First principle study of the cation vacancy in anatase TiO₂

Abstract

Diluted magnetic semiconductors (DMS) [1] are a rapidly growing research field due to their potential applications in spintronic [2] devices. Several semiconducting oxide materials such as CaO [3], ZnO [4], HfO 2 [5], SnO 2 [6], TiO 2 [7] have been shown both experimentally and theoretically to have DMS properties. Normally there exists no magnetism in these material, but it will appear when defects exist. Introducing transition metal substitutions at the cation positions is one way to produce magnetism. Cu atoms in ZnO [4], Fe in SnO 2 [6] were verified to have ferromagnetism and high Curie temperature (T C ). Another way to obtain the high temperature ferromagnetism is doping nonmetal atoms at anion positions, such as the magnetism in N, C doped CaO [8] and C in SrO [9]. Cation intrinsic vacancy also leads to the high T C magnetism -Ca and Hf vacancies in CaO [3] and HfO 2 [5] demonstrate this kind of ferromagnetism origin. As a common wide band semiconductor, TiO 2 has also been studied as a possible DMS material. Both Co doped anatase [7] and rutile [10], and Cr [11] doped anatase TiO 2 have shown high temperature ferromagnetism. And in these transition metal impurity structures, the O vacancy plays a crucial role to ferromagnetism and structure stability [12]. In this letter, we carry out first principle calculations about cation vacancy effect on the ferromagnetism of anatase TiO 2 . Our research shows that like other ionic materials HfO 2 and CaO, the cation vacancy in anatase TiO 2 also induces ferromagnetism.The calculation in this letter is carried out with the GGA [12] exchange correlation in the frame of the full po-tential linear augmented plane wave (FP-LAPW) method using the WIEN2k package [13]. We use a 48-atom supercell in our calculation. With one or two Ti vacancies, the simulated vacancy concentration is 6.25% and 12.5%, respectively. The muffin-tin radius R is chosen to be 1.5 a.u. for the Ti atom and 2.0 a.u. for O atoms. The convergence parameter (RK) max is chosen to be 7.5, where K gives the largest number of the k-vector in the plane wave expansion. This gives well-converged basis sets consisting of approximately 23570 plane waves. Brillouin zone integrations are performed by summations over a 4 × 4 × 3 Monkhorst-Pack [15] special k-point mesh. The calculations are iterated to self-consistency when the total energy change was less than 0.00005 Ry.In anatase, one Ti atom is surrounded by six O atoms, forming a distorted octahedral structure (Fig. 1). The O atoms can be clarified into two classes. We mark them as O1 and O2.According to molecular orbital theory, the 3d and 4s electrons of Ti and the 2p electrons of O form σand π-orbitals, and when the neutral Ti atom is taken from the structure, it will introduce four holes in the molecular orbital. According to the theoretical research of CaO and HfO 2 , the holes will be arranged spin-parallel in the orbital because of Hund's coupling rules and the on-site Coulomb repulsion energy U pp between the holes. Our first principle calculation sh...

Oxygen vacancy induced ferromagnetism in rutile TiO2–x

“…Several semiconducting oxide materials such as ZnO 3, HfO 2 4, SnO 2 5 have been shown to have DMS properties. Normally there exists no magnetism in semiconducting oxide materials, but it will appear when defects exist, such as transition metal (TM) substitutions at cation positions 3, 5, nonmetal atom doping at anion positions 6, or cation intrinsic vacancies 4, 7. As a common wide band semiconductor, TiO 2 has also been studied as a possible DMS material.…”

Density-functional characterization of antiferromagnetism in oxygen-deficient anatase and rutileTiO2

“…Both oxygen vacancy and titanium vacancy were proposed to be responsible for the ferromagnetism. On one hand, theoretical studies indicated that the cation vacancy or divacancy are ferromagnetically coupled, 13,14 similar to the case of undoped HfO 2 . 6 But on the other hand, more and more experimental evidences show that the magnetic property of undoped TiO 2 is strongly related to oxygen vacancy, and thus it was thought to be the source of room-temperature ferromagnetism in undoped semiconducting or insulating oxides.…”

“…Similar to the case of HfO 2 6 and CaO 26 , the presence of cation vacancy causes a clear spin split in the valence band, and a total magnetic moment of 4.0 μ B was produced, mainly contributed by the six adjacent oxygen ions around the titanium vacancy which is consistent with results of previous calculations based on LSDA or GGA functional. 13,14 Further calculations were carried out to assess the relative stability of the ferromagnetic and antiferromagnetic alignments between the magnetic moments localized on different titanium vacancies using the 96-atom 2 × 2 × 2 supercell where the distance between two titanium vacancies is 7.6 Å, and the FM state is found to be more stable than the AFM state by 112 meV, indicating a substantially long-range ferromagnetic ordering of cation vacancy induced by local magnetic moments in titanium-deficient TiO 2 . As a result, it is proposed that the carriers, i.e., holes from the p orbitals of these oxygen ions, are thought to 8 induce the long-range ferromagnetism, and similar ferromagnetically coupled state is also expected in other cation-deficient semiconductors such as In 2 O 3 , SnO 2 , and CdS.…”

Ferromagnetism induced by intrinsic defects and carbon substitution in single-walled ZnO nanotube

“…The experimental results suggest that the observed FM comes from oxygen vacancies for oxides HfO 2 , TiO 2 , In 2 O 3 and SnO 2 [1][2][3][4][5], but from cation vacancies for MgO [6,7]. Most of ab initio calculations demonstrate that cation vacancies are responsible for the magnetic moments in undoped oxides such as HfO 2 , TiO 2 , ZnO, SnO 2 , ZrO 2 and MgO [8][9][10][11][12][13][14][15][16]. Ferromagnetism could also be produced by doping non-magnetic sp elements such as C, N, Mg and Al in oxides, nitrides and sulfides [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”