Magnetic excitations in pure, lightly doped, and weakly metallicLa2CuO4

We report a comprehensive neutron-scattering study of the evolution of the magnetic excitations in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ for 0≤x≤0.04. We first present accurate measurements of the magnetic correlation length and the sublattice magnetization of a carrier-free ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ crystal and analyze these in the context of recent theoretical predictions. We then systematically investigate the influence of different dopants on the magnetism: Our measurements indicate that static vacancies in the ${\mathrm{La}}_2$ ${\mathrm{Cu}}_{1\mathrm{-}\mathit{y}}$ ${\mathrm{Zn}}_{\mathit{y}}$ ${\mathrm{O}}_4$ system affect the magnetic correlations in a similar manner as electrons in ${\mathrm{Pr}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Ce}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$. The magnetic correlation length is much more rapidly suppressed as a function of x in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$, and for x≤0.04 we find that it obeys the empirical relation ${\xi }^{\mathrm{-}1}$(x,T)=${\xi }^{\mathrm{-}1}$(x,0)+${\xi }^{\mathrm{-}1}$(0,T), where ξ(0,T) is the measured correlation length of the carrier-free sample. We also report an extensive set of measurements of the dynamical magnetic response function of a crystal of composition ${\mathrm{La}}_{1.96}$ ${\mathrm{Sr}}_{0.04}$ ${\mathrm{CuO}}_4$ for excitation energies 0.75≤ω≤45 meV and temperatures 1.5≤T≤500 K.