Local Lattice Instability and Superconductivity in La$_{1.85}$Sr$_{0.15}$Cu$_{1-x}$M$_x$O$_4$ (M=Mn, Ni, and Co)

Local lattice structures of La$_{1.85}$Sr$_{0.15}$Cu$_{1-x}$M$_x$O$_4$ (M=Mn, Ni, and Co) single crystals are investigated by polarized extended x-ray absorption fine structure (EXAFS). The local lattice instability at low temperature is described by in-plane Cu-O bond splitting. We find that substitution of Mn for Cu causes little perturbation of local lattice instability while Ni and Co substitution strongly suppresses the instability. The suppression of superconductivity by Cu-site substitution is related to the perturbation of lattice instability, indicating that local lattice instability (polaron) plays an important role in superconductivity.