Suppression of the outwards-dispersing branches in hour-glass magnetic spectra induced by nanoscale phase separation in La2−xSrxCoO4

Here, we reinvestigate the underlying charge and magnetic correlations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CoO}}_{4}$ within a combined study of muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), x-ray photon correlation spectroscopy, synchrotron radiation single-crystal x-ray diffraction, and neutron-scattering measurements. For ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CoO}}_{4}$ around 1/3 hole-doping, the significant charge correlations that are responsible for the emergence of hour-glass magnetic spectra are found to be slowly fluctuating checkerboard charge ordering (CBCO) correlations with an onset temperature being independent of hole-doping. This reveals a local origin of the CBCO correlations in the rather ionic cobaltates, thus being distinct from the more covalent nickelates. Moreover, we report the observation of a very similar temperature dependence of the intensities of in-plane high- and low-energy excitations within the ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CoO}}_{4}$ hour-glass spectrum. This observation shows that nano phase separation is distinct from conventional phase separation and that there is a coupling between nanometer-sized undoped and hole-doped islands. Based on this, it is possible to propose a microscopic scenario for the suppression of the outwards-dispersing branches in hour-glass magnetic spectra.