Magnetic Quantum Criticality inside the Superconducting State Revealed by Penetration Depth Scaling with Local T_{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 λ(0). Using scanning superconducting quantum interference device microscopy, we determine the local superconducting transition temperature T_{c} and λ(0). By parametrizing λ(0) in terms of the local T_{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 effective exponent exceeds the clean spin-density-wave value, consistent with a disorder-modified quantum critical regime. The enhancement of λ(0) reflects the suppression of the superfluid stiffness and is consistent with critical scaling. Our approach provides a route to uncover underlying quantum critical behavior obscured by inhomogeneity in unconventional superconductors.