Clustering of Cr in GaN nanotubes and the onset of ferrimagnetic order

A comprehensive theoretical study of the structure and magnetic properties of Cr-doped GaN nanotubes yields some interesting and unexpected results: (1) A single wall GaN nanotube constructed from the GaN wurtzite crystal relaxes to a carbon-like zigzag SWNT structure and remains stable at $300\mathrm{K}$, while a multiwall GaN nanotube retains its original wurtzite form. (2) Cr atoms prefer to form clusters and the underlying magnetism depends on the degree of clustering. (3) The coupling between two Cr atoms mediated by the neighboring N is ferromagnetic, but changes to ferrimagnetic as the cluster grows. These results are based on spin polarized density functional theory with exchange and correlation potential approximated by both the generalized gradient approximation and the local spin density approximation $+U$ methods.

Figure 1

(Color online) (a) Top view of a $7\times 7\times 3$ GaN supercell having wurtzite structure. (b) GaN-NT supercell $\left({\mathrm{Ga}}_{54}{\mathrm{N}}_{54}\right)$ which extends to infinite length along the [0001] direction.

Figure 2

Schematic representation of the initial (a) and the optimized (b) GaN NT supercell $\left({\mathrm{Ga}}_{54}{\mathrm{N}}_{54}\right)$. The lighter spheres are Ga and the darker spheres are N.

Figure 3

(Color online) (a) Total DOS corresponding to pure ${\mathrm{Ga}}_{54}{\mathrm{N}}_{54}$ NT (solid line) and ${\mathrm{Ga}}_{96}{\mathrm{N}}_{96}$ NT (dashed line); (b) partial spin DOS of Ga in ${\mathrm{Ga}}_{54}{\mathrm{N}}_{54}$; (c) partial spin DOS of N in ${\mathrm{Ga}}_{54}{\mathrm{N}}_{54}$; (d) total DOS of Cr-doped GaN-NT for ${\mathrm{Ga}}_{52}{\mathrm{Cr}}_2{\mathrm{N}}_{54}$ (solid line), ${\mathrm{Ga}}_{94}{\mathrm{Cr}}_2{\mathrm{N}}_{96}$ (dashed line), and $\mathrm{LSDA}+\mathrm{U}$ result for ${\mathrm{Ga}}_{52}{\mathrm{Cr}}_2{\mathrm{N}}_{54}$ (lighter magenta solid line); (e) partial spin DOS of Cr in ${\mathrm{G}}_{52}{\mathrm{Cr}}_2{\mathrm{N}}_{54}$; (f) partial spin DOS of Cr $3d$ and N $2p$ in ${\mathrm{Ga}}_{52}{\mathrm{Cr}}_2{\mathrm{N}}_{54}$.

Figure 4

Schematic representation of the GaN MWNT supercell $\left({\mathrm{Ga}}_{96}{\mathrm{N}}_{96}\right)$. The lighter spheres are Ga and the darker spheres are N. The atoms occupying sites marked 1 and 2 are along the [0001] direction.