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 ($\frac{\Delta g}{g}$) and ${\left(\frac{\Delta g}{g}\right)}^2$ times the isotropic superexchange energy, respectively. Higher order spin couplings are also discussed. As an example of antisymmetric spin coupling the case of Cu${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O is illustrated. In Cu${\mathrm{Cl}}_2$·2${\mathrm{H}}_2$O, 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 $\alpha$-${\mathrm{Fe}}_2$${\mathrm{O}}_3$, MnC${\mathrm{O}}_3$, and Cr${\mathrm{F}}_3$. The paramagnetic susceptibility perpendicular to the trigonal axis is expected to increase very sharply near the Néel temperature as the temperature is lowered, as was actually observed in Cr${\mathrm{F}}_3$.

• Received 25 May 1960

DOI:https://doi.org/10.1103/PhysRev.120.91