A model for the thermodynamic properties of metallic rare earth systems with an unstable valence

Abstract

Rare earth compounds and alloys were regarded for many years as classic examples of ionic magnetism in a solid. Due to the limited spatial extent of the 4f wave functions, the 4f electrons do not significantly participate in the chemical bonding, and hence retain most of their ionic character during the transition from a gas to a solid. However, recent experimental evidence on several metallic rare earth systems indicated an apparent loss of the ionic magnetic moment. Extensive measurements on these systems of the magnetic susceptibility, lattice constant, Mössbauer isomer shift, x-ray photoelectron spectrum, and heat capacity can be qualitatively understood if one postulates (as was first done by Maple and Wohlleben using a model due to Hirst) that the rare earth ion fluctuates between two ionic configurations (valence states) which differ in occupation number by one electron (4f ⁿ, 4f ⁿ⁻¹ 5d ¹). We propose to quantify this simple idea by assigning each valence configuration a finite lifetime atT=0. The two lifetimes τ _n and τ _n−1 are converted to “bands” with widthsh/τ _n andh/τ _n−1 . The states in each “band,” however, are forced to retain the ionic properties as determined from Hund's rules. The temperature-dependent contribution of the 4f shell to the magnetic susceptibility, heat capacity, and thermal expansion coefficient is then numerically computed using Fermi-Dirac statistics. By varying τ _n and τ _n−1 it is possible to quantitatively describe “different” types of magnetic behavior: integral valence (τ _n =∞, τ _n−1 =h/Δ), configuration crossover (τ _n =τ _n−1 ), and Kondo phenomena (τ _n >τ _n−1 ). The results of the model are compared to three well-studied rate earth systems with unstable valence: YbAl ₃ , CePd ₃ , and (LaCe)Al ₂ .