁶ Hartree. The atomic species were defined as C4.0-s1p1 and Co5.5-s2p2d2f1. Electronic temperature was 300.0 K and the energy cutoff was 200.0 Ry. Total spin S was accepted as a value of magnetic moment.

The computation parameters for pure Co clusters were chosen and checked as described previously in [13,14]. The idea was to calculate metal-carbon complexes using the OpenMX’s basis set, which was originally developed to simulate large systems [22]. I also used the relative assessment and internal reference. The values of magnetic moments for Co₅ and Co₁₃ clusters were obtained, such as 2.60 and 2.39 μ_B/atom respectively, which is in agreement with [28]. It is higher than for the bulk Co material, 1.62 μ_B [29]. The computational procedure was tested on Co₅- and Co₁₃-carbides giving reliable results. LDA and GGA approximations demonstrated similar outputs. However, the standard deviation of magnetic moments for Co₁₃C₁₂ carbides was bigger than for Co₅C₅ carbides after five independent runs for each system, such that 0.0521 versus 0.0004 μ_B [13]. That allowed me to use this computational approach to investigate the endohedral fullerenes Co_n@C_m (n = 5, 13; m = 60, 70, 80), then to attack the endohedral nanotubes filled with Co₁₃ cluster. The length of SWNTs was 10 Å; the number of carbon atoms varied around 60. For example, the zig-zag (7,0) tube consisted of 56 C-atoms, as well as the chiral (5,3) or (6,2) tube included 64 C-atoms. As the gradient and sub-space optimization methods did not allow always reaching a ground state for complex systems, the SCF criterion was decreased to 10⁻⁶ Hartree.

In experiments, I varied the chiral index of SWNTs to investigate the parametric space. The smallest stable endohedral structures were zigzag (7,0) and chiral (5,3) tubes having the diameter 5.48 Å with an internal space still available for doping Co₁₃ cluster 4.67 Å in size in different orientations.

When local spin density approximation (LDA functional) was applied, the zigzag (7,0) nanotube with an across oriented Co₁₃ cluster showed the magnetic moment 1.54 µ_B that is 4.8 times less than for along oriented Co₁₃ cluster with the corresponding magnetic rate 7.34 µ_B. In the case of generalized gradient approximation (GGA functional), the values were 2.99 and 8.14 µ_B in across and along orientations, respectively (Figure 1).

The similar pattern of magnetic activities depending on orientation of the Co₁₃ cluster was found for the chiral (5,3) tube with the same diameter 5.48 Å as the zigzag (7,0) tube. In the frame of LDA approach, when the Co₁₃ cluster took a cross orientation to the channel, the magnetic rate was 3.42 µ_B, and when an along orientation of Co₁₃ cluster was considered, then the magnetic moment of the complex was 6.24 µ_B that is 1.8 times higher. When I used GGA method, the magnetism was estimated as 3.24 and 5.27 µ_B, respectively. It is interesting that the difference in magnetic moments depending on Co₁₃ cluster orientation was smaller for a chiral tube than for a zigzag tube with the same diameter.

An unexpected result was obtained from experiments on the chiral (6,2) tube with a bigger diameter 5.65 Å. The magnetic moments of this filled nanotube for various orientations of Co₁₃ cluster were smaller than in the case of the chiral (5,3) tube, such as 1.15 µ_B for across orien-

tation and 3.65 µ_B for longitudinal orientation with LDA calculations, as well as 0.86 and 3.37 µ_B, respectively for GGA technique.

In general, the correlation between LDA-CA and GGAPBE methods on the given experimental set was significant.

As follows from the outcome above, the Co₁₃ cluster emits more magnetism in an along orientation than in a cross orientation to the channel of a nanotube (Figure 1). This data is in good agreement with the result on doped by Co₅ elongated fullerene C₇₀-D_5h and confirms the earlier conclusion: the closer carbon and cobalt atoms, the less magnetic moment of the Co-C complex [13,14]. Nevertheless, this simple rule does not work in the matter of chiral nanotubes. As such, the Co₁₃ cluster emits less magnetism in the (6,2) tube with the diameter 5.65 Å than in the (5,3) tube with the diameter 5.48 Å, which demonstrates a nontrivial role of the carbon structure in magnetisation of Co-C complex. This finding is very interesting because the transmission electron microscopy, electron diffraction, and X-ray spectroscopy showed a structural transition of Co particles inside CNTs from hexagonal-close-packed (hcp) arrangement to face-centered-cubic (fcc) organization as a result of interaction between Co nanoparticles with CNTs [30].

Although the magnetic features of Co₁₃ cluster in nanotubes were noticeable in our calculations, the hidden mechanisms of magnetism and peculiarity of electron actions in filled nanotubes are out of DFT approach [31, 32]. The chemical structure of nanotubes is composed of sp² bonds, similar to those of graphite. Like in graphite, electrons can move along a tube, parallel to the graphene sheet. However, some tubes have a band gap like semiconductors that depends on chirality. For instance, armchair tubes are metals, chiral tubes with n-m divisible by 3 are small band gap semiconductors, all other tubes are large-band gap semiconductors [33]. Hence, experimental nanotubes with chiral indexes (7,0), (5,3), (6,2) are large-band gap semiconductors. Nonetheless, they demonstrated different properties of magnetism with introduced Co₁₃ cluster, depending on the chiral symmetry that was not observed early on regarding endohedral fullerenes with chirality types (1,1) and (2,0) [14].

The total spin magnetic moment S of Co₁₃ cluster with icosahedral symmetry decreased in the SWNT environment more significantly in the case of across orientation of the cluster than in the longitudinal orientation to a channel of nanotube. The magnetism did not monotonically descent with the decreasing diameter of filled carbon tube like endohedral fullerenes. Thus, open ends of carbon nanotubes are an important factor in the magnetic behavior of SWNTs doped with metallic cluster.

The parametric space in which the chiral vector presented the symmetry of a nanotube was partly investigated. The magnetic moment of Co₁₃ cluster embedded into carbon nanotubes of different chirality varied in a wide range. The landscape of was very ruffle and unpredictable. Most structures were hard to calculate with LDA and GGA functionals. However, I hope a protonation of nanotube’s ends and new approaches will possibly allow to investigate extensive space.

In summary, the magnetic states of endohedral carbon nanotubes were strongly dependent on the orientation of Me-cluster within nanotube and on the fine atomic structure of carbon shell, i.e. on the specific arrangements between the metal and carbon atoms.

The author thanks Heinz Eikmeyer and anonymous referees for helpful suggestions.