The study on observation technique of orbital orderingby synchrotron radiation, neutron, and electron beams.

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Three degrees of freedom (charge, spin, and orbital) play very important roles in the electronic and magnetic properties in strongly correlated electron systems. Therefore, it is necessary to observe the ordering states of the degrees of freedom. However, the experimental technique to observe the orbital ordering has been very limited compared with the charge and spin ordering. The aim of this study is to develop thetechnique using synchrotron X rays, neutrons, and electron beams.We make five groups to achieve the aim. The followings are the main results for the groups.1. Samples and the evaluations group: We have made good quality samples of transition metal oxides and f-electron systems.2. Synchrotron X rays group: We have developed a new technique to observe ferro-orbital ordering -using the interference of resonant X-ray scattering. Magnetic Compton profile has revealed the orbital state of layered manganites.3. Neutrons group: The polarized neutron diffraction has elucidated the orbital state of layered manganites coupled with the powder neutron iffraction.4. Electron beams group: We have developed the software-of the convergent electron diffraction and made clear the orbital state of the manganite.5. Theory group: We have constructed the general theory of resonant X-ray scattering to observe the orbital ordering and its fluctuation