Band-Theoretic View of Ferromagnetic Nickel

Abstract

Although the probable applicability of the itinerant electron concept to nickel has been recognized for some time, convincing support for this point of view has only emerged recently. Some of this information, notably the galvanomagnetic measurements of Fawcett and Reed1 and optical data extending to 11 eV,2 are discussed on the basis of a realistic model for the band structure of nickel which is closely related to the calculations of Hanus3 for the material in its nonferromagnetic state. The marked resemblance of many of these experimental results to those of copper is related to the corresponding similarity in the band structure of the two materials and thus supports the itinerant electron hypothesis in nickel. The assumption that the electron interaction giving rise to ferromagnetism is roughly k independent and splits the d bands in such a way that the lower spin-down bands are completely filled determines a Fermi level with respect to Hanus's calculations whose energetic position depends only weakly on the magnitude of the splitting. The resulting Fermi surfaces are shown to consist of three electron sheets and unimportant hole pockets. One electron surface, corresponding to spin-down carriers, is copper-like. The remaining surfaces are distorted spheres which do not contact any faces of the Brillouin zone. They are characterized by large anisotropies in electron velocities and large corresponding differences between optical and thermal masses. Besides being consistent with the galvanomagnetic measurement, these surfaces and their associated masses also lead to results for the magneton number, the electronic specific heat, the plasma frequency, and the dc conductivity of nickel which are in substantial agreement with experimental data. In particular, they show how the large difference between optical and thermal effective masses, reflected in the similarity of plasma frequencies in Cu and Ni on the one hand, and the order of magnitude difference between electronic specific heats on the other, may be accounted for. The structure in the optical properties at 0.3 and and 1.4 eV, and corresponding structure observed by Krinchik4 and collaborators at nearly the same energies by the ferromagnetic Kerr effect is associated with interband transitions which may be interpreted in a consistent, but not unique fashion in terms of the preceding band structure to lead to a ferromagnetic splitting of the d bands at the point L corresponding to about 1.7 eV. With the highly qualitative assumption that the splitting is rigid, the resulting band structure for the spin-down electrons would be very similar to the E vs k curves characteristic of copper as obtained by Segall, while that for the spin-up electrons would correspond to the results of Hanus, with the two sets matched at Γ1, the bottom of the s bands. The similarity in the optical properties of copper and nickel can be understood qualitatively on this basis. The fact that the position of the Fermi level, and hence the qualitative features of the Fermi surfaces, are relatively insensitive to the magnitude of the d band splitting is illustrated by the substantial agreement between the Fermi levels obtained from the present model and the one proposed independently by Phillips,5 also based on Hanus's calculations, which assumes the splitting to be between 0.5 and 0.6 eV.