Theory of spin reorientation in rare-earth orthochromites and orthoferrites

Mechanisms of the temperature-induced spin-reorientation in rare-earth orthochromites (and orthoferrites) are examined. It is concluded that the anisotropic parts of the magnetic interactions between Cr³⁺ (or Fe³⁺) and rare-earth ions, the antisymmetric and the anisotropic-symmetric exchange interactions, are generally responsible for both the rotational and the abrupt types of the spin-reorientations. These anisotropic exchange interactions produce an effective field for the Cr³⁺ up-spins in the direction perpendicular to that of these spins and an effective field for the Cr³⁺ down-spins in the direction opposite to the above. These effective fields favor rotation of the Cr³⁺ spins, retaining their original antiferromagnetic configuration. Thus, as the temperature is lowered, this effective field increases due to the increase of the rare-earth magnetization, and when the interaction energy of the Cr³⁺ spins with these effective fields exceeds the anisotropy energy of the Cr³⁺ ion, spin-reorientation. takes place. At the beginning and ending of the spin-reorientation a second-order phase-transition occurs. The first-order nature of the abrupt spin-reorientation is stressed. Anisotropic exchange interactions between Cr³⁺ and rare-earth ions also play an important role in inducing the abrupt spin-reorientation.