Thermal motion induced resonant forbidden reflections in wurtzite GaN

We report on an experimental study of forbidden reflections in GaN (wurtzite structure) by resonant X-ray scattering at the Gallium K edge. Resonant reflections are explained by the coherent sum of a Thermal Motion Induced (TMI) scattering amplitude and a temperature independent term. We show that the shape of the TMI energy spectrum is the same for a number of reflections that are exactly forbidden by spacegroup symmetry, as well as one that relies on approximate cancellation due to special atomic sites. In addition to demonstrating new selection rules, several non-trivial aspects of the theory of TMI scattering in wurtzite crystals are quantitatively verified, including dependence on temperature, energy, azimuthal angle and polarization. The temperature-dependent and temperature independent spectra of GaN are very similar to those found in ZnO, suggesting strong similarities in the anisotropy of their electronic states. This is also supported by the strong linear dichroism observed in GaN. TMI spectra are determined by the evolution of the electronic anisotropy with nuclear position, and are likely to be extremely valuable for developing theories of electronic properties at elevated temperatures.