Research on the ground state of electrons of an orbital-ordering perovskite Ti oxide by the X-ray magnetic diffraction experiment

钙钛矿氧化物YTiO_3具有特殊的固态性能；它显示轨道有序，在30K以下变成铁磁性。这两种性质的起源是钛原子的三维电子。本研究的目的是利用同步辐射x射线来阐明钙钛矿型氧化钛YTiO_3的特殊性质。我们采用了两种实验方法：1)x射线磁衍射（XMD）和2)磁康普顿散射（MCP），这两种实验方法分别是椭圆极化同步辐射x射线在磁矩作用下的弹性散射和非弹性散射。用前一种方法在倒易晶格空间（或其傅里叶变换实空间）中观察磁性电子的波函数，用后一种方法在动量空间中观察磁性电子的波函数。本研究的具体目的是通过同步辐射直接观测YTiO_3中Ti原子的电子轨道，明确其三维电子的基态。由于XMD和MCP的实验方法都要求试样的磁化达到饱和，我们在ord . More对XMD实验系统进行了升级，使其即使沿着该化合物的硬磁化方向也能产生超过2T的磁场。通过对实验系统的改进，我们可以在样品晶体沿任何晶体学方向磁化饱和的情况下进行XMD实验。我们从XMD实验中得到了以下结果：(1)我们可以测量YTiO_3所有主要结晶轴的自旋磁形状因子。(2)首次成功获得了YTiO_3自旋密度在实空间中的三维分布。(3)得到的自旋密度分布很好地代表了三维电子在t2g态的电子分布。这将是第一次在三维实际空间中直接观察到一个特定的三维电子轨道。在MCS实验中，我们首次测量了轨道有序铁磁化合物的磁性康普顿谱（MCP）。通过比较观测到的MCP与基于模型波函数计算的MCP，我们可以确定三维电子的基态波函数。综上所述，我们可以阐明YTiO_3三维电子在实空间和动量空间中的有序轨道（基态波函数）。少

Perovskite oxide YTiO_3 has peculiar solid-state properties; it shows orbital ordering and becomes ferromagnetic below 30K. Origin of the both properties is 3d electrons of Ti atoms. The aim of this research is to elucidate the peculiar properties of the perovskite titanium oxide YTiO_3 by using synchrotron radiation X-rays. We utilize two kinds of experimental methods, l) the X-ray magnetic diffraction (XMD) and 2) the magnetic Compton scattering (MCP), which are elastic and inelastic scattering of elliptically polarized synchrotron radiation X-rays by magnetic moments. Wavefunctions of magnetic electrons are observed in the reciprocal lattice space(or its Fourier transformed real space) by the former method, and in the momentum space by the latter method. Concrete purpose of this study is to clarify the ground state of the 3d electrons of Ti atoms in YTiO_3 through direct observation of the electrons orbital by synchrotron radiation.We have upgraded the XMD experimental system in ord … More er to produce magnetic field of over 2T that is needed for saturating the magnetization even along the hard magnetization direction of this compound, as both experimental methods of XMD and MCP require the magnetization of the specimen to be saturated. By this upgrade of the experimental system we ca perform the XMD experiment under the condition in which the magnetization of the specimen crystal is saturated along any crystallographic direction.We have obtained the following results from the XMD experiment.(1) We could measure spin magnetic form factor for all principal crystallographic axes of YTiO_3.(2) We have succeeded in obtaining three dimensional distribution of spin density of YTiO_3 in the real space for the first time.(3) The obtained spin density distribution was represented very well by the electron distribution of 3d-electons in the t2g state. This would be the first direct observation of a specific 3d electron orbital in the three dimensional real space. In the MCS experiment we could measure the magnetic Compton profile (MCP) of an orbital-ordering ferromagnetic compound for the first time. By comparing the observed MCP with the calculated MCP based on a model wavefunction we could determine the ground-state wavefunction of the 3d electron. In conclusion we could elucidate the ordered orbital (ground state wavefunction) of the 3d electrons of YTiO_3 in the real space and momentum space. Less