The resistivity of rare earth impurities diluted in Lanthanum (Part I)

TL;DR

This paper investigates the temperature-independent resistivity caused by rare-earth impurities in Lanthanum, analyzing how band structure and impurity characteristics influence electronic scattering and resistivity.

Contribution

It introduces a detailed model for impurity-induced resistivity considering different band structures and impurity effects, using the T-matrix formalism.

Findings

Exchange parameters significantly affect spin resistivity.

Band structure influences resonant scattering and virtual bound states.

Impurity charge and symmetry breaking impact resistivity.

Abstract

In this work we study the temperature independent resistivity of rare-earth magnetic (Gd, Tb, Dy) and non-magnetic (Lu) impurities diluted in dhcp Lanthanum. We considered a two-band system where the conduction is entirely due to $s$-electrons while the screening of the charge difference induced by the impurity is made by the $d$-electrons. We obtain an expression of the resistivity using the $T$-matrix formalism from the Dyson equation. As the electronic properties depend strongly on the band structure, we have considered two types of bands structure, a "parabolic" band and a more realistic one calculated by first principles with VASP. We verify that the exchange parameters appearing as cross products strongly affect the magnitude of the spin resistivity term; And that the role of the band structure in resonant scattering or virtual bound states, depends on the band structure. Our study, also includes the influence of the translational symmetry breaking and the excess charge introduced by the {\it rare-earth} impurity on the resitivity.