The resistivity of liquid rare earths

The resistivities of various liquid rare earths were calculated in a single-site t-matrix approximation. Good agreement with experiment is achieved. Spin disorder scattering is shown to be unimportant in the liquid state. The experimental resistivity data of liquid rare earths (RE) shows the following behavior [l, 21 : The resistivity p increases across the series of the trivalent RE's. The temperature coefficient (TC) changes from slightly positive for La to slightly negative for Lu. The divalent Eu and Yb behave exceptionally : Eu has the highest and Yb the lowest p-value of all liquid RE's. They both have negative TC's. We have calculated p for La, Eu, Gd, Yb and Lu in a single-site scattering approximation. The interaction between a conduction electron and the ions contains a potential and an exchange contribution : H = x [ V M T ( r R,) + J(r R,)s.S,]. (1) n Here s is the electron spin and S,, the 4f-spin of an ion at position R,. The muffin-tin potentials V, were constructed in the usual way [3]. The S-f-exchange function J was taken from Freeman's work for crystalline Gd 141. We first sketch our calculations for a system without S-f-exchange. The single site expression for p is 3 nQo 2 k ~ dqq3 S(d I t(q) I' (2) P = 4 fie v, k, Q,, k, and v, being atomic volume, Fermi wave vector and velocity, respectively. The static structure factor S(q) is taken from experiment [5] and the t-matrix is determined by the phase shifts 6, of V,. Typically 6 , and 6, are negative, 6, shows resonance-like behavior and 6, is very small. In the same approximation the integrated density of states (DS) is given by the free electron part N, plus a single-site correction : E, is determined by requiring N(EF) to be equal to the valence. For Eu and Yb we obtained the Fermi wave vector according to This is the only choice consistent with the free electron (FE) boundary conditions used to evaluate 6, [6]. It corresponds to using a FE conduction band with E(k) = k212 m. The relation yields an effective number n, of conduction electrons per ion. The difference in p between Eu and Yb can be traced back to differences in the atomic potentials. Using S(q) for two different temperatures, as measured by Waseda et al. [5], we calculated dp/dT and indeed found negative TC's in good agreement with experiment. For La, Gd and Lu the choice (4) for k , would yield too high values for n, and p. This is due to the fact that the bottom energy E, of the conduction band lies higher than the muffin-tin zero in these substances, as band structure calculations for the crystals show. Therefore we use the partial S-p-DS