II. Exploring the role of the Crystal Electric Field in the vicinity of a Quantum Critical Point
Very low temperature thermodynamic properties of the Yb$M_{5-x}X_x$ (with $M$= Ni, Cu, and $X$= Cd, Mg, Au, Zn, Ag) cubic compounds are analyzed covering a broad range of behavior between magnetic and Fermi-liquid ground states GS using the {\it chemical doping}: $\zeta$ as control parameter. This allows to gain insight into the evolution of the GS behavior including a quantum critical point QCP. Doniach-Lavagna phase diagram limitations are improved by taking into account crystal electric field CEF splittings. Three regions are recognized as a function of $\zeta$: i) a magnetic one with long range magnetic order and $T_{ord}\propto T_N \approx 1$\,K, that weakens the interactions between $0.8\,K \geq T_m\geq 0.4$\,K, exhibiting very low Kondo temperature $T_K^{GS}$ in respective doublets GS. Then, for $T_Q\leq 0.4$\,K, quantum fluctuations start to dominate the scenario with the specific heat $C_{4f}/T(T\geq T_Q)$ showing $T$ power law dependencies, and a very heavy-fermion {\it plateau} below $T_Q$. ii) beyond the QCP the typical Non-Fermi-Liquid logarithmic $T$ dependence: $C_{4f}/T \propto \ln(T/T_0)$, with traces of magnetic order. At the non-magnetic limit: iii) the alloys behave as valence-fluctuation systems with growing $T_K$ that overcomes the CEF splitting. With this experimental information, a realistic phase diagram can be drawn around the QCP where the scenario is dominated by low lying quantum fluctuations, without $C_{4f}/T|_{Lim T\to 0}$ divergences but a clear drop entering into the non-magnetic phase.