Quantum criticality of Ce1−xLaxRu2Si2 : the magnetically ordered phase

One important issue in the study of quantum criticality in itinerant electron systems is the determination of the dynamical spin susceptibility and of its relation to the anomalous bulk properties observed near the quantum critical point (QCP). To this aim, the description of 3d itinerant electron systems was achieved by the spin fluctuation theory of Moriya. In 4f electron systems, the occurence of the Kondo effect with a related energy scale of order 10 K leads to a more complex problem. Basically, two scenarii emerge for these systems: the conventional spin fluctuation scenario in the line of Moriya’s theory [1,2,3] and the local scenario [4]. Their respective description of the intrinsic nature of quantum criticality deeply differ. In the spin-density wave scenario, the fluctuations of the order parameter, i.e. at the wave-vector of ordering, are leading to the transition as in a classical phase transition. A difference with a finite temperature phase transition is that the effective dimension of the system is increased due to quantum fluctuations [2,3]. In this theory, the Kondo effect evolves smoothly accross the QCP. On the contrary, in the so-called local scenario, the low frequency spin dynamics is critical everywhere in the Brillouin zone. In this model, this is associated with a destruction of the Kondo effect at the QCP. Over several decades, numerous neutron scattering experiments were performed on the archetypal Pauli paramagnet heavy fermion compound CeRu2Si2 for various dopings leading to long range magnetic ordering [5,6,7, 8]. For Ce1−xLaxRu2Si2, sine-wave modulated magnetic ordering occurs for x ≥ xc=0.075 at the incommensurate wavevector k1=(0.31, 0, 0), the magnetic moments being aligned along the c-axis of the tetragonal structure, due to the strong Ising anisotropy originating from the crystal field. In the present paper, we report recent data taken in the magnetically ordered phase for x=0.13 (TN=4.4 K) and x=0.2 (TN=5.8 K) that extends the works performed in the past for x=0.13 [9], x=0.2 [10,11] and x=0.3 [12]. Figure 1 shows the magnetic specific heat divided by the temperature for several concentrations accross the critical point (data for x=0 and x=0.075 are taken from Ref.[5]). While focus is usually made on the critical concentration, the most striking features occur in the ordered phase. For x=0.13, Cm/T is almost constant in the ordered phase. For x=0.2, the slow decrease of Cm/T below TN is amplified below a second transition temperature TL = 1.8 K. For x=0.13, the low transition occurs at TL ≈ 600 mK. We note that the decrease of Cm/T below TL for x=0.13 is far smaller than the one reported earlier [14]. The huge effective mass related to the high value of Cm/T for T → 0 at x=0.13 already suggests that itinerant magnetism is characteristic of the ordered phase. The anomalous shape of the x=0.13 specific heat curve can be qualitatively understood as a the sum of a large spin fluctuation contribution and of a specific heat jump related