Effects of different hydrogen distributions on the magnetic properties of hydrogenated single-walled carbon nanotubes

The magnetic properties of the hydrogenated single-walled carbon nanotubes (SWNTs) have been studied by the first-principles calculations. It is found that different distributions of hydrogen atoms on the SWNT surfaces have a significant effect on the magnetic order of the hydrogenate SWNTs. More importantly, it has been shown that in general there exist two types of the hydrogen adsorption sites on the SWNT external surface, forming two different structures of the hydrogenated SWNTs, i.e., the so-called $AA$ and $AB$ structure, among which the latter has lower total energy than the former. The flat bands appear at the Fermi energy in the $AA$ structures, favoring spontaneous magnetism, but not in the $AB$ structures, making the composite system always stay in the nonmagnetic ground state.

Figure 1

Schematic of the geometrical structures of the hydrogenated (a) (4, 4) SWNT and (b) (8, 0) SWNT. Here, the dark and white balls represent the carbon and hydrogen atoms, respectively.

Figure 2

(Color online) A plane picture of Fig. 1, obtained by cutting the SWNT along its tube axis. (a) (4, 4) SWNT; (b) (8, 0) SWNT. The bigger and smaller balls represent the $A$ and $B$ sites of carbon atoms, which are marked by some integers. C1 is the atom bonded by ${\mathrm{H}}^{\left(1\right)}$, and then ${\mathrm{H}}^{\left(2\right)}$ is made to bond to different carbon atoms in the dashed frame, respectively, obtaining other different structures. In the frame, relative to C1, the carbon atoms marked by $4^{\prime }$, $6^{\prime }$, $8^{\prime }$ are equivalent to C4, C6, C8, respectively.

Figure 3

(Color online) The isosurfaces of the magnetization density at (a) $0.012{\mu }_B{\mathrm{\AA }}^{-3}$ and (b) $-0.012{\mu }_B{\mathrm{\AA }}^{-3}$, on the ${\mathrm{H}}^{\left(2\right)}\text{−}\mathrm{C}2$ structure of the (8, 0) SWNT.

Figure 4

(Color online) The $\mathrm{LSDA}+U$ electronic band structures of some different configurations for the (4, 4) SWNT, in which the spin-up and spin-down channels are represented by dark and light (blue and red online) lines, respectively. (a) ${\mathrm{H}}^{\left(2\right)}\text{−}\mathrm{C}2$, (b) ${\mathrm{H}}^{\left(2\right)}\text{−}\mathrm{C}7$, (c) ${\mathrm{H}}^{\left(2\right)}\text{−}\mathrm{C}13$. (d) The structure of a two-periods length of (4, 4) tube with only one hydrogen atom adsorbed on it.