| The following studies are presented: theory of K-edge resonant inelastic x-ray scattering and its application for La0.5Sr 1.5MnO4, effects of rare earth ion size on the stability of the coherent Jahn-Teller distortions in undoped perovskite manganites, and symmetry-mode-based classical and quantum mechanical formalism of lattice dynamics.;Theoretical study is then introduced on the relation between the size of the rare earth ions, often known as chemical pressure, and the stability of the coherent Jahn-Teller distortions in undoped perovskite manganites. Using a Keating model expressed in terms of atomic scale symmetry modes, it is shown that there exists a coupling between the uniform shear distortion and the staggered buckling distortion within the Jahn-Teller energy term. It is found that this coupling provides a mechanism by which the coherent Jahn-Teller distortion is more stabilized by smaller rare earth ions. Further analysis shows the appearance of the uniform shear distortion below the Jahn-Teller ordering temperature; the Jahn-Teller ordering temperature is estimated and its variation between NdMnO3 and LaMnO3, and the relations between distortions are obtained. A good agreement is found between theoretical results and the experimental data.;Finally, the classical and quantum mechanical descriptions of lattice dynamics are presented, from the atomic to the continuum scale, using atomic scale symmetry modes and their constraint equations. This approach is demonstrated for a onedimensional chain and a two-dimensional square lattice on a monatomic basis. For the classical description, it is found that rigid modes, in addition to the distortional modes found before, are necessary to describe the kinetic energy. The long wavelength limit of the kinetic energy terms expressed in terms of atomic scale modes is shown to be consistent with the continuum theory, and leading order corrections are obtained. For the quantum mechanical description, conjugate momenta for the atomic scale symmetry modes are presented. In direct space, graphical rules for their commutation relations are obtained. Commutation relations in the reciprocal space are also calculated. As an example, phonon modes are analyzed in terms of symmetry modes. The approach presented here based on atomic scale symmetry modes could be useful for the study of complex emerging materials, in which competing structural phases and non-linearity of the lattice energy play an important role.;The formula based on tight-binding approach for the calculation of K-edge resonant inelastic x-ray scattering (RIXS) spectrum for transition metal oxides is presented first, by extending the previous existing result to include explicit momentum dependence and a basis with multiple core-hole sites. This formula is applied to layered charge, orbital and spin ordered manganites, La 0.5Sr1.5MnO4, and good agreement with experimental data was obtained, in particular, with regard to the large variation of the intensity with momentum. As a consequence, it is established that the electron screening in La0.5Sr1.5MnO4 is highly localized around the core hole site and demonstrates the potential of K-edge RIXS, as a probe for the screening dynamics in materials. |
