LAUSR

For half-doped manganese oxides that have a perovskite structure, $R{E}_{1\ensuremath{-}\mathrm{x}}A{E}_{\mathrm{x}}\mathrm{Mn}{\mathrm{O}}_{3}$ ($x=0.5$) (RE and AE are rare-earth and alkaline-earth elements, respectively), the phase competition (stability) between the antiferromagnetic charge- or orbital-ordered insulator (CO/OO AFI), ferromagnetic metal (FM), layered (A-type) antiferromagnetic phase [AF(A)], and spin-glass-like insulator (SGI), have been studied using single crystals prepared by the floating zone method. The CO/OO AFI, FM, AF(A), and SGI are displayed on the plane of the disorder (the variance of the RE and AE cations) versus the effective one-electron bandwidth (the averaged ionic radius of the RE and AE). In the plane of the disorder versus the effective one-electron bandwidth, similar to the phase diagram of $R{E}_{1\ensuremath{-}\mathrm{x}}A{E}_{\mathrm{x}}\mathrm{Mn}{\mathrm{O}}_{3}$ ($x=0.45$), the CO/OO AFI, FM, and SGI dominate at the lower-left, right, and upper regions, respectively. However, the CO/OO AFI for $x=0.5$ is more stable than that for $x=0.45$, and it expands to the plane points that correspond to the $R{E}_{0.5}\mathrm{S}{\mathrm{r}}_{0.5}\mathrm{Mn}{\mathrm{O}}_{3}$ ($RE=\mathrm{Nd}$ and Sm) specimens as the hole concentration is commensurate with the ordering of $\mathrm{M}{\mathrm{n}}^{3+}$/$\mathrm{M}{\mathrm{n}}^{4+}$ with a ratio of 1/1. The $y$-dependent electronic phases for $R{E}_{0.5}{(\mathrm{S}{\mathrm{r}}_{1\ensuremath{-}\mathrm{y}}\mathrm{B}{\mathrm{a}}_{\mathrm{y}})}_{0.5}\mathrm{Mn}{\mathrm{O}}_{3}$ ($0\ensuremath{\le}y\ensuremath{\le}0.5$) ($RE=\mathrm{Sm}$, $\mathrm{N}{\mathrm{d}}_{0.5}\mathrm{S}{\mathrm{m}}_{0.5}$, Nd, and Pr) show that the AF(A) intervenes between the CO/OO AFI and FM. Besides the region around ${(\mathrm{L}{\mathrm{a}}_{1\ensuremath{-}\mathrm{y}}\mathrm{P}{\mathrm{r}}_{\mathrm{y}})}_{0.5}\mathrm{S}{\mathrm{r}}_{0.5}\mathrm{Mn}{\mathrm{O}}_{3}$ ($0\ensuremath{\le}y\ensuremath{\le}1$) that has a smaller disorder, the AF(A) also exists at the regions around $R{E}_{0.5}{(\mathrm{S}{\mathrm{r}}_{1\ensuremath{-}\mathrm{y}}\mathrm{B}{\mathrm{a}}_{\mathrm{y}})}_{0.5}\mathrm{Mn}{\mathrm{O}}_{3}$ ($0lyl0.3$) ($RE=\mathrm{Sm}$ and $\mathrm{N}{\mathrm{d}}_{0.5}\mathrm{S}{\mathrm{m}}_{0.5}$) that have a relatively larger disorder. This indicates that the AF(A) is rather robust against the increased disorder, even though an ordering of the (${x}^{2}\ensuremath{-}{y}^{2}$) orbital occurs. This study has comprehensively investigated the effects of the disorder on the AF(A) as well as on the competition between the CO/OO AFI, FM, and AF(A) that is unique to $x=0.5$. The comparison of phase diagrams between $x=0.45$ and 0.5 brings further insights into the understanding of the rich electronic phases of manganites.