Experimental energy-band dispersions and exchange splitting for Ni

Angle-resolved polarization-dependent photoelectron spectroscopy using synchrotron radiation has been used to determine the energy-versus-momentum band dispersions and magnetic exchange splitting of Ni. Using Ni(111) and Ni(100) crystals, the band dispersions along the $\Gamma -L$ and $\Gamma -X$ lines have been determined for the $s$ and $d$ bands. The temperature-dependent magnetic exchange splitting $\Delta E_{\mathrm{ex}}$ of the upper ${\Lambda }_3$ band has been directly observed and found to be independent of momentum $\overrightarrow{\mathrm{k}}$ for a large region of the Brillouin zone. The experimental value of $\Delta E_{\mathrm{ex}}=0.31\mathrm{}\pm 0.03$ eV is smaller than recent calculated values ($0.6\le \Delta E_{\mathrm{ex}}\le 0.9$ eV) obtained with spin-polarized self-consistent band calculations. Also, calculated $d$-band widths are larger (typically 40%) than measured (3.4 eV at $L$). Our results are consistent with Fermi-surface data and the polarization reversal observed in spin-polarized photoemission. A number of previous contradictory photoemission studies of Ni are discussed in view of our results. The observed bands show that ferromagnetic nickel can be described by a Stoner-Wohlfarth-Slater spin-split band model.