These last years, the properties of heavy-fermion systems in high magnetic fields have been investigated intensively. It was found that the phase diagrams established in magnetic fields show strong similarities with those obtained under pressure or with chemical doping. Indeed, the application of a magnetic field induces a reduction of the itinerant character of f electrons, whose localization increases with the field. Also, in heavy-fermion systems, a magnetic field-induced transition to a polarized regime is associated with quantum criticality and associated phenomena (critical ferromagnetic fluctuations , “non-Fermi liquid” regime , reentrant superconductivity ).
Typical heavy-fermion phase diagrams obtained in high magnetic fields are shown in Figure 2. Application of a magnetic field induces a magnetic polarization of the system, whatever the nature of the initial state (antiferromagnetic order or paramagnetic Fermi liquid). “Non-Fermi liquid” behavior is found in the neighboring of the magnetic field characteristic of the transition to the polarized regime, i.e., Hc if the initial state if magnetically ordered or Hm if the initial state if a paramagnetic Fermi liquid. It is crucial to understand the nature of field-induced quantum criticality or of the related phenomena (“non-Fermi liquid, superconductivity ...). At the present time, a single example of superconductivity developing at a field-induced quantum phase transition has been reported (cf. URhGe ). The discovery of new materials becoming superconducting in magnetic fields would be a major step for understanding unconventional superconductivity, whose mechanism may be related to critical quantum magnetic fluctuations.
Figure 2 : Typical phase diagram of heavy-fermion systems in a magnetic field
 M. Sato et al., J. Phys. Soc. Japan 70 Suppl. A, 118 (2001) ; J. Flouquet et al., J. Magn. Magn. Mat. 272-276, 27 (2004).
 J. Custers et al., Nature 424, 524 (2003) ; Perry et al., Phys. Rev. Lett. 86, 2661 (2001).
 F. Levy et al., Science 309, 1343 (2005).