Abstract text (incl. figure legends and references)

The effect of anisotropic atomic vibrations on Ti L_2,3-edge spectrum of SrTiO₃ was reported in previous research[1]. Our group revealed that the Ti L_2,3-edge experimental spectra could be reproduced by crystal field multiplet calculation considering the anisotropic atomic vibrations model. The thermal vibration factors are very sensitive to the reproduction of spectral shape, but not all elemental thermal vibration factors have the same effect. Therefore, in the present work, we report the relation between individual atomic vibration and L_2,3-edge spectrum quantitatively by monochromated STEM-EELS and crystal field multiplet calculation.

Firstly, we investigated the importance of individual thermal vibration factors to the Ti L_2,3-edge spectrum in the perovskite cubic structure. In SrTiO₃, Ti and Sr show isotropic vibration, and oxygen atoms show anisotropic ellipsoid thermal vibration, as shown in Figure 1. Our result indicated that the effect of atomic vibrations on the L_2,3-edge is related to specific elements in the crystal and their vibration directions. It reveals that thermal vibrations of Ti and O have effects on the Ti L_2,3-edge spectral shape, whereas Sr has almost no effect on it. In particular, the vibration effect on the spectrum is mainly dominated by the oxygen thermal factor along the Ti-O direction (U_O(Ti)); thermal vibration of Ti (U_Ti) and oxygen along SrO plane (U_O(Sr)) show small and similar effects. Hence, as the inverse problem, we tried to extract the temperature dependence of Debye-Waller factors of oxygen from the experimental Ti L_2,3-edge spectrum by fitting with the multiplet calculation spectrum. High-temperature Debye-Waller factors are difficult to be refined in diffraction experiments because of the low intensity and experiment instability. In this case, using STEM-EELS, the spectra can be obtained with small sample thermal drift and high S/N ratio in local region. As a result, temperature-depended anisotropic Debye-Waller factor of oxygen can be obtained and shows good agreement with those determined by theoretical calculation[2], gamma-ray[3], synchrotron[4], and x-ray[5] experiment, as shown in Figure 2.

This work presents a method that can potentially extract thermal factors in local regions such as interface and surface, which cannot be obtained in other ways. In the presentation, we will discuss the thermal factor extraction method and atomic vibration effects on the Ti L_2,3-edge spectrum in detail.

This work was supported by Kakenhi Grants-in-Aid No. 22H01956 from the Japan Society for the Promotion of Science (JSPS).

Reference:
[1] M. Haruta et al., Appl. Phys. Lett., 119, 232901 (2021).
[2] A. Uldry et al., Phys. Rev. B 85, 125133 (2012).
[3] W. Jauch and M. Reehuis, Acta Cryst. A61, 411-417 (2005)
[4] E. N. Maslen et al., Acta Cryst. B51.939-942 (1995)
[5] Y. A. Abramov et al., Acta Cryst. B51, 942 (1995).

Figure1: Graphic representation of the anisotropic thermal ellipsoids for SrTiO₃.

Figure 2: Anisotropic thermal factors of oxygen extracted from experimental Ti L-edge in SrTiO₃ (blue) comparing with theoretical values[2] (gray), gamma-ray[3] (green), and x-ray[5] (red). The circle marker represents U_O(Ti), and the square marker represents U_O(Sr). The data points are averaged of 3 fitting results, and the error bar corresponds to the stander deviation of each fitting result.