Summary of research on orbital orders and fluctuations

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This project has revealed new properties of matter due to orbital degrees of freedom by performing comprehensive study of systems ranging from 2p, 3d, to 4f and 5f electrons with "orbital order" and "orbital fluctuation" taken as key words. Furthermore, we have found new functionary materials by controlling the orbital degrees of freedom. In particular we mention the discovery of high-temperature superconductivity MgB2 and elucidation of its fundamental properties. The material has both sigma and pi orbitals which have very different properties. The coexistence influences essentially the physical property of MgB2. It has not been possible to grow large single crystals during the period of the project, but the project has paved the way for future development. On the other hand, we have reported a new high-temperature ferromagnet CaB2C2, and checked in detail the property of CaB6 and related materials. However, we have not yet excluded the possibility that Fe impurities may play an important role in realizing the ferromagnetism. For f electron systems, we have revealed characteristics of the orbital ordering in CeB6 and related materials, hidden order in URSu2Si2, and one-dimensional magnetism in Yb4As3, among other things.We organized every year domestic meetings open to general audience and a special meeting after the discovery of MgB2. In 2002 we organized an international conference in Sendai having about 150 participants and active discussions with high quality. The proceedings were published as supplement of the Physical Society of Japan.