J. Phys. Chem. Solids 23, 1631 (1962). Anomalous skin effect measurements on polycrystalline samples of W, Mo, and Cr show that the total Fermi surface area is much less than that for a valence-six nearly-free-electron model. Phys. Rev. 128, 154 (1962). This paper reports kinks in the (100) magnetoresistance near (100) at 13° and 26° for W and at 18° for Mo. The nearly-free-electron model is shown to be inapplicable. 3 E. Fawcett and W. A. Reed, Phys. Rev. 134, A723 (1964). This paper reports less than 10 -4 open cyclotron orbits per atom for Mo and less than 10~7 for W. 4
High-field magnetoresistance, Hall effect, planar Hall effect, and transverse even effect have been measured on gallium single crystals at 4.2 °K with the current along the crystallographic axes and the magnetic field in the major crystallographic planes. The results are interpreted in terms of the Lifshitz, Azbel', and Kaganov theory. The magnetoresistance is quadratic in the magnetic field except when both the current and the field are in the ab plane, where it saturates. These results are attributed to a surface which permits open orbits along the k c axis and to compensation between the number of holes and electrons. In addition, subsidiary minima are observed in the magnetoresistance rotation curves, but the field dependence remains quadratic at these points. The Hall and planar Hall data are highly dependent upon the magnetic field direction and show some features similar to the magnetoresistance. The nearly-free-electron (single-orthogonalized-plane wave) Fermi surface has been constructed for gallium and it is found that, after certain modifications, the sixth band predicted by this model has the basic topological features required by these data. The origin of the transverse even voltage is discussed in terms of the Lifshitz theory. 6 C. S. Barrett (private communication).Atomic arrangement, unit cell, and Brillouin zone of metallic gallium are described, including notations for the various symmetry directions. The point and space groups are discussed, including character tables, and basis functions in the form of symmetrized plane waves for electronic wave functions of each symmetry type. The free-electron approximation is used as a first step toward finding the energy bands and Fermi surfaces. This work is preparatory toward a study of energy bands which is under way using the augmentedplane-wave method.
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