Paramagnetic labeling as a method for the soft spectroscopy of electronic states

A self-consistent microscopic theory of the relaxation of the crystal-field levels of an impurity ion in a state with an integer valence implanted in a normal metal is devised. A microscopic approach based on the Coqblin-Schrieffer-Cooper approach, rather than the formal model of the sf exchange interaction, makes it possible to take into account the specific details of both the crystal-field states of the impurity ion and the electronic band spectrum of the metal. A new method for the soft spectroscopy of electronic states based on measurements of the temperature dependence of the width Γ_MM′(T) of transitions between the crystal-field states |M〉 of a paramagnetic ion implanted in the compound being studied is proposed. To make specific use of this method in neutron and optical spectroscopy, a classification of the types of temperature dependence of the natural relaxation width γ _M (T) of the levels is devised, and procedures for possible experimental methods are proposed. A nonzero value of the natural relaxation width γ _G (T) of the crystal-field ground state | G〉 of an impurity ion at zero temperature is obtained within the proposed self-consistent model, but is beyond the scope of perturbation theory. It is shown that the widely accepted estimate of the characteristic temperature of Kondo systems T*=Γ _G(T=0)/2 from the quasielastic scattering width at zero temperature Γ _G (T=0)/2 is incorrect in the case of strong relaxation in a system with soft crystal fields. The proposed model is applied to the quantitative analysis of the relaxation of the crystal-field levels of paramagnetic Pr³⁺ ions implanted in CeAl₃ and LaAl₃. The results of the calculations are in quantitative agreement with the experimental data. Zh. éksp. Teor. Fiz. 113, 1843–1865 (May 1998)