Ferromagnetism and piezomagnetic behavior in Mn-doped germanium nanotubes

Using ab initio density functional calculations, we show that pentagonal and hexagonal nanotubes of Ge can be stabilized in the antiprism structure by doping with Mn atoms. In both cases the infinite nanotubes are metallic and ferromagnetic. Hexagonal nanotubes have the highest average magnetic moments of $3.06{\mu }_B$ per Mn atom found so far in metal doped nanotubes of semiconductors, while the pentagonal nanotubes show a transition from a ferromagnetic to a ferrimagnetic state upon compression with an abrupt change in the magnetic moments, leading to the possibility of these nanotubes to act as a nano-piezomagnet.

Figure 1

Optimized structures of ${\text{Ge}}_{12}\text{Mn}$ cluster: (a) Icosahedral, (b) hexagonal antiprism, (c) optimized structure from a decahedraon, (d) distorted cagelike structure, which is similar to (c), and (e) distorted hexagonal prism. (a) and (b) are nearly degenerate. Electronic states of (a) and the corresponding icosahedral ${\text{Ge}}_{12}$ cage are shown with labels according to the spherical potential model. $1s$, $1p$, $1d$, $1f$ (3 states), $2s$, $1f$ (4 states), $2p$ (3 states), and $1g$ (5 states) are occupied for ${\text{Ge}}_{12}$ cage with 2 holes in the down-spin $1g$ state. The $3d$ state corresponds to the Mn atom. Broken lines show the unoccupied states.

Figure 2

(Color) Optimized structures of the infinite nanotubes: (a) Pentagonal antiprism ${\text{Ge}}_{20}{\text{Mn}}_4$ unit cell, (b) ${\text{Ge}}_{24}{\text{Mn}}_4$ hexagonal antiprism unit cell. (c) and (d) show the excess of the electronic charge density for pentagonal ${\text{Ge}}_{20}{\text{Mn}}_4$ and hexagonal ${\text{Ge}}_{24}{\text{Mn}}_4$ infinite nanotubes, respectively. The charge is seen to be nearly uniformly spread between the M atoms and the Ge nanotube.

Figure 3

(Color) (a) Magnetic phase diagram for the infinite pentagonal nanotube. A corresponds to the F state while B and C, to ferrimagnetic states. B is marginally metallic while C is semiconducting as shown in the corresponding band structures in (b). The broken lines show the Fermi level.