Neutron scattering experiments were performed on single crystals of layered cobalt-oxides La2-xCaxCoO4 (LCCO) to characterize the charge and spin orders in a wide hole-doping range of 0.3<x<0.8. For a commensurate value of x=0.5 in (H,0,L) plane, two types of superlattice reflections concomitantly appear at low temperature; one corresponds to a checkerboard charge ordered pattern of Co2+/Co3+ ions and the other is magnetic in origin. Further, the latter magnetic-superlattice peaks show two types of symmetry in the reflections, suggesting antiferromagnetic-stacking (AF-S) and ferromagnetic-stacking (F-S) patterns of spins along the c direction. From the hole-doping dependence, the in-plane correlation lengths of both charge and spin orders are found to give a maximum at x=0.5. These features are the same with those of x=0.5 in La1-xSr1+xMnO4 (LSMO), a typical checkerboard and spin ordered compound. However, in (H,H,L) plane, we found a magnetic scattering peak at Q=(1/4,1/4,1/2) position below TN. This magnetic peak can not be understood by considering the Co2+ spin configuration, suggesting that this peak is originated from Co3+ spin order. By analyzing these superlattice reflections, we found that they are originated from high-spin state of Co3+ spin order.
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