Research Achievements

October 28, 2020 

Direct observation of a single electron's butterfly-shaped distribution in titanium oxide

A valence electron in titanium oxide has been imaged at a resolution of 0.2 Angstroms using synchrotron X-ray diffraction and a new Fourier synthesis method that can determine the orbital states in materials regardless of their physical properties.


A research team led by Nagoya University has observed the smeared-out spatial distribution of a single valence electron at the centre of a titanium oxide molecule, using synchrotron X-ray diffraction and a new Fourier synthesis method also developed by the team. The method can determine the orbital states in materials regardless of their physical properties and without the need for difficult experiments or analytical techniques. The work was published recently in Physical Review Research.


The functions and physical properties of solid materials, such as magnetic order and unconventional superconductivity, are greatly influenced by the orbital state of the outermost electrons (valence electrons) of the constituent atoms. In other words, it could be said that the minimal unit that determines a solid material's physical properties consists of the orbitals occupied by the valence electrons. Moreover, an orbital can also be considered a minimal unit of "shape," so the orbital state in a solid can be deduced from observing the spatially anisotropic distribution of electrons (in other words, from how the electron distribution deviates from spherical symmetry).


The orbital states in elements are basic knowledge that can be found in quantum mechanics or quantum chemistry textbooks. For example, it is known that the 3d electrons in transition elements such as iron and nickel have characteristic butterfly-type or gourd-type shapes (see Fig. 1(a)). However, until now, it has been extremely difficult to observe the real-space distribution of such electron orbitals directly.


Now, a research collaboration between Nagoya University, University of Wisconsin-Milwaukee, Japan's RIKEN and Institute for Molecular Science, the University of Tokyo, and the Japan Synchrotron Radiation Research Institute (JASRI), has observed the butterfly-shaped spatial distribution of a single valence electron at the centre of an octahedron-shaped titanium oxide molecule, using synchrotron X-ray diffraction (see Fig. 1(b)).


Figure 1. (a) Distribution of a butterfly-shaped 3d electron orbital. (b) Valence electron density distribution around the titanium (Ti3+) ion at the centre of the titanium oxide (TiO6 ) octahedron obtained by the CDFS analysis developed by the research team for this project. CREDIT: Shunsuke Kitou


To analyse the X-ray diffraction data from the titanium oxide sample, the team developed a Fourier synthesis method in which data from each titanium ion's inner shell electrons - which do not contribute to the compound's physical properties - are subtracted from the total electron distribution of each ion, leaving only the butterfly-shaped valence electron density distribution. The method is called core differential Fourier synthesis (CDFS).


Furthermore, a closer look at the butterfly-shaped electron density revealed that high density remained in the central region (see Fig. 2(a)), in contrast with bare titanium in which electrons do not exist at the centre because of the  node of the 3d orbital (see Fig. 1(a)). After careful data analysis, it was found that the electron density at the centre consists of the valence electrons occupying the hybridized orbital generated by the bond between titanium and oxygen. First-principles calculations confirmed this non-trivial orbital picture and reproduced the results of the CDFS analysis very well (see Fig. 2(b)). The image directly demonstrates the well-known Kugel-Khomskii model of the relationship between the magnetic and orbital-ordered states.


Figure 2. Cross-sectional view of the valence electron density distribution of Ti3+ ion obtained by (a) the CDFS analysis and (b) the first-principles calculation.  CREDIT: Shunsuke Kitou


The CDFS method can determine the orbital states in materials regardless of the physical properties and can be applied to almost all elements and without the need for difficult experiments or analytical techniques:  the method requires neither quantum-mechanical nor informatic models, so bias introduced by analysts is minimized.   The results may signal a breakthrough in the study of orbital states in materials. The CDFS analysis will provide a touchstone for a complete description of the electronic state by first-principles or other theoretical calculations.




This work was supported by a Grant-in-Aid for Scientific Research (No. JP23244074, JP19J11697) from JSPS. The synchrotron radiation experiments were performed at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2011B0083, and No. 2019A0070).


The paper

"Collapse of the simple localized 3d1 orbital picture in Mott insulator" was published in Physical Review Research on September 28, 2020, at DOI: 10.1103/PhysRevResearch.2.033503



Shunsuke Kitou, Taishun Manjo, Naoyuki Katayama, Tatsuya Shishidou, Taka-hisa Arima, Yasujiro Taguchi, Yoshinori Tokura, Toshikazu Nakamura, Toshihiko Yokoyama, Kunihisa Sugimoto, and Hiroshi Sawa.


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Shunsuke Kitou,


About Nagoya University

Nagoya University has a history of about 150 years, with its roots in a temporary medical school and hospital established in 1871, and was formally instituted as the last Imperial University of Japan in 1939. Although modest in size compared to the largest universities in Japan, Nagoya University has been pursuing excellence since its founding. Six of the 13 Japanese Nobel Prize-winners since 2000 did all or part of their Nobel Prize-winning work at Nagoya University:  four in physics - Maskawa and Kobayashi in 2008, and Akasaki and Amano in 2014  - and two in Chemistry - Noyori in 2001 and Shimomura in 2008. In mathematics, Mori did his Fields Medal-winning work at Nagoya University. A number of other important discoveries have been made at Nagoya University, including the Okazaki DNA Fragments by Reiji and Tsuneko Okazaki in the 1960s; and depletion forces by Asakura and Oosawa in 1954.

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