Point Measurements of Fermi Velocities by a Time-of-Flight Method

The present paper describes in detail a new method of obtaining information about the Fermi velocity of electrons in metals, point by point, along certain contours on the Fermi surface. It is based on transmission of microwaves through thin metal slabs in the presence of a static magnetic field applied parallel to the surface. The electrons carry the signal across the slab and arrive at the second surface with a phase delay which is measured relative to a reference signal; the velocities are derived by analyzing the magnetic field dependence of the phase delay. For silver we have in this way obtained one component of the velocity along half the circumference of the centrally symmetric orbit for $\overrightarrow{\mathrm{B}}\parallel \mathrm{}\left[100\right]\mathrm{}$. The results are in agreement with current models for the Fermi surface. For $\overrightarrow{\mathrm{B}}\parallel \mathrm{}\left[011\right]\mathrm{}$, the electrons involved are not moving in a symmetry plane of the Fermi surface. In such cases one cannot immediately derive the velocity components, but the method can still be used to provide a comparison of different Fermi surface models. Such a comparison has been made of an augmented-plane-wave model (Christensen) and a Fourier model (Halse), both yielding the experimentally determined areas and cyclotron masses for symmetry orbits of the Fermi surface, but differing slightly at general points. The comparison favors the Fourier model.