  The spin reorientation (SR) phenomenon of the square-lattice antiferromagnets
RMnAsO (R = Ce, Nd) was investigated by analyzing the spin exchange
interactions between the rare-earth and transition-metal ions (R3+ and Mn2+,
respectively) on the basis of density functional calculations. It is found that
the symmetry and strength of the Dzyaloshinskii-Moriya (DM) interaction are
determined primarily by the partially filled 4f states of the R3+ ions, and
that the DM and biquadratic (BQ) exchanges between the R3+ and Mn2+ ions are
unusually strong and control the observed spin reorientation phenomenon. Below
their SR temperature, the Mn2+ and Ce3+ moments are orthogonal in CeMnAsO but
are collinear in NdMnAsO, because the DM interaction dominates over the BQ
interaction for CeMnAsO while the opposite is the case for NdMnAsO. Experiments
designed to test the implications of our findings are proposed.
