Generalized magnetic susceptibilities in metals: Application of the analytic tetrahedron linear energy method to Sc

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A detailed study of the generalized susceptibility χ(→q) of Sc metal determined from an accurate augmented-plane-wave method calculation of its energy-band structure is presented. The calculations were done by means of a computational scheme for χ(→q) derived as an extension of the work of Jepsen and Andersen and Lehmann and Taut on the density-of-states problem. The procedure yields simple analytic expressions for the χ(→q) integral inside a tetrahedral microzone of the Brillouin zone which depends only on the volume of the tetrahedron and the differences of the energies at its corners. Constant-matrix-element results have been obtained for Sc which show very good agreement with the results of Liu, Gupta, and Sinha (but with one less peak) and exhibit a first maximum in χ(→q) at (0, 0, 0.31)2πc [vs (0, 0, 0.35)2πc obtained by Liu et al.] which relates very well to dilute rare-earth alloy magnetic ordering at →qₘ=(0, 0, 0.28)2πc and to the kink in the LA-phonon dispersion curve at (0, 0, 0.27)2πc.