Element-specific probe of quantum criticality in $\mathrm{CeCoIn_{5}}$

Employing the elemental sensitivity of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), we study the valence and magnetic order in the heavy fermion superconductor CeCoIn$_5$. We probe spin population of the f-electrons in Ce and d-electrons in Co as a function of temperature (down to 0.1 K) and magnetic field (up to 6 T). From the XAS we find a pronounced contribution of Ce$^{4+}$ component at low temperature and a clear temperature dependence of the Ce valence below 5 K, suggesting enhanced valence fluctuations, an indication for the presence of a nearby quantum critical point (QCP). We observe no significant corresponding change with magnetic field. The XMCD displays a weak signal for Ce becoming clear only at 6 T. This splitting of the Kramers doublet ground state of Ce$^{3+}$ is significantly smaller than expected for independent but screened ions, indicating strong antiferromagnetic pair interactions. The unconventional character of superconductivity in CeCoIn$_5$ is evident in the extremely large specific heat step at the superconducting transition.