We study the low-energy spin fluctuations and superfluid density of a series of pure and Zn-substituted high-$T_c$ superconductors (HTS) using the muon spin relaxation and ac-susceptibility techniques. At a critical doping state, $p_c,$ we find (i) simultaneous abrupt changes in the magnetic spectrum and in the superconducting ground state and (ii) that the slowing down of spin fluctuations becomes singular at $T=0.\mathrm{}$ These results provide experimental evidence for a quantum transition that separates the superconducting phase diagram of HTS into two distinct ground states.

• Received 29 March 2002

DOI:https://doi.org/10.1103/PhysRevB.66.064501