Experimental energy-band dispersions and magnetic exchange splitting for cobalt

Abstract

We have determined $E$ vs $\overrightarrow{\mathrm{k}}$ energy-band dispersions of cobalt for $s$ and $d$ bands along the hexagonal axis $\Gamma \Delta A$ ([0001] direction) via angle-resolved photoelectron spectroscopy from a Co(0001) face using synchrotron radiation. We obtain the magnetic exchange splitting at $\Gamma$ for the upper $d$ band (0.85 ± 0.2 eV) and lower $d$ band (1.2±0.3 eV). The overall occupied $d$-band width (∼ 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 $\Gamma$-centered minority-electron pocket at $E_F$ which explains previously unidentified de Haas-van Alphen orbits. We present dipole selection rules for the $\Delta$ axis of an hcp lattice and show that the number of allowed transitions is reduced drastically for emission along the $\Delta$ axis. The allowed transitions can be interpreted in the same way as those for emission normal to a (111) face of an fcc lattice.