Direct Relation between the Low-Energy Spin Excitations and Superconductivity of Overdoped High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>Superconductors

Abstract

The dynamic spin susceptibility, ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$, has been measured over the energy range of $2\ensuremath{\le}\ensuremath{\omega}\ensuremath{\le}10\text{ }\mathrm{meV}$ for overdoped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$. Incommensurate (IC) spin excitations are observed at 8 K for all superconducting samples for $0.25\ensuremath{\le}x\ensuremath{\le}0.28$ with ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}$ peaking at $\ensuremath{\sim}6\text{ }\mathrm{meV}$. The IC peaks at 6 meV become smaller in intensity with increasing $x$ and, finally, become unobservable for a sample with $x=0.30$ which has no bulk superconductivity. The maximum ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}$ decreases linearly with ${T}_{c}$(onset) in the overdoped region, implying a direct cooperative relation between the spin fluctuations and the superconductivity.