Impurities In Antiferromagnetic Transition-metal Oxides – Symmetry And Optical Transitions
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The study of antiferromagnetic transition-metal oxides is an extremely active area in the physical sciences, where condensed matter physics, inorganic chemistry, and materials science blend together. The sheer number of potential commercial applications is staggering, but much of the fundamental science remains unexplained. This is not due to a lack of effort, however, as theorists have been struggling to understand these materials for decades – particularly the character of the band edges and first optical transitions. The difficulty lies in the strong correlation or Coloumb attraction between the electrons in the anisotropic d orbitals, which conventional band theory cannot describe adequately. The correlation problem is approached here by the well-accepted method of adding a Hubbard potential energy term to the ground state Hamiltonian, calculated within Density Functional Theory. The frequency-dependent complex dielectric function is calculated within the Independent Particle Approximation, and optical transitions are evaluated in multiple different ways. Peaks in the imaginary part of the dielectric function are compared energetically to orbitally decomposed density of states calculations. Optical transitions are typically analyzed in terms of atomic orbitals, which, strictly speaking, gives misleading results. Here, however, from the calculated data, two alternative interpretations are analyzed for each material studied. The first employs rigorous group theoretical analysis to determine allowed electric-dipole transitions, taking into account both orbital hybridization and crystal symmetry. The second interpretation is that of metal cation site hopping. In this interpretation, carriers hop from the x2 – y2 d orbital of one metal cation lattice site to the next metal cation site which is antiferromagnetically aligned. At times, thoughout this work, one interpretation is favorable to the other. Which interpretation is most valid depends on the material considered. For example, simple rock-salt transition-metal oxides are quite different from the high temperature superconducting cuprates. A range of materials is studied here, in order to gain a greater understanding of optical transitions in highly-correlated systems. In this work, O vacancies are introduced in NiO, along with Fe impurities, to understand better the band filling in the insulating behavior observed experimentally. These results are compared with those of La2NiO4, La2CuO4, La2-xSrxNiO4, and La2-xSrxCuO4. to elucidate the mechanisms behind the symmetry breaking phenomena in the Sr doped systems. As it turns out, indeed, the x2 – y2 orbital in these materials plays a critical role in spatial charge distribution, magnetic, and spin densities which are coupled to the dopant position in the lattice. The in-depth study of electronic and optical properties of transition-metal oxides presented here provides theoretical characterization of the infamous pseudogap in the cuprates – one of the greatest mysteries of modern solid state physics. In addition, via Density Functional Perturbation Theory, the phonon coupling with charge-density wave is explored in La2-xSrxNiO4 and found to be the dominant contributing factor to the colossal dielectric constant.