La139 NMR investigation of the charge and spin order in a La1.885Sr0.115CuO4 single crystal

$¹³⁹\mathrm{La}$ NMR is suited for investigations into magnetic properties of ${\mathrm{La}}₂{\mathrm{CuO}}₄$-based cuprates in the vicinity of their magnetic instabilities, owing to the modest hyperfine interactions between $¹³⁹\mathrm{La}$ nuclear spins and Cu electron spins. We report comprehensive $¹³⁹\mathrm{La}$ NMR measurements on a single-crystal sample of high-${T}_c$ superconductor ${\mathrm{La}}_1.885{\mathrm{Sr}}_0.115{\mathrm{CuO}}₄$ in a broad temperature range across the charge and spin order transitions $({T}_{\mathrm{charge}}\ensuremath{\simeq}80$ K, ${T}_{\mathrm{spin}}^{\mathrm{neutron}}\ensuremath{\simeq}{T}_c=30$ K). From the high-precision measurements of the linewidth for the nuclear spin ${I}_z=+1/2$ to $\ensuremath{-}1/2$ central transition, we show that paramagnetic line broadening sets in precisely at ${T}_{\mathrm{charge}}$ due to enhanced spin correlations within the ${\mathrm{CuO}}₂$ planes. Additional paramagnetic line broadening ensues below $\ensuremath{\sim}35$ K, signaling that Cu spins in some segments of ${\mathrm{CuO}}₂$ planes are on the verge of three-dimensional magnetic order. A static hyperfine magnetic field arising from ordered Cu moments along the $ab$ plane, however, begins to develop only below ${T}_{\mathrm{spin}}^{\ensuremath{\mu}SR}=15--20$ K, where earlier muon spin rotation measurements detected Larmor precession for a small volume fraction $(\ensuremath{\sim}20%)$ of the sample. Based on the measurement of $¹³⁹\mathrm{La}$ nuclear-spin-lattice relaxation rate $1/{T}₁$, we also show that charge order triggers enhancement of low-frequency Cu spin fluctuations inhomogeneously; a growing fraction of $¹³⁹\mathrm{La}$ sites is affected by enhanced low-frequency spin fluctuations toward the eventual magnetic order, whereas a diminishing fraction continues to exhibit a behavior analogous to the optimally superconducting phase even below ${T}_{\mathrm{charge}}$. These $¹³⁹\mathrm{La}$ NMR results corroborate our recent $⁶³\mathrm{Cu}$ NMR observation that a very broad, anomalous winglike signal gradually emerges below ${T}_{\mathrm{charge}}$, whereas the normally behaving, narrower main peak is gradually wiped out [T. Imai et al., Phys. Rev. B 96, 224508 (2017)]. Furthermore, we show that the enhancement of low-energy spin excitations in the low-temperature regime below ${T}_{\mathrm{spin}}^{\mathrm{neutron}}\phantom{\rule{4pt}{0ex}}(\ensuremath{\simeq}{T}_c)$ depends strongly on the magnitude and orientation of the applied magnetic field.