Temperature-induced distortions of electronic states observed via forbidden Bragg reflections in germanium

Abstract

According to the adiabatic approximation, the electronic states of atoms in solids are bound up with thermal atomic motion. As a result, thermal-motion-induced ͑TMI͒ anisotropy of x-ray susceptibility can appear for atoms occupying positions with high symmetry. We report evidence for this effect found in the very strong temperature dependence of the 006 forbidden Bragg reflections from a germanium single crystal. The intensity of these reflections increases or decreases drastically as the temperature rises from 30 K to 300 K, in contrast with nonforbidden reflections. It is found that the TMI anisotropy of the structure amplitude scales with the temperature as the mean square of the atomic displacements. This observation is very important for understanding the intricate interplay between phonon and electronic properties of solids. Forbidden x-ray reflections, excited exclusively owing to anisotropy of the atomic susceptibility, can be observed in crystals near x-ray absorption edges. Such reflections are referred to as ATS ͑anisotropy of the tensor of susceptibility͒ reflections. The ATS can violate the glide-plane and screwaxis selection rules for forbidden reflections so that most of them become nonforbidden. The physical reason for this violation is that the anisotropic susceptibility is not invariant under rotations and mirror transformations. The ATS is related to electronic resonant transitions and is caused by distortions of the electronic states in an anisotropic environment. Therefore reflections of this type provide direct evidence for the distortions of electronic states in crystals.Up to now much effort has been spent to study the dynamic changes of the electronic states during thermal motion, phase transitions, or chemical reactions in solids ͑there is no need to explain the evident importance of such studies͒. However, those changes are hardly accessible even with ultrafast optical techniques and the optical probes are often poor indicators of atomic structure. By contrast the x-ray technique developed here, based on ATS reflections, is an effective structural probe sensitive to dynamic changes of local atomic environments. Of course, the time evolution of the distortions cannot be measured in our experiments.ATS reflections have been observed in a NaBrO 3 cubic crystal near the K edge of the Br atoms. 1 Then they were studied for many crystals: TiO 2 , 2 Cu 2 O, 2 Fe 2 O 3 , 3 etc., and even for liquid crystals. 4 The theory of these reflections was developed first in the dipole approximation 5 and then in higher approximations. 6 It was shown recently that ATS reflections can be excited owing to the orbital ordering in colossal magnetoresistance materials, manganites and vanadite. 7-9 Earlier we studied the ATS scattering from Fe atoms, in pyrite 10 (FeS 2 ) and magnetite 11 (Fe 3 O 4 ), where the iron atoms are surrounded by slightly distorted octahedra of sulfur and oxygen atoms, respectively ͑see also a very recent study of magnetite. 12 ͒ The polarization and azimuthal dependences of the measu...

Proton configurations in the hydrogen bonds ofKH2PO4as seen by resonant x-ray diffraction

“…, and cannot account for the temperature dependence of forbidden reflections in Ge, ZnO and GaN, in which the E1E1 term also vanishes [28][29][30][31] : in these systems, the intensity of forbidden reflections increases with temperature, despite the Debye-Waller effect, and the intensity growth is accompanied by a change of spectrum that can only be explained by interference with a second scattering process 30,31 . The latter was ascribed to thermal-motion induced (TMI) scattering 32 .…”

Mechanisms of the paraelectric to ferroelectric phase transition in RbH2PO4probed by purely resonant x-ray diffraction

“…These "forbidden" reflections provide the possibility to study small contributions to the atomic scattering factor caused by various multipole transitions or displacements of the atoms from their average sites [29][30][31][32][33]. Even slight atomic displacements due to thermal vibrations influence the resonant atomic scattering factor resulting in the so-called thermal motion induced (TMI) scattering contribution, which was successfully observed in Ge [34,35], ZnO, and GaN [36,37]. Its main feature is the growth of the integrated intensity with temperature in contrast to conventional Bragg reflections, whose intensity decreases with temperature according to the Debye-Waller factor.…”

Chirality-induced `forbidden' reflections in X-ray resonant scattering

“…It was found recently that the re¯ections caused by the symmetric part of the high-rank tensors might also appear for dipole±dipole transitions owing to thermal atomic motion or point defects (Dmitrienko et al, 1999;Dmitrienko & Ovchinnikova, 2000). In particular, the forbidden re¯ections in Ge, originally attributed to the thirdrank symmetric contribution (Templeton & Templeton, 1994), are caused mainly by the thermal motion effect (Kokubun et al, 2001). The antisymmetric part cannot be imitated this way.…”