Calculation of the knight shift in the system CaCd1‐xTlx by using relativistic APW wave functions

Abstract

AbstractFor the intermetallic system CaCd1‐xTlx, 0 ⩽ x ⩽ 1, the Knight shift Ks of the Cd‐NMR and the Tl‐NMR were calculated as a function of x, Ks = Ks (x). The theoretical investigations were performed on the basis of relativistic augmented‐plane‐wave (RAPW) band‐structure calculations for the boundary phases CaCd and CaTl respectively, and by using the rigid band model for the ternary phases. The density of states and the matrix elements of the relativistic hyperfine operator for electron states at the Fermi surface were calculated in detail. The obtained values were compared with nonrelativistic calculations. The effect of using different exchange potentials was studied for Ks (Tl).For the Cd‐NMR the relativistic effects enhance the nonrelativistic results by a factor of about 1.4. The theoretical value for the Knight shift is smaller than the experimental one by a factor of 1.13. The band structure for CaTl differs significantly for the relativistic and the nonrelativistic approximation. Also an essential contribution to Ks due to negative dipolar terms in the hyperfine matrix elements is found, whereas these terms are non existent in the nonrelativistic theory. Therefore, considering the shift of the Tl‐NMR, no scale factor for the description of the relativistic effects can be used. The dependence of Ks(Tl) from the composition x of the alloys is different within the APW‐and the RAPW scheme. The slope of the function Ks(Tl) = f(x), found in the relativistic calculations matches the experimental results qualitatively. However, the quotient of Ks(Tl)cal/Ks(Tl)exp is about 2.1.