Anisotropic Superexchange Interaction and Weak Ferromagnetism

A theory of anisotropic superexchange interaction is developed by extending the Anderson theory of superexchange to include spin-orbit coupling. The antisymmetric spin coupling suggested by Dzialoshinski from purely symmetry grounds and the symmetric pseudodipolar interaction are derived. Their orders of magnitudes are estimated to be (g) and ({g) }^2 times the isotropic superexchange energy, respectively. Higher order spin couplings are also discussed. As an example of antisymmetric spin coupling the case of CuCl₂2H₂O is illustrated. In CuCl₂2H₂O, a spin arrangement which is different from one accepted so far is proposed. This antisymmetric interaction is shown to be responsible for weak ferromagnetism in -Fe₂O₃, MnCO₃, and CrF₃. The paramagnetic susceptibility perpendicular to the trigonal axis is expected to increase very sharply near the N\'eel temperature as the temperature is lowered, as was actually observed in CrF₃.