Temperature dependence and intermediate valence on magnetic hyperfine field at a Ce impurity diluted in RZn

In this work, we theoretically study the influence, at finite temperature, of the intermediate valence on the local moment formation and the magnetic hyperfine field at a Ce impurity diluted in RZn (R = Gd, Tb, Dy). The temperature dependence of the local magnetic moments and related hyperfine magnetic interaction is calculated by a functional integral approach in the static approximation, thereby extracting the 4f Ce valence at the range of temperature T ≤ TC (TC = critical temperature). Our self-consistent calculation shows that the intermediate valence model, focusing on the temperature dependence, explains the experimentally observed magnetic hyperfine fields at Ce impurity in these compounds, in particular exhibiting the two regimes of the magnetic hyperfine fields (and local magnetic moments) with temperature.