Theory of Orbital Ordering, Fluctuation and Resonant X-ray Scattering in Manganites

A theory of resonant x-ray scattering in perovskite manganites is developed by applying the group theory to the correlation functions of the pseudospin operators for the orbital degree of freedom. It is shown that static and dynamical informations of the orbital state are directly obtained from the elastic, diffuse and inelastic scatterings due to the tensor character of the scattering factor. We propose that the interaction and its anisotropy between orbitals are directly identified by the intensity contour of the diffuse scattering in the momentum space.Comment: 4 pages, 1 figur

Spin and orbital excitation spectrum in the Kugel-Khomskii model

We discuss spin and orbital ordering in the twofold orbital degenerate superexchange model in three dimensions relevant to perovskite transition metal oxides. We focus on the particular point on the classical phase diagram where orbital degeneracy is lifted by quantum effects exclusively. Dispersion and damping of the spin and orbital excitations are calculated at this point taking into account their mutual interaction. Interaction corrections to the mean-field order parameters are found to be small. We conclude that quasi-one-dimensional Neel spin order accompanied by the uniform d_{3z^2-r^2}-type orbital ordering is stable against quantum fluctuations.Comment: 4 pages with 3 PS figures, 1 table, RevTeX, accepted to Phys. Rev. B. Rapid Communicatio

Magnetic Ordering, Orbital Ordering and Resonant X-ray Scattering in Perovskite Titanates

The effective Hamiltonian for perovskite titanates is derived by taking into account the three-fold degeneracy of $t_{2g}$ orbitals and the strong electron-electron interactions. The magnetic and orbital ordered phases are studied in the mean-field approximation applied to the effective Hamiltonian. A large degeneracy of the orbital states in the ferromagnetic phase is found in contrast to the case of the doubly degenerate $e_g$ orbitals. Lifting of this orbital degeneracy due to lattice distortions and spin-orbit coupling is examined. A general form for the scattering cross section of the resonant x-ray scattering is derived and is applied to the recent experimental results in YTiO$_3$. The spin wave dispersion relation in the orbital ordered YTiO$_3$ is also studied.Comment: 10 pages, 6 figure

Ferromagnetic insulating phase in Pr{1-x}Ca{x}MnO3

A ferromagnetic insulating (FM-I) state in Pr0.75Ca0.25MnO3 has been studied by neutron scattering experiment and theoretical calculation. The insulating behavior is robust against an external magnetic field, and is ascribed to neither the phase separation between a ferromagnetic metallic (FM-M) phase and a non-ferromagnetic insulating one, nor the charge ordering. We found that the Jahn-Teller type lattice distortion is much weaker than PrMnO3 and the magnetic interaction is almost isotropic. These features resembles the ferromagnetic metallic state of manganites, but the spin exchange interaction J is much reduced compared to the FM-M state. The theoretical calculation based on the staggered type orbital order well reproduces several features of the spin and orbital state in the FM-I phase.Comment: REVTeX4, 10 pages, 9 figure

Reciprocal transmittances and reflectances: An elementary proof

We present an elementary proof concerning reciprocal transmittances and reflectances. The proof is direct, simple, and valid for the diverse objects that can be absorptive and induce diffraction and scattering, as long as the objects respond linearly and locally to electromagnetic waves. The proof enables students who understand the basics of classical electromagnetics to grasp the physical basis of reciprocal optical responses. In addition, we show an example to demonstrate reciprocal response numerically and experimentally.Comment: 6 pages, 5 figures. RevTEX4. Improved wording. Physics Educatio