4D texture of circular dichroism in soft-x-ray photoemission from tungsten

Photoemission-intensity distributions I-RCP/LCP (E-B, k) measured for right- and left-circularly polarized soft x-rays revealed a large circular dichroism in angular distribution (CDAD) in the 4D parameter space (E-B binding energy, k momentum vector). Full-field k-imaging combined with time-of-flight energy recording at a high-brilliance soft x-ray beamline allowed mapping the CDAD in the bulk Brillouin zone of tungsten and the entire d-band complex within a few hours. CDAD-asymmetries are very high (up to 90%), persist throughout the whole photon-energy range (300-1300 eV) and show a pronounced dependence on momentum k and binding energy E-B, visualized as movies or sequences of cuts through the 4D object. One-step photoemission calculations for the same photon energies show fair agreement with the measured results. In addition to the requirement of a 'handed' experimental geometry, known from previous experiments on adsorbates and surface states, we find an anti-symmetric behavior of the CDAD with respect to two bulk mirror planes. A new symmetry condition along the perpendicular momentum k(z) makes CDAD a valuable tool for an unambiguous identification of high-symmetry planes in direct transitions in the periodic zone scheme. Technically, the method provides a circular polarimeter for soft, tender and hard x-rays.