Magnetic excitations in pure, lightly doped, and weakly metallic ${\mathrm{La}}_2$${\mathrm{CuO}}_4$

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.

The dc conductivity of this crystal exhibits three different regimes: metallic for T≥100 K, weakly localized for 100≥T≥10 K, and strongly localized below ∼1 K. Our neutron measurements show that the generalized susceptibility of this sample follows a surprisingly simple scaling function in the variable ω/T. This observation allows us to relate our data to a variety of normal-state properties of the layered copper oxides, in particular the dc and ac conductivities. Finally, at temperatures below ∼20 K a ‘‘central peak’’ with a characteristic energy scale of less than 0.1 meV becomes prominent. Its relation to the localization of the charge carriers at low temperatures remains speculative.