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The spin reorientation (SR) phenomenon of the square-lattice antiferromagnetsRMnAsO (R = Ce, Nd) was investigated by analyzing the spin exchangeinteractions between the rare-earth and transition-metal ions (R3+ and Mn2+,respectively) on the basis of density functional calculations. It is found thatthe symmetry and strength of the Dzyaloshinskii-Moriya (DM) interaction aredetermined primarily by the partially filled 4f states of the R3+ ions, andthat the DM and biquadratic (BQ) exchanges between the R3+ and Mn2+ ions areunusually strong and control the observed spin reorientation phenomenon. Belowtheir SR temperature, the Mn2+ and Ce3+ moments are orthogonal in CeMnAsO butare collinear in NdMnAsO, because the DM interaction dominates over the BQinteraction for CeMnAsO while the opposite is the case for NdMnAsO. Experimentsdesigned to test the implications of our findings are proposed.

Spin reorientation in the square-lattice antiferromagnets RMnAsO (R =  Ce, Nd): Density functional analysis of the spin exchange interactions  between the rare-earth and transition-metal ions