Distorted perovskite with $e_g^1$ configuration as a frustrated spin system

The evolution of spin- and orbital-ordered states has been investigated for a series of insulating perovskites $R{\mathrm{MnO}}_3$ $(R=\mathrm{L}\mathrm{a},\mathrm{P}\mathrm{r},\mathrm{N}\mathrm{d},\dots ).\mathrm{}$ $R{\mathrm{MnO}}_3$ 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.