Distorted perovskite with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>configuration as a frustrated spin system

The evolution of spin- and orbital-ordered states has been investigated for a series of insulating perovskites $R{\mathrm{MnO}}_{3}$ $(R=\mathrm{L}\mathrm{a},\mathrm{P}\mathrm{r},\mathrm{N}\mathrm{d},\dots{}).$ $R{\mathrm{MnO}}_{3}$ with a large ${\mathrm{GdFeO}}_{3}$-type distortion is regarded as a frustrated spin system having ferromagnetic nearest-neighbor and antiferromagnetic (AF) next-nearest-neighbor (NNN) interactions within a ${\mathrm{MnO}}_{2}$ plane. The staggered orbital order associated with the ${\mathrm{GdFeO}}_{3}$-type distortion induces the anisotropic NNN interaction, and yields unique sinusoidal and up-up-down-down AF ordered states in the distorted perovskites with ${e}_{g}^{1}$ configuration.