Band Structure and Fermi-Surface Properties of Ordered $\beta$-Brass

The band structure of ordered $\beta$-brass (${\beta }^{\prime }-\mathrm{CuZn}$) has been calculated throughout the Brillouin zone by the augmented-plane-wave method. The present band model differs from previous calculations with respect to the position and width of the $\mathrm{Cu}3d$ band. The derived dielectric function ${\epsilon }_2\left(\omega \right)$ and the photoemission spectra agree well with experiments. We find that the main absorption edge as observed in the ${\epsilon }_2$ trace has contributions from conduction-band transitions as well as transitions from the $\mathrm{Cu}d$ states. The comparison to photoemission results indicates that the calculated $\mathrm{Cu}d$ bands are too narrow, but that their position relative to the Fermi level is correct. The derived Fermi-surface model allows a detailed interpretation of the de Hass-van Alphen (dHvA) data. The present model has no open orbit along <100> for $\overrightarrow{B}\parallel 〈110〉$. This agrees with dHvA as well as magnetoresistance measurements. Four new extremal cross sections have been found and related to previously unexplained dHvA frequencies. In general, the Fermi-surface dimensions agree extremely well with dHvA measurements, and the ratios between the experimental and the calculated cyclotron masses vary between 1.18 and 1.43.