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To explore the spiral and $E$-type magnetic orders observed in orthorhombic perovskite manganites $R{\text{MnO}}_{3}$ ($R$: rare-earth element), we have studied the magnetic superexchange interaction in $R{\text{MnO}}_{3}$ based on the microscopic model incorporating the ${\text{GdFeO}}_{3}$-type octahedral tilting and the Jahn-Teller (JT) distortion. We have found that (i) the account of ${t}_{2g}$ electrons is essential to describe both the nearest-neighbor (NN) and next-nearest-neighbor (NNN) superexchange interactions, (ii) the JT distortion angle as well as the octahedral tilting and the JT distortion strength is an important factor for the superexchange interactions, and (iii) two NNN interactions in the $ab$ plane are anisotropic but are both antiferromagnetic. We have determined the magnetic-phase diagram of $R{\text{MnO}}_{3}$ and discussed the magnetic ground states in relation to the experiments.

physical review b

Nearest and next-nearest superexchange interactions in orthorhombic perovskite manganites<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mrow><mml:mtext>MnO</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mtext>rare</mml:mtext></mml:mrow></mml:math>earth)

Nearest and next-nearest superexchange interactions in orthorhombic perovskite manganitesRMnO3(R=rareearth)