We report strongly momentum-dependent short-ranged charge screening dynamics in CE-type charge, orbital, and spin ordered La 0.5 Sr 1.5 MnO 4 , based on Mn K-edge resonant inelastic x-ray scattering data. Through a comparison with theoretical calculations, we show that the observed momentum dependence reflects highly localized, nearest-neighbor screening of the transient local charge perturbation in this compound with an excitonlike screening cloud, rather than delocalized screening. The size of the screening cloud is estimated to be about 0.4-0.5 interatomic distances.

We analyze the essential role played by complex energy landscapes in the nanometer-to micron-scale inhomogeneities observed in perovskite manganites using a model expressed in terms of symmetrized atomic-scale lattice distortion modes. We also examine the stability of large metal and insulator domains in the absence of defects. Our results demonstrate that an intrinsic mechanism, which involves long-range interactions between strain fields, the Peierls-Nabarro energy barrier, and complex energy landscapes with multiple metastable states, rather than an extrinsic mechanism such as chemical randomness, is responsible for the inhomogeneity in perovskite manganites.

Effects of rare earth ion size on the stability of the coherent Jahn-Teller distortions in undoped perovskite manganites and LaMnO 3 , and obtain the relations between distortions. We find good agreement between theoretical results and experimental data.

We present classical and quantum mechanical descriptions of lattice dynamics, from the atomic to the continuum scale, using atomic scale symmetry modes and their constraint equations. This approach is demonstrated for a one-dimensional chain and a two-dimensional square lattice with a monatomic basis. For the classical description, we find 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 the leading order corrections are obtained. For the quantum mechanical description, we find conjugate momenta for the atomic scale symmetry modes. 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. We emphasize that the approach based on atomic scale symmetry modes could be useful, for example, for the description of multiscale lattice dynamics and the dynamics near structural phase transition.

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