Glassy slowing of stripe modulation in(La,Eu,Nd)2−x(Sr,Ba)xCuO4: A63Cuand139LaNQR study down to 350 mK

Abstract

${}^{63}\mathrm{Cu}$ and ${}^{139}\mathrm{La}$ nuclear quadrupole resonance and Zeeman perturbed nuclear magnetic resonance experiments are performed on the striped phase of the high-temperature superconductors ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{CuO}}_{4}$ and ${\mathrm{La}}_{2\ensuremath{-}x\ensuremath{-}y}(\mathrm{N}\mathrm{d},\mathrm{E}\mathrm{u}{)}_{y}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}.$ The first goal of the present study is to utilize the fact that ordered Cu magnetic moments exert a static hyperfine field on the ${}^{63}\mathrm{Cu}$ and ${}^{139}\mathrm{La}$ nuclei to deduce the charge density and ordered moment within the ${\mathrm{CuO}}_{2}$ planes. A hyperfine-broadened nuclear quadrupole resonance (NQR) line shape is observed in both ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{CuO}}_{4}$ and ${\mathrm{La}}_{1.80\ensuremath{-}x}{\mathrm{Eu}}_{0.20}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ for $x\ensuremath{\approx}\frac{1}{8}.$ Detailed numerical analysis of the ${}^{63}\mathrm{Cu}$ NQR line shape establishes that widely accepted models of periodic sinusoidal or square-well-shaped modulations of spin density waves with maximum moment $\ensuremath{\sim}0.3 {\ensuremath{\mu}}_{B},$ as inferred from elastic neutron scattering and muon spin rotation $(\ensuremath{\mu}\mathrm{SR})$ measurements, cannot account for the NQR line shape unless we assume a relatively small ordered moment $\ensuremath{\sim}0.15 {\ensuremath{\mu}}_{B}$ with a comparably large distribution. The second goal of the present work is to establish the temperature dependence of the fluctuation frequency scale of stripes. We find that the fraction of missing ${}^{63}\mathrm{Cu}$ NQR intensity below charge ordering temperature ${T}_{\mathrm{charge}}$ accurately tracks the temperature dependence of the charge order parameter as measured by scattering methods. By fitting a single model to the temperature dependences of the wipeout fraction $F(T)$ for ${}^{63}\mathrm{Cu}$ and ${}^{139}\mathrm{La}$ NQR, the spin order parameter measured by elastic neutron scattering, and the $\ensuremath{\mu}\mathrm{SR}$ data, we deduce the spatial distribution of the spin fluctuation frequency scale $\ensuremath{\Gamma}$ and its temperature dependence. These results indicate that as soon as the charge dynamics slow down, the spin fluctuations begin to slow dramatically with spin stiffness $2\ensuremath{\pi}{\ensuremath{\rho}}_{s}^{\mathrm{eff}}\ensuremath{\sim}200 \mathrm{K}.$ By extending the analysis to other hole concentrations, we demonstrate a qualitative difference in the spatial variation of electronic states induced by slowing the charge dynamics above and below $x=\frac{1}{8}.$