Semi-metallic Ferromagnetism Of Cro <sub> 2 </ Sub> First Principle Of The Surface Geometry And Electronic States

A half-metallic ferromagnet (HMF) is a novel material with special band structures. That is, for electrons of one spin direction (called majority) it behaves as a metal, while for the opposite spin direction (minority) it has a gap at E_F like a semiconductor or an insulator, resulting in electrons at E_F being 100% spin polarization, that is, the Fermi level lies in a gap between occupied and unoccupied bands for minority spins. Because of its high spin polarization, HMF has a promising potential for applications on spintronics devices. It was theoretically predicted that chromium dioxide is a HFM, a unique one with HFM among transition-metal (TM) oxides. However, in contrast to theoretical predictions, an early photoemission measurement on CrO₂(001) found an extremely low intensity near E_F, inconsistent with its metallic behavior. Its authors concluded that CrO₂ was also a Mott insulating-like material as other TM oxides. However, most photoemission measurements on CrO₂ displayed a small but finite intensity near E_F. A recent study on CrO₂(100) by the same group of the early photoemission observation found a weak but finite intensity near E_F. Considering this controversy, the group deduced that the vanishing of photoemission intensity near E_F at the CrO₂(001) surface found by their early work was likely due to defects such as an oxygen deficiency at the surface. Many experimental and theoretical investigations have been devoted to understanding this controversy. However, up to now there are not any credible explanations for the strange observation.In this work, using first principles calculations we will systematically study this puzzle, which remains for nearly 20 years. After introducing the motivation and the theoretical framework for our study, we begin our discussion with bulk properties of CrO₂ in chapter 3.We find that for bulk CrO₂, O 2s and 2p bands are fully occupied, implying that four of six electrons per Cr atom transfer to the O 2p bands, leaving two electrons in a d² configuration as a Cr⁴⁺ ion. CrO₂ crystallizes in a rutile structure with a tetragonal unit cell consisting of two formula units, each of which has one Cr surrounded by six O in an octahedron. Cr occupies the center, while O atoms occupy two apexes and four square-corners in the equatorial plane of the octahedron. Two units are rotated by 90° about the direction of the c-axis. Therefore, Cr can be seen as an ion octahedrally surrounded by six O. The structure, in which Cr is surrounded by O, plays an important role in determining the properties of CrO₂, even if surface existence.It is well established that five-degenerate d-orbitals of Cr under an octahedral crystal field are split into a triplet t_2g and a doublet e_g with the t_2g low-lying. Due to distortion of the octahedron, the t_2g will split further into a singlet d_xy and a doublet d_xz and d_yz with d_xy low-lying. Due to on-site exchange interaction of d-electrons of Cr, the two remaining d-electrons of the Cr ion will occupy the t_2g of the majority bands, leaving 3d bands of the minority empty, and the 3d bands of the minority is thus shift up to above the Fermi level to form a gap in minority between O 2p and Cr 3d bands. For majority bands the doublet d_xz and d_yz is half-filled, therefore, the majority exhibits a metallic nature. That is half metallicity.From the above discussion, the key to understand the HMF of CrO₂ using Hund's rule is: (1) the ionic nature of Cr surrounded by O-the electrons of Cr will fill the splitting orbirals under the crystal field of the surrounded O; (2) the structure of the surrounded O, which determines the energy order of splitting orbitals. Here the structure symmetry of crystal field created by O surrounding Cr plays an important role. When CrO₂ is cut to form a surface, the octahedra inner are only slightly distorted due to the surface existence. Hence, the crystal field symmetry will not be greatly changed. However, for octahedra at surface the structural symmetry will be totally different to that in inner and therefore will change the splitting order of d-orbitals of the Cr ion at surface, and further determine if CrO₂ surface remain half-metallic ferromagnet.Therefore in chapter 4, we will study geometric structures of low-index CrO₂ surfaces. When CrO₂ is cut to form a surface, Cr and O at the surface will relax to search for a stable configuration, which can be understood by orbital physics.In bulk CrO₂, each O is shared by three octahedra: in which O is as an apex for one octahedron, and a square corner in the equatorial plane for other two octahedra. Therefore, each O is 3-fold coordinated and bonds with three Cr in three adjacent octahedra. Therefore, it is sp² hybridization. Due to surface existence, surface O as an apex or a square-corner of an octahedron may lose one Cr. Therefore, instead of 3-fold coordinated the surface O will be 2-fold coordinated, that is, sp³ hybridization. A surface 0 may not lose Cr, but the octahedron relative to the surface O may lose O atoms, whose Cr may change its charge transfer to the surrounded O, leading to that the surface O forms lone pair. Therefore, the hybridization of the surface O is also changed from sp² to sp³. If O's hybridization is changed from sp² to sp³, its bond angles will change, leading to relaxation of the surface O and Cr. Therefore, the surface Cr prefers a stable configuration surrounded by O, and is separated from other Cr.In this way, the surface Cr may lose an O to be 5-fold coordinated, or two O to be 4-fold coordinated, still in a configuration surrounded by O. In the orientations of (100), (110) and (011), the surface Cr loses an O to be 5-fold coordinated, and lies in a rectangular cone surrounded by O after relaxation; while in the (001) orientation the surface Cr loses two square corner O to be 4-fold coordinated, and lies in a tetrahedron surrounded by O.According to those results of geometric structures for the low-index CrO₂ surfaces in chapter 4, we then study electronic structures relative to the geometric information.Like the bulk case, four 3d electrons of the surface Cr transfer to the O 2p bands, leaving two electrons for the Cr in the d² configuration. We have determined that the surface Cr of CrO₂(001) lies in a tetrahedron surrounded by O. We first check if the d orbital splitting of the surface Cr follows the features in a tetrahedral crystal field.The surface Cr atom at CrO₂(001) prefers a tetrahedral configuration, leading to the inversion of the e_g—t_2g splitting of the d-orbitals of the surface Cr with the e_g low-lying. We can clearly identify the feature of an e_g—t_2g splitting in the tetrahedral crystal field, which is that the e_g (d_z² and d_x²-y²) is really low-lying. There is an obvious gap between the e_g and t_2g (d_xy, d_yz and d_xz) crossing the Fermi level. Two d electrons of the surface Cr ion will completely occupy the e_g, leaving the t_2g empty. If LSDA+U calculations with a reasonable U value are performed, the splitting betweene_g—t_2g in the LDOS of the surface layer will extend to about 1.2 eV.This finding explains the puzzle, which remains nearly 20 years: the observed very low photoemission intensity near the Fermi level is only a surface effect. The photoemission experiment with photon energy of 21.2 eV was very surface-sensitive and most likely revealed a local electronic structure at the surface, which was mainly caused by the unusual structure at the CrO₂(001) surface. However, most other measurements were either for deeper layers due to bigger escape-depth of higher photon energy or for surfaces not in the (001) orientation, in which the surface Cr is not in a tetrahedron but in a rectangular cone. We find also that there is a pseudogap near E_F to separates the d_xz+yz and d_xz-yz bands of the bulk Cr, which overlap near the Γ point. Therefore, electronic intensity near E_F is quite small in this orientation even for deeper layers due to this pseudogap.We emphasize here the role of the relaxed structure in the surface layer. If we carry out the same LSDA calculations on an ideal, unrelaxed CrO₂(001) surface, we cannot expect this kind of splitting. This is reasonable, since in fact for an unrelaxed CrO₂(001) surface only two O in the equatorial plane are moved away from an octahedron. Compared with the bulk case, the interaction of d_z² with surrounding O is unchanged, while the interaction of the other d-orbitals are weaker due to the absence of two O atoms in the equatorial plane. We also calculate electronic structures of the unrelaxed CrO₂(001) with the same correlation effect, but no gap can be found near E_F for local electronic structures at the surface layer.The coordination of the surface Cr plays an important role in opening a gap as discussed above, it is an unique reason for inversion of the e_g—t_2g- The CrO₂(001) is unique, with the surface Cr being 4-fold coordinated among low-index orientations such as the (100), (110), (011) and (001) orientation. The surface Cr in the (100), (110) and (011) orientations are all five-fold coordinated. Therefore, we cannot find a similar splitting for these orientations to explain the low electronic density of states near the Fermi energy.The group, who found the puzzle, deduced due to the controversy that the very low photoemission intensity near E_F may be induced by O deficiency at CrO₂ surfaces. In chapter 6 we also carry out calculations on reduced surfaces for all low-index surfaces of CrO₂, in which one O atom is moved from the surface unit cell. The results showthat there is no gap crossing E_F in local electronic structures at surfaces for spin-up electrons.