A first-principles study on magnetic properties of the intrinsic defects in wurtzite ZnO

The TiO2 based diluted magnetic semiconductors (DMSs) have aroused the considerable interest as one of the promising candidates for the spintronic devices accommodating both charge and spin of electrons in a single substance. Unfortunately, however, throughout most of the published papers, the question how to clearly elucidate the role of defects which may be played in the experimentally observed room temperature ferromagnetism (RTFM) remains open, especially after a new concept of d(0) ferromagnetism. In such a case, to further understand this issue and also to explore the origin of the RTFM in rutile TiO2, we here first perform a first principles calculation on the magnetic properties of the intrinsic defects, namely oxygen vacancy (V-O), Ti vacancy (V-Ti), Ti interstitial (Ti-in), oxygen interstitial (O-in) and two complex defects of VO + O-in and V-Ti+Ti-in. Combining the density functional theory and the Perdew-BurkeErnzerhof functional of the generalized gradient approximation, we calculate various model structures of rutile TiO2 constituted by 48-atom 2 x 2 x 2 supercell. The cutoff energies in these calculations of the planewave basis are all set to be 340 eV and the Monkhorst-Pack scheme k points are set to be 3 x 3 x 4 for an irreducible Brillouin zone. The convergence threshold for self- consistent field iteration is 0.1455 x 10(-6) eV/atom. Structural relaxation is taken into account in each of all calculations. It is found that each defect we created in the structure leads to a lattice expansion and that the positive value for spin up and the negative value for spin down of the density of states (DOS) of the structure without defect are symmetric, suggesting that the perfect rutile TiO2 lattice is nonferromagnetic. For the system with one VO, the total energy of the spin-polarized system is 200 meV lower than that of the non-spin-polarized system, which indicates ferromagnetic behavior in this system. The defect brings in an impurity state near Fermi level located at about 0.7-1.0 eV down below the conduction band, resulting in an excess of spin up over spin down for the presences of the two localized electrons left by the vacancy. At this point the supercell bears a magnetic moment of about 1.62 x B. In contrast, VTi also brings in an impurity state near Fermi level but above the valence band, which reveals a p-type characteristic semiconductor nature. Since a lower total energy requires more spin- up electrons, the asymmetric DOS induces a magnetic moment of 2.47 x B. When a neutral Ti occupies an interstitial lattice site, the system requires it to be oxidized into a Ti-3 + ion to increase the stabilization of the system. The three delocalized electrons tend to occupy the 3d or 4s orbital of the neighbor Ti-4 + ions and then have strong exchange interactions with the 2p electrons of the local O atom. This can distort octahedral symmetry and give rise to a ferromagnetic moment of 3.91 x B. Oin defect in the supercell is extremely unstable. It can easily be reduced and escape from the host in terms of an oxygen molecule so that the system is in a manner similar to the perfect lattice, showing no ferromagnetism. It is interesting to note that the properties of the system with the complex defect of one VO and Oin are similar to that of the structure with one VO and the magnetic moment of this system is 1.63 mu B. For the Ti-com complex defect, our results point out the fact that the magnetic properties of the supercell are related to the distance between V-Ti and Ti-in. The spin up and spin down states are symmetric when they are close to each other, while, in addition to some ferromagnetic behavior, the system mainly exhibits antiferromagnetism when the distance increases.