Magnetic Quantum Criticality inside the Superconducting State Revealed by Penetration Depth Scaling with Local $T_{\mathrm c}$

We demonstrate a magnetic quantum critical point embedded within the superconducting state of Zn-doped CeCoIn$_5$, revealed by a pronounced peak in the magnetic penetration depth at zero temperature $\lambda(0)$. Using scanning SQUID microscopy, we determine the local superconducting transition temperature $T_{\mathrm c}$ and $\lambda(0)$. By parameterizing $\lambda(0)$ in terms of the local $T_{\mathrm c}$ rather than nominal Zn substitution, we circumvent the ambiguity caused by doping inhomogeneity and enable a more precise extraction of the critical exponent. The extracted exponent exceeds the clean spin-density-wave value, indicating a disorder-modified quantum critical regime. The enhancement of $\lambda(0)$ reflects the suppression of the superfluid stiffness and is consistent with critical scaling. Our approach provides a route to uncover intrinsic quantum critical behavior hidden by inhomogeneity in unconventional superconductors.