Experimental energy-band dispersions and magnetic exchange splitting for cobalt

Abstract

We have determined $E$ vs $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ energy-band dispersions of cobalt for $s$ and $d$ bands along the hexagonal axis $\ensuremath{\Gamma}\ensuremath{\Delta}A$ ([0001] direction) via angle-resolved photoelectron spectroscopy from a Co(0001) face using synchrotron radiation. We obtain the magnetic exchange splitting at $\ensuremath{\Gamma}$ for the upper $d$ band (0.85 \ifmmode\pm\else\textpm\fi{} 0.2 eV) and lower $d$ band (1.2\ifmmode\pm\else\textpm\fi{}0.3 eV). The overall occupied $d$-band width (\ensuremath{\sim} 3.8 eV at $L$) is about 20% narrower than a state-of-the-art self-consistent band calculation using a local-density theory of exchange correlation. The top of the majority-spin $d$ bands is 0.35 eV below ${E}_{F}$. There is a small $\ensuremath{\Gamma}$-centered minority-electron pocket at ${E}_{F}$ which explains previously unidentified de Haas-van Alphen orbits. We present dipole selection rules for the $\ensuremath{\Delta}$ axis of an hcp lattice and show that the number of allowed transitions is reduced drastically for emission along the $\ensuremath{\Delta}$ axis. The allowed transitions can be interpreted in the same way as those for emission normal to a (111) face of an fcc lattice.