Evidence for spin-fluctuation-mediated superconductivity in electron-doped cuprates

In conventional, phonon-mediated superconductors, the transition temperature $T_c$ and normal-state scattering rate $1/\tau$ - deduced from the linear-in-temperature resistivity $\rho(T)$ - are linked through the electron-phonon coupling strength $\lambda_{\rm ph}$. In cuprate high-$T_c$ superconductors, no equivalent $\lambda$ has yet been identified, despite the fact that at high doping, $\alpha$ - the low-$T$ $T$-linear coefficient of $\rho(T)$ - also scales with $T_c$. Here, we use dc resistivity and high-field magnetoresistance to extract $\tau^{-1}$ in electron-doped La$_{2-x}$Ce$_x$CuO$_4$ (LCCO) as a function of $x$ from optimal doping to beyond the superconducting dome. A highly anisotropic inelastic component to $\tau^{-1}$ is revealed whose magnitude diminishes markedly across the doping series. Using known Fermi surface parameters and subsequent modelling of the Hall coefficient, we demonstrate that the form of $\tau^{-1}$ in LCCO is consistent with scattering off commensurate antiferromagnetic spin fluctuations of variable strength $\lambda_{\rm sf}$. The clear correlation between $\alpha$, $\lambda_{\rm sf}$ and $T_c$ then identifies low-energy spin-fluctuations as the primary pairing glue in electron-doped cuprates. The contrasting magnetotransport behaviour in hole-doped cuprates suggests that the higher $T_c$ in the latter cannot be attributed solely to an increase in $\lambda_{\rm sf}$. Indeed, the success in modelling LCCO serves to reinforces the notion that resolving the origin of high-temperature superconductivity in hole-doped cuprates may require more than a simple extension of BCS theory.