Antishielding Effect of the Conduction Electrons on the Crystalline Electric Field in Rare-Earth Metals

The lattice contributions to the crystalline electric field (CEF) parameters for the rare-earth metals have been calculated, taking into account both the point charges and the induced quadrupole moments at the ionic sites. The induced quadrupolar contributions are found to be negligibly small compared with the point-charge contributions. The antishielding factors ${\delta }_l$ due to the conduction electrons are evaluated by comparing the calculated CEF with the experimental results for thulium, cerium, and terbium metals, giving ${\delta }_2=0.44\mathrm{}$, ${\delta }_4=1.6\mathrm{}$, and ${\delta }_6=0.77\mathrm{}$, respectively. These values of ${\delta }_l$ explain fairly well the available information about the CEF parameters of praseodymium, terbium, and dysprosium. The possibility of getting antishielding effects from the direct contributions of the conduction electrons in the neighboring Wigner-Seitz cells is also indicated.