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

具有强关联电子系统的过渡金属氧化物由于电荷、自旋和轨道自由度而表现出各种量子现象。轨道自由度被认为隐藏在其他自由度之后。然而，最近，实验方法的发展使得我们能够研究轨道物理，诸如具有轨道波函数的长程有序的轨道有序、作为轨道有序中的激发的轨道波、以及不具有轨道波函数的长程有序的轨道液体。因此，轨道物理学从实验和理论角度都引起了极大的注意。在本研究中，我们利用核磁共振实验研究了具有t_电子的三维过渡金属氧化物的轨道态<2g>，其中预期会出现量子效应。我们发现YTiO_3由于量子效应而具有较大的轨道涨落，而YTiO_3的轨道有序模型是没有轨道涨落的。这是首次用核磁共振方法观测到t_^1体系中的轨道涨落<2g>。用核磁共振方法研究了Lu_2V_2O_7的轨道状态和轨道有序性。因此，核磁共振技术是有用的研究轨道状态。该技术是极化中子散射和共振X射线散射方法的补充，是强大的检测轨道波函数和电子四极矩。在某些情况下，如钒青铜β-Na_<0.33>V_2O_5和η-Na_<1.286>V_2O_5，轨道自由度决定了电荷和自旋自由度之后的物理性质。我们发现β-Na_<0.33>V_2O_5的电子结构与晶体结构不相似，这是由于轨道有序性导致的，它是由弱耦合的三阶梯结构组成的模型。讨论了η-Na_ V_2O_5中自旋能隙的来源和控制交换作用的轨道有序<1.286>。

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.