Incommensurate charge and spin ordering in doped layered Co perovskite oxides: small-polaron charge glass

Using neutron diffraction, we have investigated two families of cobalt-based layered perovskite oxides, Pr$_{2-x}$Ca$_{x}$CoO$_{4}$ (0.39 $<$ x $<$ 0.73) and La$_{2-x}$Sr$_{x}$CoO$_{4}$ (x=0.5, 0.61), which are relatives of high-Tc cuprate superconductors. In the range of heavy doping, 0.5 $<$ x $<$ 0.75, we have discovered the doping-dependent incommensurate short-range ordering of charges and magnetic moments, whose scattering signatures look somewhat similar to those previously found in cuprates and nickelates. The average incommensurability of charge order (CO) propagation vector, \textbf{Q}c = ($\varepsilon _{c}$,0,l), scales roughly linearly with doping and is proportional to the concentration of Co$^{2+}$ ions, $\varepsilon _{c} \sim $ (1-x). CO exists already at room temperature and shows no change on cooling. In cobaltites, this CO can be understood as a glassy state formed by nano-scale patches of commensurate small-polaron superlattices, whose average period is determined by the doping, x, but the long-range coherence is frustrated by the charge neutrality requirement. Static magnetic spin order in cobaltites only develops at low T $<$ 40 K. Its period is roughly twice that of CO, indicating dominant antiferromagnetic correlation between the nearest Co$^{2+}$ spins.