Thermodynamic analysis of the quantum critical behavior of Ce-lattice compounds

Abstract

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 (Cm) and entropy (Sm) results, three different types of phase diagrams are recognized: i) with the entropy involved into the ordered phase (SMO) decreasing proportionally to the ordering temperature (TMO), ii) those showing a transference of degrees of freedom from the ordered phase to a non-magnetic component, with their Cm(TMO) jump (∆Cm) vanishing at finite temperature, and iii) those ending in a critical point at finite temperature because their ∆Cm do not decrease with TMO producing an entropy accumulation at low temperature. Only those systems belonging to the first case, i.e. with SMO → 0 as TMO → 0, can be regarded as candidates for quantum critical behavior. Their magnetic phase boundaries deviate from the classical negative curvature below T ≈ 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 ∂Cm/∂T discontinuity strongly affected by magnetic field and showing an increasing remnant entropy at T → 0. Physical constraints arising from the third law at T → 0 are discussed and recognized from experimental results.