Versatile and competing spin-charge-orbital orders in the bilayered manganite systemPr(Sr1−yCay)2Mn2O7

Abstract

Electronic-phase competition has been investigated for single crystals of half-doped bilayer-structure manganites, $\mathrm{Pr}{({\mathrm{Sr}}_{1\ensuremath{-}y}{\mathrm{Ca}}_{y})}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ $(0\ensuremath{\leqslant}y\ensuremath{\leqslant}1.0)$, with controlled one-electron bandwidth $(W)$. For $y\ensuremath{\leqslant}0.4$, the A-type antiferromagnetic (AF) state with ${x}^{2}\ensuremath{-}{y}^{2}$ orbital order shows up as the ground state while accompanying the short-range vertical charge order with the periodicity of $\ensuremath{\approx}4{a}_{0}$ $({a}_{0}\ensuremath{\approx}0.4\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. For $y>0.4$, with reduced $W$, the CE-type AF state emerges with the ordered staggered orbitals $(3{x}^{2}\ensuremath{-}{r}^{2}∕3{y}^{2}\ensuremath{-}{r}^{2})$ whose diagonal stripes undergo the 90\ifmmode^\circ\else\textdegree\fi{} rotation with decreasing temperature, perhaps coupled with the evolution of spin correlation.