Compared with conventional semiconductors, the diluted magnetic semiconductors, in which the cations are substi-tuted by transition metal ions, have attracted a great deal of attention due to their promising applications in spintronics. Recently, the unexpected room temperature ferromagnetism has been found in many undoped oxides. These findings challenge our understanding of magnetism in these systems, because neither cations nor anions have unpaired d or f electrons. Generally, the candidate defects responsible for the unexpected ferromagnetism must fulfill two conditions at the same time: (ⅰ) the defects should prefer a spin-polarized ground state with a nonzero local magnetic moments;(ⅱ) the exchange interactions between local magnetic moments induced by defects should be ferromagnetic energetically. Among these oxides, TiO2 has recently attracted much attention because of its unique properties and potential applica-tions in spintronics, laser diodes and biomaterials. In order to explore the origin of ferromagnetism in such an undoped TiO2 system, the electronic structures and magnetic properties of oxygen vacancy (VO) and Ti vacancy (VTi) in anatase TiO2 have been studied systematically by the first-principles calculation based on the density functional theory with the LDA+U method (UTi-3d =5.8 eV). It is found that two electrons introduced by VO are captured by two neighbor Ti4+ ions, and thereby the Ti4+ ions are restored to Ti3+ ions with opposite spin orientation. Therefore, the single VO cannot induce local magnetic moment. The defect energy level locates near the Fermi level for VTi. Six oxygen atoms neighboring VTi constitute an octahedron, and the defect energy level is split into a single state A, a double state E and a triple state T in the octahedral crystal field. The occupation of four unpaired electrons introduced by six oxygen atoms is a1+t3+t0?e0 (subscripts "+" and "?" mean up-spin and down-spin, respectively), and the VTi can induce 4 μB local moments. Furthermore, the magnetic coupling interaction between local magnetic moments induced by two VTi is ferromagnetic, and the magnetic coupling constant (J0) is 88.7 meV. It means the ferromagnetism can continue up to room-temperature. The VO cannot induce local magnetic moment, but it can enhance the coupling strength between two VTi, which can explain the origin of ferromagnetism observed experimentally in undoped anatase TiO2, i.e., the VTi induces local magnetic moment, while VO enhances the long range ferromagnetic coupling interaction between VTi. Especially, for the ferromagnetic coupling between local magnetic moments, we have proposed 'the second type direct exchange interaction' model, which has been recommended in detail.%运用第一性原理的方法研究了锐钛矿相TiO2中O空位(VO)和Ti空位(VTi)的电子结构和磁学性质.计算结果表明,单独的VO并不会诱发局域磁矩,VTi可以产生大小为4μB(1μB=9.274×10?21 emu,CGS)的局域磁矩,主要分布在其周围的O原子上.这两种缺陷产生局域磁矩的原因在文中做了详细的介绍.此外,由两个VTi诱发的局域磁矩之间的磁耦合相互作用为铁磁耦合,其交换耦合系数J0为88.7 meV,意味着VTi间的铁磁耦合可以持续到室温.虽然VO并不会产生局域磁矩,但是引入VO可以进一步提升两个VTi之间的耦合强度,这可以对非掺杂锐钛矿结构的TiO2体系中铁磁性的来源作出解释:VTi产生了局域磁矩,而VO增强了VTi间长程的铁磁耦合相互作用.此外,还提出了局域磁矩之间耦合的第二类直接交换作用模型.
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