Nondirect transitions in variable-temperature angle-resolved photoemission from metals

Temperature-dependent angle-resolved photoemission spectra have been obtained from Cu(001) for normal-emission conditions corresponding to direct transitions originating from various points along the Γ–Δ–X line. Photon energies were varied from 40 to 106 eV, and specimen temperatures were chosen between 77 and 977 K. Strong temperature dependence was observed at all photon energies, and this has been interpreted in terms of nondirect transitions localized about the expected direct transitions. Such phonon-assisted nondirect transitions are found to contribute significantly, even at low temperature. These nondirect transitions are also found to be semiquantitatively described by a simple modification of the direct-transition model incorporating cylindrical wave-vector broadening centered on the direct transition. Comparing experiment and theory permits estimating the degree of Brillouin-zone averaging involved at a given temperature. This modification of the direct-transition model is based on a more accurate theoretical treatment of such non-direct-transition effects. The consequences of such localized zone averaging due to nondirect transitions on earlier temperature-dependent data for Cu(110) and on studies of ferromagnetic metals near $T_c$ are also discussed.