Properties Of Sr₂MO₄ Single-crystal From First Principles

One recent great discovery from laboratory to commerciallization is the giant magnetoresistance effect (GMR), discovered by P.Grunberg and Fert in the Fe/Cr multi-layer films, which has been applied from sensors, magnetic heads, magnetic information storages to spintransistors and all-metal computers. As a consequence, P.Grunberg and Fert won the Nobel Prize of physics in 2007. With the development of nano-technology, people found that some transition metal oxides have similar structures and characters with Fe/Cr multi-layer films.J.Matsuno first synthesized the single-crystal samples of Sr₂MO₄ (M=Ti - Co) on the epitaxial growth by plused-laser deposition (PLD) in 2005 and measured their optical conductivity spectra at -7K (except for M=Ti that was measured at room temperature). Their different electronic structures could be systematically studied as the occupation of d orbitals increases from empty (d0 for Ti⁴⁺) to half-filled (d5 for Co⁴⁺). Particularly, Sr₂VO₄ has almost the same structure as La₂CuO₄ with one 3d electron on V site in the former and one 3d hole on Cu site in the latter. Thus, the study on electron structures of Sr₂MO₄ (M=Ti - Co) will help us understand the mechanism of high-temperature superconductors.In this dissertation, we study Sr₂MO₄ with density functional theory (DFT), concerning their geometric structures, energy bands and magnetic orders.In the first chapter, we review both experimental and theoretical researches on colossal magneto resistance (CMR) and other interesting features of transition metal oxides, taking La_1-xSr_xMnO₃ as an example. The orbital ordering in the manganese oxides occasionally accompanies the concomitant charge ordering, which attracts us to investigate J. Matsuno's on Sr₂MO₄ (M=Ti - Co).In chapter 2, the elementary theory of DFT is introduced. DFT calculation is one of the most important methods that used widely to describe the structural, electronic, and optical properties of single-crystal without any empirical parameters. We briefly discuss the Born-Oppenheimer approximation, Hohenberg-Kohn theorem, Kohn-Sham equation, exchange and correlation functionals, and finally BSTATE- the DFT packages we use in this dissertation .In chapter 3, we report the calculated electron structures of signal-crystal Sr₂MO₄ with BSTATE (the functionals for exchange and correlation are GGA and GGA+U).We reach the following conclusion with comparing all kinds of spin states:1. Sr₂TiO₄ is a Mott insulator and the optical conductivity spectra is consistent with the experimental result .The transition energy from the oxygen 2p states to the empty conducting band is around 2.2eV.2. We have validated the insulator ground state for Sr₂VO₄ with the GGA approximation. In order to take account of the strong electron-electron correlations, we add the Hubbard U term and find that ab plane anti ferromagnetic (AFM) state has the lowest energy. A metal-to-insulator transition happens near U=2eV and the d electron eventually occupies dyz/zx, which is consistent with Weng's calculations. The calculated polarized optical conductivity spectra with electric field E parallel and perpendicular to the c axis also accord with experimental results.3. The Sr₂CrO₄ has the same electron structure with Sr₂VO₄. A metal-to- insulator phase transition happens near U=4eV.4. As for Sr₂MnO₄, the electron-electron correlation effect is also taken into account in our calculations and we find that the ab plane AFM has the lowest energy. Sr₂MnO₄ is proved to be a Mott-Hubbard insulator from our calculated optical conductivity spectra and density of states (DOS), which is consistent with J.Mastsuno's experiment.