Disappearance of antiferromagnetic spin excitations in overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$

We have used time-of-flight neutron spectroscopy to study magnetic excitations, for energies up to $\sim $100 meV, in overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x$ = 0.25 and 0.30 [1]. Comparison of spectra integrated over the width of an antiferromagnetic Brillouin zone demonstrates that the magnetic scattering at intermediate energies, 20$<\omega <$100 meV, progressively decreases with overdoping. Previous work has shown that the low-energy magnetic excitations also disappear with overdopoing [2]. This strongly suggests that the magnetism is a vestige of the parent antiferromagnet; spatial segregation of the doped holes, as in the stripe picture, provides a natural way for this to occur. Both the magnetism and superconductivity disappear as the system becomes a homogeneous metal. [1] S. Wakimoto \textit{et al}., Phys. Rev. Lett. \textbf{98}, 247003 (2007). [2] S. Wakimoto \textit{et al}., Phys. Rev. Lett. \textbf{92}, 217004 (2007).