The Impacts Of Spin Degree Of Freedom On The Material Physics In Correlated Electron System: First-Principles Study

The competition and cooperation of the lattice, charge, spin and orbital degrees of freedom (DOF) in transition metal oxides (TMO) have gave rise to profuse physical properties and fascinating physical phenomena. They are significant not only for theoretical investigation but also for potentially practical application. Recently, the extensive technology-applications of the Giant Magnetoresistance (GMR) materials and the flourish of spintronics (or spin electronics) as well as quantum calculation have attracted considerable attention and interest. The theoretical investigations on spin DOF and the interplay with other DOF in correlated electron system have been one of the hottest topics for condensed-matter physics.Motivated by the development of the computer technology and the advancement of theoretical methods, the first-principles (or ab initio) methods based on density functional theory (DFT) have become effective supplement to the experimental means. The theoretical calculations not only can help us to analyze the experimental results and explain the experimentally observed phenomena, but also can explore unknown materials characteristics by absolutely theoretical prediction independent of experiment.In this thesis, we study some typical vanadate materials of the correlated electron system, including the quasi one-dimensional spin chain, quasi two-dimensional spin ladder and three-dimensional multiferroic materials. The ultrasoft pseudopotential plane-wave methods and the spin-polarized generalized gradient approximation (GGA) are employed to perform first-principles investigations. We pay our attention principally to the impacts of spin DOF on the macroscopically physical characters by electronic structure calculations. The available experimental results and phenomena are analyzed, discussed and interpreted. We also predict unknown materials properties by carrying out absolutely theoretical calculations and computer simulations independent of experiment.First of all, we study the electronic structure of the room-temperature (RT) phase of the quasi one-dimensional spin-Peierls compoundα'-NaV₂O₅. The band structure of the crystallographic unit cell shows nonmagnetic (NM) metallic characteristics by non-spin-polarized GGA calculations. The NM metallic solution is consistent with other theoretically reported results, but can not explain the experimentally observed insulating behavior. Adopting the spin-polarized GGA method and considering the spin DOF, we can obtain an insulating ferromagnetic (FM) band structure for the unit cell, but can not explain the experimental results of the RT magnetic susceptibility and angle resolved photoemission spectroscopy (ARPES). We enlarge the crystallographic unit cell along the b axis to construct a 1×2×1 supercell, the system relaxes to the antiferromagnetic (AFM) ground state with insulating band structure. Total energies calculations indicate that the NM metallic state is instable with respect to the magnetic ordering states, and the AFM insulating state is the most stable. The dxy orbital is separated from other V 3d orbitals by the VO5 square-pyramidal crystal field, and has the lowest energy. The V 3d electron occupy the dxy orbital and is shared by two V ions, which is hopping on the same rung and forming H2+-type V-O-V molecular orbital. The magnetic S = ? effective electrons align anti-parallel with each other along the chain with AFM magnetic coupling interactions, which explains well the magnetic behavior of one-dimensional Heisenberg linear AFM chain observed in the RT magnetic susceptibility experiment. The intra-rung vanadium dxy orbitals form the bonding-antibonding orbitals splitted by inter-orbital interactions. It is not the on-site Coulomb repulsion interaction, but the AFM spin exchange couplings that lead to the half-filled bonding orbitals splitting and form a magnetic insulating gap. The essence of the insulating behavior has given rise to much controversy. The present spin-polarized DFT calculations unambiguously reveal that RT phase ofα'-NaV₂O₅ is a Slater insulator, rather than Mott-Hubbard insulator or charge-transfer insulator. Calculated electronic structure explains the controversial topics of absorption peak in the optical spectra and energy loss peak in resonant inelastic X-ray scattering (RIXS) well.Second, the electronic structure, magnetic exchange interactions and spin gap of the ladder structural vanadate CaV₂O₅ have been studied by spin-polarized GGA method for the first time. Geometry optimization and electronic structure calculations are performed for four possible spin-ordered states. The crystal structure is independent of the magnetic ordering states. The calculated results are in line with the experimental data. The four spin ordering states have been successfully simulated, which are proved by the Mulliken population analysis. The experimentally observed insulating behavior has been reproduced successfully in the framework of the band theory by introducing the magnetic ordering. The insulating band gap has increased further provided that the spin DOF has been took into account, which is derived from the spin exchange coupling but not the Coulomb repulsion interactions. Calculated results reveal that the true magnetic ground state of CaV₂O₅ is the AFM state with AFM exchange interactions both inside the rungs and along the ladder legs. Differentiate from previous theoretical methods using in the reported literature, we calculated exchange parameters by a combination of DFT calculations and Noodleman's broken symmetry method. The spin exchange parameters are fit quantitatively by mapping the energy differences of the four possible spin-ordered states to Heisenberg model. The calculated results are in good agreement with other theoretical results and experimental data. The magnetic coupling interactions in CaV₂O₅ show prominent anisotropic characteristic. The intra-rung AFM interaction is much stronger than that along the legs, which leads to spin-dimer on the same rung. The spin-dimer are weakly coupled along the leg with AFM interaction, whereas the inter-ladder coupling is weak FM. Calculated results indicate that the spin-dimer on the rung plays an crucial role in the electronic structure and magnetic characteristics of the ladder structural compound CaV₂O₅. The spin-dimer forms spin-singlet along with temperature descending, which brings on the nonmagnetic ground state of the system. There is a spin gap between the ground state and the first excited state. The existence of inter-ladder weak FM interactions results in an obvious decrease of the spin gap.Third, the electronic structure, magnetic property and origin of ferroelectricity in multiferroic material PbVO₃ are investigated. Four typical spin ordering states in perovskite compound are considered during the study process. The FM state of the tetragonal phase displays a half-metallic characteristic. The insulating ground state of tetragonal phase has been reproduced successfully in the framework of the band theory by introducing the experimentally observed AFM spin configuration, which is characterized by C-type two-dimensional AFM magnetic ordering in the ab plane. The crystal-field splitting associated with the magnetic ordering lead to the insulating behavior in tetragonal PbVO₃. The 3d electrons of the V4+ ions occupy the dxy orbital and hybridize with O px/py orbitals to form the two-dimensional C-AFM magnetic coupling. The V atom and vertical O atom in the VO5 square-pyramid form a very short V-O bond, which results in strong hybridization effects between O 2p and V 3d states. The hybridization effects weaken the short-range repulsion and reduce the system energy, which is favored by the ferroelectric (FE) distortion of the tetragonal phase. In addition, the lone paired state of the Pb 6s orbitals hybridize with O 2p states, which also reduce the system energy and enhance the stability of the tetragonal FE structure. The equilibrium unit cell volume V and bulk modulus B at ambient pressure are deduced by fitting the equation of states (EOS) for the tetragonal and cubic phases PbVO₃. The calculated results are 72.58 and 59.79 A³, 41 and 163 GPa for the tetragonal and cubic phases PbVO₃, respectively. The bulk modulus of tetragonal phase is remarkable smaller than that of the cubic phase, which implies the former is much more compressible relative to the latter. The tetragonal phase transforms to a cubic perovskite structure corresponding to the FE to paraelectric (PE) phase transition at 1.25 GPa. The discontinuous changes of the lattice parameters indicate the first-order phase transition characteristic. The phase transition accompanies by coordinate environment transformation from VO5 square-pyramid to VO6 octahedron for the V⁴⁺ ions, which give rise to the volume collapse and dramatic changes of the lattice parameters. Electronic structure calculations reveal that the FM state is the ground state of the cubic phase, which exhibits the representative characteristic of FM half metal. The majority-spin states display metallic character, whereas the minority-spin states have an energy gap around the Fermi level (E_F). As a result, only electrons of majority-spin states contribute toward conduction electrons yielding 100% spin polarization at the E_F. The theoretical calculations predict that the cubic phase PbVO₃ is a possible candidate material for applications in spintronics.