Generalized Susceptibility Function for Rare Earths and Thorium and Their Alloys

The results of calculations of the generalized susceptibility function $\chi \left(\overrightarrow{\mathrm{q}}\right)$ for the rare-earth metals and thorium and its alloys with rare earths are presented. For the heavy rare earths Gd, Tb, Dy, Er, and Lu, the calculation was confined to the $\Gamma A$ direction, and a mesh of 450 000 points in the Brillouin zone was used. For the double-hexagonal close-packed crystals Nd and Pr, a mesh of 400 000 points in the Brillouin zone was chosen, while for thorium and its fcc alloys with rare earths, a mesh of 2 048 000 points in the Brillouin zone was used. The results of calculations on Sc and Y have also been included for the sake of comparison with the heavy rare earths. The matrix elements, which couple the $f$ electron and the conduction electron, appearing in the expression for the generalized susceptibility function, were taken to be constant. Our calculations show that the $\chi \left(\overrightarrow{\mathrm{q}}\right)$ curves obtained in this way are reasonably smooth and the scatter of points along the curves is less than 3%. The results have been compared with the experimental data on turn angles, spin-wave dispersion curves, and phonon spectra where available.