  We present a theory of a single point, line or plane defect coupling to the
square of the order parameter in a metallic system near a quantum critical
point at or above its upper critical dimension. At criticality, a spin droplet
is nucleated around the defect with droplet core size determined by the
strength of the defect potential. Outside the core a universal slowly decaying
tail of the droplet is found, leading to many dissipative channels coupling to
the droplet and to a complete suppression of quantum tunneling. We propose an
NMR experiment to measure the impurity-induced changes in the local spin
susceptibility.
