Doping dependence of the spatially modulated dynamical spin correlations and the superconducting-transition temperature

Systematic low-energy neutron-scattering studies have been performed on float-zone-grown single crystals of (Formula presented) with (Formula presented) extending from zero doping, (Formula presented), to the overdoped, weakly superconducting regime, (Formula presented). For (Formula presented) beyond a critical doping value of (Formula presented) the low-energy spin-fluctuation peak position shifts from ((Formula presented), (Formula presented)) to ((Formula presented)±δ, (Formula presented)), and ((Formula presented), (Formula presented)±δ); (Formula presented) also represents the onset concentration for superconductivity. For (Formula presented) the incommensurability (Formula presented) follows approximately the quantitative relation (Formula presented). However, beyond (Formula presented) the incommensurability tends to saturate around (Formula presented). The superconducting-transition temperature (Formula presented) for stoichiometric samples at a given doping scales linearly with (Formula presented) up to the optimal doping value of (Formula presented). The peak momentum width of the spin fluctuations at low energies is small throughout the superconducting concentration region except in the strongly overdoped region. An anomalously small width is observed for (Formula presented). The incommensurate spatial modulation is found to be robust with respect to pair-breaking effects that lower (Formula presented) such as deoxygenation of the sample or replacement of Cu by Zn.