Mixed valencies: Structure of phase diagrams, lattice properties and the consequences of electron hole symmetry

Abstract

Symmetry properties and phonon phenomena of mixed valence compounds are discussed within the framework of the periodic Anderson model which was extended to include the interaction of 4f electrons with longitudinal optical phonons. The temperature anomaly in the thermal expansion found in CeSn₃ (positive thermal expansion coefficientα) and YbCuAl (negativeα) is correctly described. Within the model the anomaly is a consequence of the particle hole symmetry of the underlying Hamiltonian. Moreover, the theory gives the positive slope of the phase boundary in the pressure-temperature phase diagram (dP/dT>0), for example for Ce, and predicts a negative slope (dP/dT<0) for Yb compounds.

Furthermore, the quite unusual low temperature features of the pressure-temperature phase diagram have been calculated. It is found that the lattice vibrational contribution renormalizes the two essential parameters of the periodic Anderson model. The hybridization energyV ₀ of 4f and 5d−6s states is changed to$\tilde V$ =V ₀−aφ−b〈ϕ ²〉 whereas the energy of the 4f stateE ₀ with respect to the 5d band becomes$\tilde E$ =E ₀−a′φ−b′〈ϕ ²〉.φ, being proportional to the lattice constant, is determined by minimizing the Gibbs free energy, while 〈ϕ ²〉 is proportional to the mean square displacement of the rare earth ions. The strong temperature dependence ofφ and 〈ϕ ²〉 determines the behaviour of the phase boundary and for large enough coefficientsb andb′ the phase boundary terminates at two critical points. An argument is given why the unusual low temperature features are more expressed in dirty mixed valence compounds as Sm_1−x Gd _x S than in the pure compound SmS. Furthermore, the theory predicts a quite unusual behaviour of the plasma-like phonon mode in the mixed valence phase: It softens at the critical temperature and at an intermediate temperature.