Distorted Perovskite with e_g^1 Configuration as a Frustrated Spin   System
  The evolution of spin- and orbital-ordered states has been systematically investigated for a series of insulating perovskites $R$MnO$_3$ ($R$=La,Pr,Nd,...). $R$MnO$_3$ with a large 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 MnO$_2$ plane. The staggered orbital order associated with the GdFeO$_3$-type distortion induces the anisotropic NNN interaction, and yields the unique sinusoidal and $E$-type ("up-up-down-down") AF ordered states in the distorted perovskites with $e_g^1$ configuration. 
T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K.   Ishizaka, and Y. Tokura