Magnetic Symmetry of Rare-Earth Orthochromites and Orthoferrites

A new magnetic symmetry of the rare-earth orthochromites and orthoferrites ($\mathrm{RM}{\mathrm{O}}_3$) below the second Néel temperature due to the reordering of the rare-earth spins is proposed. It is shown that the magnetic symmetry group is lowered to the subgroup of index two, thereby keeping the unit cell invariant. The proposed symmetry is shown to be consistent with the previously observed spin configuration of $\mathrm{RM}{\mathrm{O}}_3$ such as GdCr${\mathrm{O}}_3$, DyFe${\mathrm{O}}_3$, and DyCr${\mathrm{O}}_3$, and would also be consistent with those of other $\mathrm{RM}{\mathrm{O}}_3$. Although symmetry arguments and the calculation of the free energy show that two spin configurations are stable, in GdCr${\mathrm{O}}_3$, a future measurement of the magnetoelectric tensor would determine which configuration GdCr${\mathrm{O}}_3$ has. It is further predicted that the magnetoelectric effect should be observed in any $\mathrm{RM}{\mathrm{O}}_3$ below the second Néel temperature.