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

Abstract

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 $E\left({\overrightarrow{\mathrm{k}}}_{\parallel }\right)$ energy dispersion relations of peaks in the spectra at the photon energy $\hslash \omega =9.7\mathrm{}$ eV are shown to be in excellent agreement with bulk band theory. The variation in peak intensity with parallel wave vector $k_{\parallel }$ 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 ($k_{\parallel }=0\mathrm{}$) 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.