In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu$_2$Si$_2$, fully-gappe
d d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu$_2$Si$_2$. In YbRh$_2$Si$_2$, superconductivity appears to be suppressed at $Tgtrsim~10$ mK by AF order ($T_N$ = 70 mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at $T_A$ slightly above 2 mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at $T_c$ = 2 mK. Like the pressure - induced QCP in CeRhIn$_5$, the magnetic field - induced one in YbRh$_2$Si$_2$ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-$T$ unconventional heavy - fermion superconductors and other families of unconventional superconductors with higher $T_c$s, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.
The effect of magnetic field on the static and dynamic spin correlations in the non-centrosymmetric heavy-fermion superconductor CePt$_3$Si was investigated by neutron scattering. The application of a magnetic field B increases the antiferromagnetic
(AFM) peak intensity. This increase depends strongly on the field direction: for B${parallel}$[0 0 1] the intensity increases by a factor of 4.6 at a field of 6.6 T, which corresponds to more than a doubling of the AFM moment, while the moment increases by only 10 % for B${parallel}$[1 0 0] at 5 T. This is in strong contrast to the inelastic response near the antiferromagnetic ordering vector, where no marked field variations are observed for B${parallel}$[0 0 1] up to 3.8 T. The results reveal that the AFM state in CePt$_3$Si, which coexists with superconductivity, is distinctly different from other unconventional superconductors.
Superconductivity in lanthanide- and actinide-based heavy-fermion metals can have different microscopic origins. Among others, Cooper pair formation based on fluctuations of the valence, of the quadrupole moment or of the spin of the localized 4f/5f
shell have been proposed. Spin-fluctuation mediated superconductivity in CeCu2Si2 was demonstrated by inelastic neutron scattering to exist in the vicinity of a spin-density-wave quantum critical point. The isostructural HF compound YbRh2Si2 which is prototypical for a Kondo-breakdown quantum critical point has so far not shown any sign of superconductivity down to approximately 10mK. In contrast, results of de-Haas-van-Alphen experiments by Shishido et al. (J. Phys. Soc. Jpn. 74, 1103 (2005)) suggest superconductivity in CeRhIn5 close to an antiferromagnetic quantum critical point beyond the spin-density-wave type, at which the Kondo effect breaks down. For the related compound CeCoIn5 however, a field-induced quantum critical point of spin-density-wave type is extrapolated to exist inside the superconducting phase.
The origin of unconventional superconductivity, including high-temperature and heavy-fermion superconductivity, is still a matter of controversy. Spin excitations instead of phonons are thought to be responsible for the formation of Cooper pairs. Usi
ng inelastic neutron scattering, we present the first in-depth study of the magnetic excitation spectrum in momentum and energy space in the superconducting and the normal states of CeCu2Si2. A clear spin excitation gap is observed in the superconducting state. We determine a lowering of the magnetic exchange energy in the superconducting state, in an amount considerably larger than the superconducting condensation energy. Our findings identify the antiferromagnetic excitations as the major driving force for superconducting pairing in this prototypical heavy-fermion compound located near an antiferromagnetic quantum critical point.
The apparently inimical relationship between magnetism and superconductivity has come under increasing scrutiny in a wide range of material classes, where the free energy landscape conspires to bring them in close proximity to each other. This is par
ticularly the case when these phases microscopically interpenetrate, though the manner in which this can be accomplished remains to be fully comprehended. Here, we present combined measurements of elastic neutron scattering, magnetotransport, and heat capacity on a prototypical heavy fermion system, in which antiferromagnetism and superconductivity are observed. Monitoring the response of these states to the presence of the other, as well as to external thermal and magnetic perturbations, points to the possibility that they emerge from different parts of the Fermi surface. This enables a single 4$f$ state to be both localized and itinerant, thus accounting for the coexistence of magnetism and superconductivity.
