Quantum criticality in cubic heavy fermion compounds remains much less explored than in quasi-two-dimensional systems. However, such materials are needed to broadly test the recently suggested global phase diagram for heavy fermion quantum criticality. Thus, to boost these activities, we review the field, with focus on Ce-based systems with temperature-magnetic field or temperature-pressure phase diagrams that may host a quantum critical point. To date, CeIn3 and Ce3Pd20Si6 are the only two among these compounds where quantum critical behaviour has been systematically investigated. Interestingly, both show Fermi surface reconstructions as function of the magnetic field that may be understood in terms of Kondo destruction quantum criticality.Comment: invited review paper, 3 figures, 102 references, to appear in J. Phys. Soc. Jpn., Section: Special Topics "Advances in Physics of Strongly Correlated Electron Systems

AC-specific heat measurements remain as the foremost thermodynamic experimental method to underpin phase transitions in tiny samples. However, its performance under combined extreme conditions of high-pressure, very low temperature and intense magnetic fields needs to be broadly extended for investigation of quantum phase transition in strongly correlated electron systems. In this communication, we discuss the determination of specific heat on the quantum paramagnetic—insulator SrCu2(BO3)2 by applying the AC-specific heat technique under extreme conditions. In order to apply this technique to insulating samples we sputtered a metallic thin film-heater and attached thermometer onto sample. Besides that, we performed full frequency scans with the aim to get quantitative specific heat data. Our results show that we can determine the sample heat capacity within 5% of accuracy respect to an adiabatic technique. This allows to uncover low energy scales that characterize the ground state of quantum spin entanglement in SrCu2(BO3)2.

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