Zn-induced spin dynamics in overdoped La$_{2-x}$Sr$_x$Cu$_{1-y}$Zn$_y$O$_4$

Spin fluctuations and the local spin susceptibility in isovalently Zn-substituted La$_{2-x}$Sr$_{x}$Cu$_{1-y}$Zn$_y$O$_4$ ($x=0.25$, $y\approx0.01$) are measured via inelastic neutron scattering techniques. As Zn$^{2+}$ is substituted onto the Cu$^{2+}$-sites, an anomalous enhancement of the local spin susceptibility $\chi^{\prime\prime}(\omega)$ appears due to the emergence of a commensurate antiferromagnetic excitation centered at wave vector \textbf{Q}$=(\pi, \pi, 0)$ that coexists with the known incommensurate SDW excitations at \textbf{Q}$_{HK}=(\pi\pm\delta,\pi), (\pi,\pi\pm\delta)$. Our results support a picture of Zn-induced antiferromagnetic (AF) fluctuations appearing through a local staggered polarization of Cu$^{2+}$-spins, and the simultaneous suppression of T$_c$ as AF fluctuations are slowed in proximity to Zn-impurities suggests the continued importance of high energy AF fluctuations at the far overdoped edge of superconductivity in the cuprates.