k -resolved inverse photoelectron spectroscopy and its application to Cu(001), Ni(001), and Ni(110)

Experimental results on Cu(001), Ni(001), and Ni(110) with the use of the newly developed technique of k-resolved inverse photoelectron spectroscopy (or angle-resolved ultraviolet bremsstrahlung isochromat spectroscopy) are presented and compared with the predictions of bulk band-structure theory. A theoretical model is obtained by inverting the well-known three-step model for ordinary photoemission taking the optical transitions to be direct. Detailed band calculations are performed with full inclusion of momentum matrix elements using a combined interpolation scheme. A two-band approximation is also propounded and is found to be adequate in some circumstances. Results obtained on Cu(001) and Ni(001) for the E(→k_∥) energy dispersion relations of peaks in the spectra at the photon energy ω=9.7 eV are shown to be in excellent agreement with bulk band theory. The variation in peak intensity with parallel wave vector k_∥ shows agreement with calculated momentum matrix elements. For Ni(001), the relative intensities of transitions into the s, p bands and into the unoccupied minority-spin d bands are qualitatively understood in terms of direct transitions. In the case of normal incidence (k_∥=0) on Ni(110), it appears that bulk direct transitions are insufficient to explain the data, and it is necessary to invoke density-of-states contributions. Some speculations on future directions are advanced.