First-principles Study Of The Electronic Structure And Magnetic Properties Of Reduced TiO₂Surface

In recent years， room-temperature d₀ferromagnetism was found in someundoped oxides （ZnO, SnO₂and TiO₂）, nitrides （AlN、GaN、InN、BN） and sulfides（ZnS、CdS）. As an important wide-band-gap semiconductor in the field of spintronics,the magnetic property of undoped TiO₂has been extensively studied. Recently, therehave been many experimental reports about high-temperature d₀ferromagnetism ofundoped TiO₂films and nano-particles. However, there is controversy about theorigin of the observed d₀ferromagnetism in undoped TiO₂. A number of experimentsindicate that d₀ferromagnetism in undoped TiO₂films and nano-particles is related tooxygen vacancies and low dimensionality. For example, it has been experimentallyreported that the magnetization of thin films of undoped TiO₂are larger than that ofthick films and the films annealed oxygen atmosphere for8hours lose theirferromagnetism. These results mean that O vacancies at surface play a key role inturning d₀ferromagnetism in undoped TiO₂films. Recently, there have been manyreports on the electronic structure and magnetic properties of the reduced TiO₂（110）surface. Up to now there has not been a report on the magnetic properties of thereduced TiO₂（100）,（101） and （001） surfaces. Accordingly, in the precent work, theelectronic structure and magnetic properties of the reduced （100）,（101） and （001）surfaces of TiO₂are investigated using first-principles calculations based on thedensity functions theory. The main results are as follows1. Similar to bulk TiO₂, stoichiometric （100）,（101） and （001） surfaces arenon-magnetic.2. The oxygen vacancies at surfaces induce a set of spin splitting defect statesnear the bottom of the conduction band. The defect states are mostly formed by3dorbitals of the Ti atoms. A oxygen vacancy at the （100） and （101） surfaces produce amagnetic moment of2.0Band the magnetic moment produced by VOis mainly contributed by partially filled3d orbitals of the Ti atoms around VO. Whereas avacancy at the （001） surface produce a magnetic moment of1.1Band the momentis mainly contributed by partially filled3d orbitals of the Ti atoms located in thesecond and third Ti layers.3. The calculated energy for ferromagnetic coupling between the momentsinduced by two vacancies at surfaces is lower than that for antiferromagnetic coupling.The calculated DOS and spin density distribution show that the spins orientations ofthe Ti atoms around oxygen vacancy are parallel to each other under d-d hybridizationinteraction between Ti atoms. As a result, all of the Ti atoms between two oxygenvacancies in the supercell are polarized. These polarizations between two vacanciesare able to effectively mediate an indirect long-range FM coupling between themagnetic moments induced by vacancies.In summary, our investigations reveal that observed d₀ferromagnetism in TiO₂films or nanoparticles is generated by oxygen vacancies at surface.