Thermodynamic analysis of the Quantum Critical behavior of Ce-lattice compounds

A systematic analysis of low temperature magnetic phase diagrams of Ce compounds is performed in order to recognize the thermodynamic conditions to be fulfilled by those systems to reach a quantum critical regime and, alternatively, to identify other kinds of low temperature behaviors. Based on specific heat ($C_m$) and entropy ($S_m$) results, three different types of phase diagrams are recognized: i) with the entropy involved into the ordered phase ($S_{MO}$) decreasing proportionally to the ordering temperature ($T_{MO}$), ii) those showing a transference of degrees of freedom from the ordered phase to a non-magnetic component, with their $C_m(T_{MO})$ jump ($\Delta C_m$) vanishing at finite temperature, and iii) those ending in a critical point at finite temperature because their $\Delta C_m$ do not decrease with $T_{MO}$ producing an entropy accumulation at low temperature. Only those systems belonging to the first case, i.e. with $S_{MO}\to 0$ as $T_{MO}\to 0$, can be regarded as candidates for quantum critical behavior. Their magnetic phase boundaries deviate from the classical negative curvature below $T\approx 2.5$\,K, denouncing frequent misleading extrapolations down to T=0. Different characteristic concentrations are recognized and analyzed for Ce-ligand alloyed systems. Particularly, a pre-critical region is identified, where the nature of the magnetic transition undergoes significant modifications, with its $\partial C_m/\partial T$ discontinuity strongly affected by magnetic field and showing an increasing remnant entropy at $T\to 0$. Physical constraints arising from the third law at $T\to 0$ are discussed and recognized from experimental results.