First Principle Study Of D~0Ferromagnetism In Low-dimensional System

Recently, the phenomenon of unexpected d0ferromagnetism which was observed in the experiments challenged our conventional theory of magnetism. It triggered a heated debate in magnetic field and became a hot spot. As an important method for correlating theory with experiment, the computational simulation method is the essential way in the process of exploring the real mechanism of physics behind the d0ferromagnetism. Using electronic structure calculations based on the density functional theory (DFT), we have systematically studied the d0ferromagnetism of low-dimensional system which may exist in transition metal oxides (TiO2, HfO2), amphoteric oxide (SnO2) and alkaline oxide (MgO). We provide very important theoretical basis to reveal the d0ferromagnetic phenomena. The main achievements and conclusions in this paper are as follows:1. Results of our first principles GGA+U calculations show that the oxygen vacancy at the ridge (VOA) on the anatase TiO2(001) surface has the lowest formation energy for the vacancy defects. The spins induced by the VOA form a stable ferromagnetic state, and the anion vacancy can result in a magnetic moment of1.63μB. The magnetic moment which is produced by the VOA mainly comes from the3d orbitals of Ti atoms adjacent to the oxygen vacancy; meanwhile the defect states of spin polarization at about0.94eV below the conduction band minimum (CBM) can be induced by VOA.Although the spin dimerization will be formed along with the decrease of Ti-Ti distance when the distance is5.340A between two VOA’s on the surface, which can result in a low spin state, the results also show that the two VOA’s on the anatase TiO2(001) surface are mainly coupled ferromagnetically. In addition, the other kind of oxygen vacancy at the valley (VOB) is similar to the VOA, and it can also induce the local magnetic state on the anatase TiO2(001) surface (1.48μB). The two VOB’s on the surface are coupled ferromagnetically in different distances.2. Using electronic structure calculations,the calculated results show that only the vacancy of threefold-coordinated oxygen (VO3c) can introduce the magnetism on anatase TiO2(101) surface. The spins induced by the VO3c will form a stable ferromagnetic state, and it can produce a magnetic moment of1.05;μB moreover, the magnetic moment mainly results from the3d orbitals of Ti atoms around the VO3c; the defect states of spin polarization at about0.22eV below the Fermi energy can be induced by the VO3c.And the two VO3c’s on the (101) surface are mainly coupled ferromagnetically in different distances.3. Results of our first-principle calculations reveal that VO1is the most stable oxygen vacancy at the interface in the system of TiO2/SrTiO3. Isolated VO3c1can produce a magnetic moment of0.36μB.The magnetic moment mainly comes from the3d-orbitals of Ti atoms around the VO1. The results also show that structural relaxation has a profound impact on the magnetism. After relaxation, the Ti-Ti bond around the VO1will be increasing, which the spin dimerization will not be formed, and the system can transform from a low spin state before the relaxation to a high spin state. In addition, the two VO1’s at the interface are always coupled ferromagnetically.4. Based on the density functional theory (DFT), the calculated results of monoclinic HfO2(111) and (111) surface show that each kind of oxygen vacancy (VO) alone will not introduce the magnetism on the surface. However, the complex defects of oxygen vacancies (CDOV) which are composed of two VO’s can produce the local magnetic moment on the HfO2(111) and (111) surface. The CDOV have to meet two prerequisites:non ground state of ferromagnetism exists for one Vo in the CDOV; and the distance between the two VO’s in the CDOV should be less than or equal the critical distance (dCDOV).The results show that the dCDOV is2.792A on (111) surface and on (111) surface the dCDOV is2.957A. The studies reveal that the CDOV which meet the two prerequisites can produce stable ferromagnetism on the surface, and they can produce a magnetic moment of2.0μB. The magnetic moments mainly results from the d orbitals of Hf atoms around the CDOV.5. The first-principle calculations show that neither one single Vo nor complex defects of oxygen vacancies which are composed of two nearest VO’s can introduce the local magnetic state on rutile SnO2(001) and (110) surface. And the systems are both nonmagnetic. 6. Results of first-principle GGA calculations show that not only one single Vo but also complex defects of oxygen vacancies which are composed of two nearest Vo’s do not introduce the local magnetic moment on MgO (001)surface; however, the Mg vacancy can produce the magnetism on the (001) surface, and the results show that one single Mg vacancy can introduce a magnetic moment of0.35μB.In addition, the magnetic compling between the two nearest Mg vacancies is antiferromagnetic; however, the two second nearest Mg vacancies will be ferromagnetic compling, and they can produce the magnetic moment of4.00μB, the calculated results show that the magnetic moments mainly come from the2p orbitals of O atoms.