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...

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Both magnetic and nonmagnetic x-ray diffraction has been studied near the Fe K-edge of hematite ͑␣-Fe 2 O 3 ͒ and the Cr K-edge of eskolaite ͑Cr 2 O 3 ͒ and compared to the symmetry-based calculations. These crystals have identical atomic structures but different magnetic orderings. The observed "forbidden" 111 and 333 reflections in both crystals show a resonant peak only in the pre-edge energy region. In eskolaite, the azimuthal angle dependence of the resonant 111 and 333 reflections exhibits threefold symmetry, which is in good agreement with the calculated curves based on electric dipole-quadrupole and quadrupole-quadrupole scattering channels. This threefold symmetry is the first reliable evidence for antisymmetric terms in dipolequadrupole scattering and hence for local chirality of atoms in centrosymmetric crystals. In hematite, nonresonant and resonant scattering has been observed for the forbidden reflections. The azimuth dependence of the nonresonant intensity shows the twofold symmetry. From the azimuthal symmetry and temperature dependence of the nonresonant diffraction, it is revealed that the nonresonant intensity is due to magnetic scattering caused by the antiferromagnetic structure. The azimuth dependence of the 111 resonant peak in hematite shows almost threefold symmetry similar to eskolaite. On the other hand, the resonant 333 reflection in hematite shows complicated azimuth dependence, nearly mirror symmetry, at room temperature. As a result of least-squares analysis of the azimuth dependence and the low-temperature measurement, we conclude that the nonresonant magnetic scattering has a significant influence on the resonant electric scattering though its intensity is much smaller. Thus the interference between the magnetic and electric scatterings plays a very important role in hematite and opens new ways for studying additional details of the magnetic structure.

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Polarization tunability and analysis of X-rays is one of the most advancing features of thirdgeneration synchrotron radiation sources. In order to apply such developments to the observation of magnetic effects, a diffractometer for X-ray magnetic absorption and scattering experiments was constructed on BL39XU at SPring-8. The ef®ciency of the apparatus is clearly demonstrated by several observations of the magnetic effects. In particular, a diamond phase plate plays an essential role in regulating both circular and linear polarization states.