Rare earth impurities in liquid aluminium

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Abstract
The magnetic susceptibility and solvent Knight shift changes caused by the rare earth series of elements dissolved in liquid aluminium have been measured for solute concentrations less than 2 at. %. Except for the cases of Eu and Yb, the impurity susceptibility conforms quite closely to the theoretical predictions obtained from the theory of Van Vleck for trivalent ions. Eu and Yb are best approximated by divalent ion core states. The observed Knight shifts are interpreted using partial wave scattering theory. Phase shifts describing the screening due to different core orbitals are treated as independent. Since the susceptibility is in close agreement with spin–orbit coupling theory for free ions, one must regard the orbitals as completely occupied or unoccupied. The different orbitals are associated with phase shifts of π or 0 at the Fermi surface in the respective cases. Very good agreement between theory and experiment is achieved when the core states are taken to be about 0·5 ev wide and the splitting between the spin sub-bands in heavier elements is about 1 ev. The results are not consistent with perturbation theory predictions of the Ruderman–Kittel–Yosida type, and an alternative form of spin polarization near magnetic impurities is presented.