Ordered Phases and Quantum Criticality in Cubic Heavy Fermion Compounds

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 behavior 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.