X-ray natural birefringence in reflection from graphene

Abstract

The existence of natural birefringence in x-ray reflection on graphene is demonstrated at energies spanning the carbon 1s absorption edge. This new x-ray effect has been discovered with precision measurements of the polarization-plane rotation and the polarization-ellipticity changes that occur upon reflection of linearly polarized synchrotron radiation on monolayer graphene. Extraordinarily large polarization-plane rotations of up to 30∘, accompanied by a change from linearly to circularly polarized radiation have been measured for graphene on copper. Graphene on single crystalline cobalt, grown on tungsten, exhibits rotation values of up to 17∘. Both graphene systems show resonantly enhanced effects at the π∗ and σ∗ energies. The results are referenced against those obtained for polycrystalline carbon and highly oriented pyrolytic graphite (HOPG), respectively. As expected, polycrystalline carbon shows negligible rotation, whereas a huge maximum rotation of 140∘ has been observed for HOPG that may be considered a graphene multilayer system. HOPG is found to exhibit such large rotation values over a broad energy range, even well beyond the π∗ resonance energy due to the contributions of numerous graphene layers. To explain the origin of the observed natural birefringence of graphene, the Stokes parameters as well as the x-ray natural linear dichroism in reflection have been determined. It is shown that the birefringence directly results from the optical anisotropy related to the orthogonal alignment of π∗ and σ∗ bonds in the graphene layer. Our polarization analysis reveals a strong bonding of graphene on Co with a reduced σ∗ excitation energy and a strong tilt of 50% of the p z orbitals towards diagonal orientation. In contrast, graphene on Cu is weakly bound with an orthogonal orientation of the p z orbitals. Exhibiting such a large natural birefringence that can be controlled through substrate choice, and because of excellent heat conductivity, graphene materials have a potential to be used as tunable x-ray phase shifting λ/4 or λ/2 plates in the design of future high-intensity light sources.