Interplay of the CE-type charge ordering and the A-type spin ordering in a half-doped bilayer manganite La{1}Sr{2}Mn{2}O{7}

We demonstrate that the half-doped bilayer manganite La_{1}Sr_{2}Mn_{2}O_{7} exhibits CE-type charge-ordered and spin-ordered states below $T_{N, CO}^A = 210$ K and below $T_{N}^{CE} \sim 145$ K, respectively. However, the volume fraction of the CE-type ordering is relatively small, and the system is dominated by the A-type spin ordering. The coexistence of the two types of ordering is essential to understand its transport properties, and we argue that it can be viewed as an effective phase separation between the metallic $d(x^{2}-y^{2})$ orbital ordering and the charge-localized $d(3x^{2}-r^{2})/d(3y^{2}-r^{2})$ orbital ordering.