Feedback spin resonance in superconducting CeCu$_2$Si$_2$ and CeCoIn$_5$

Abstract

We show that the recently observed spin resonance modes in heavy-fermion superconductors CeCoIn$_5$ and CeCu$_2$Si$_2$ are magnetic excitons originating from superconducting quasiparticles. The wave vector ${\bf Q}$ of the resonance state leads to a powerful criterion for the symmetry and node positions of the unconventional gap function. The detailed analysis of the superconducting feedback on magnetic excitations reveals that the symmetry of the superconducting gap corresponds to a singlet $d_{x^2-y^2}$ state symmetry in both compounds. In particular this resolves the long-standing ambiguity of the gap symmetry in CeCoIn$_5$. We demonstrate that in both superconductors the resonance peak shows a significant dispersion away from ${\bf Q}$ that should be observed experimentally. Our results suggest a unifying nature of the resonance peaks in the two heavy-fermion superconductors and in layered cuprates.