Scaling Approach to Doniach Phase Diagram: Application to CeRu₂Ge₂ and EuCu₂(Ge_1-xSi_x)₂

We calculate the Doniach phase diagram of heavy-fermion systems containing Ce and Eu ions, using the scaling solution of the periodic Anderson model, and compare the results with the experimental data on CeRu₂Ge₂ and EuCu₂(Ge_1-xSi_x)₂. The temperature-pressure (T-p) phase diagram emerges from the competition between the pressure-dependent Kondo interaction and the temperature- and pressure-dependent RKKY interaction. Both are derived using scaling equations in the presence of crystal-field effects: Kondo temperature TK is related to the coupling constant g(p), where p is the control parameter, and the temperature-dependent renormalized coupling g(T,TK(g)). For comparison with the experiment, we assume a linear dependence of g on the control parameter, which could be pressure or composition. The Néel temperature TN(p) is obtained by comparing the free energies of the system in the antiferromagnetic and paramagnetic states. The resulting asymmetric TN(p) arises naturally from the exponential growth of TK(p) and a much slower polynomial growth of the RKKY interaction. Phase diagrams for CeRu₂Ge₂ and EuCu₂(Ge_1-xSi_x)₂ successfully capture key experimental features: pressure-induced suppression of magnetic order, the peak of RKKY interaction energy, and crossover to a heavy-Fermi-liquid regime at high coupling strength. Our work provides the first quantitative, material-specific construction of Doniach diagrams, clarifies the entropy removal at low temperatures and offers predictive insight for future experiments under extreme conditions.