Optical Properties and Fermi Surface of Nickel

Abstract

Dielectric constants for Ni obtained from reflectance data at room temperature are reported for photon energies extending to 11 eV. The structure at 0.3 and 1.4 eV and that observed by Krinchik and collaborators at nearly the same energies by the ferromagnetic Kerr effect is reinterpreted in terms of interband transitions probably between $d$ bands and the Fermi surface. Low-energy interband transitions, which would be expected to occur in many transition metals, cause the reflectance in the infrared to fall off more rapidly than in the noble metals. For photon energies above 4 eV there is a marked resemblance between Ni and Cu. The peak in the energy loss function occurs at nearly the same energy in both materials. As a framework for discussing these results, a model for the band structure and Fermi surface of ferromagnetic Ni is proposed. This model consists of a simple adaptation of band calculations for nonferromagnetic Ni and Cu. The two-band structures, which are assumed to correspond to the energy levels of spin-up and spin-down electrons, respectively, are essentially matched at the bottom of the $4s$ band. The resulting exchange splitting of the $d$ band is about 2 eV. A Fermi level appropriate to the required $s$ and $d$ electron concentration is postulated. The resulting Fermi surfaces consist of three electron sheets and unimportant hole pockets. One electron surface, corresponding to the spin-down carriers, is copper-like. The remaining surfaces do not contact any zone faces. They are characterized by large anisotropies in electron velocities and large corresponding differences between optical and thermal masses. These results are consistent with the magnetoresistance and Hall effect measurements of Fawcett and Reed and are in semiquantitative agreement with the observed structure in the optical properties, the magneton number, the electronic specific heat, and the plasma frequency.