A study of quantum phenomena governed by orbital degrees of freedom in transition metal oxides with strongly correlated electron systems

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Transition metal oxides with strongly correlated electron systems show various quantum phenomena due to the charge, spin, and orbital degrees of freedom. Orbital degrees of freedom had been considered to be hidden behind the other ones. Recently, however, the development of experimental methods has enabled us to study orbital physics such as the orbital ordering with a long-range order of an orbital wave function, the orbital wave which is the excitation in the orbital ordering, and the orbital liquid having no long-range order of the orbital wave function. Consequently, orbital physics has attracted much attention from experimental and theoretical points of view. In this study, we have made NMR experiments to investigate the orbital state in the 3d transition metal oxides with t_<2g> electrons where quantum effects are expected. We found that YTiO_3, where an orbital ordering model with no orbital fluctuations had been proposed, has large orbital fluctuations due to quantum effects. This is the first NMR observation of orbital fluctuations in the t_<2g>^1 systems. Also we clarified the orbital state and the orbital ordering in Lu_2V_2O_7 by means of NMR. Thus the NMR technique is concluded to be useful for studying the orbital state. This technique, which is complimentary to the polarized neutron scattering and resonant X-ray scattering methods, is powerful to detect an orbital wave function and an electron quadruple moment. In some cases such as the vanadium bronzes β-Na_<0.33>V_2O_5 and η-Na_<1.286>V_2O_5, the orbital degrees of freedom govern physical properties behind the charge and spin ones. We found that β-Na_<0.33>V_2O_5 has an electronic structure not similar to the crystal structure due to the orbital ordering which leads to a model composed of the weakly coupled three ladders. Also we discussed the origin of the spin gap and the orbital ordering which governs exchange interactions in η-Na_<1.286>V_2O_5.