PACS numbers: * Electronic address: stockert@cpfs.mpg.de 1The 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. Using 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 CeCu 2 Si 2 . 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.While conventional superconductivity (SC) is generally incompatible with magnetism, magnetic excitations seem to play an important role in the Cooper pair formation of unconventional superconductors such as the high-T c cuprates or the low-T c organic and heavyfermion (HF) superconductors. Since the discovery of SC in CeCu 2 Si 2 1 , antiferromagnetic (AF) spin excitations have been proposed as a viable mechanism for SC 2-4 . The discovery of SC at the boundary of AF order in CePd 2 Si 2 5 has pushed this notion into the framework of AF quantum criticality 6 . Unfortunately, such quantum critical points (QCPs) proximate to HF superconductors typically arise under pressure, which makes it difficult to probe their magnetic excitation spectrum.Here, we report a detailed study of the magnetic excitations in CeCu 2 Si 2 , which exhibits SC below T c ≈ 0.6 K. This prototypical HF compound is ideally suited for our purpose, since SC here is in proximity to an AF QCP already at ambient pressure (cf. Fig. 1(a)).As displayed in Fig. 1(b) CeCu 2 Si 2 crystallises in a structure with body-centred tetragonal symmetry and is one of the best studied HF superconductors and well characterised by low-temperature transport and thermodynamic measurements 7 . Moreover, those measurements in the field-induced normal state have already provided evidence that the QCP in this compound is of the three-dimensional (3D) spin-density-wave (SDW) type 8 . The spatial anisotropy of the spin fluctuations in superconducting CeCu 2 Si 2 was measured at T = 0.06 K and at an energy transfer ω = 0.2 meV and is shown in Fig. 1(c). These magnetic correlations display only a small anisotropy (a factor of 1.5) in the correlation lengths 2 between the [110] and the [001] direction. Therefore, these quite isotropic spin fluctuations are in line with thermodynamic and transport measurements exhibiting C/T = γ 0 − a √ T or ρ − ρ 0 = AT α , α = 1 − 1.5 8,9 , and strongly support a three-dimensional quantum critical SDW scenario 10 . We are able to identify the magnetic excitations in the normal state of paramagnetic, ...

We report on the magnetic excitation spectrum in the normal state of the heavy-fermion superconductor CeCu92)Si(2) on approaching the quantum critical point (QCP). The magnetic response in the superconducting state is characterized by a transfer of spectral weight to energies above a spin excitation gap. In the normal state, a slowing-down of the quasielastic magnetic response is observed, which conforms to the scaling expected for a QCP of spin-density-wave type. This interpretation is substantiated by an analysis of specific heat data and the momentum dependence of the magnetic excitation spectrum. Our study represents the first direct observation of an almost critical slowing-down of the normal state magnetic response at a QCP when suppressing superconductivity. The results strongly imply that the coupling of Cooper pairs in CeCu(2)Si(2) is mediated by overdamped spin fluctuations.

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