Effect of Antisymmetric Exchange Interaction on the Magnetization and Resonance in Antiferromagnets

The magnetization curves and the resonance frequencies are calculated for two types of antiferromagnets with an antisymmetric exchange interaction of the form ${\mathbf{D}}_{\mathrm{ij}}·{\mathbf{M}}_i\times {\mathbf{M}}_j$ and a uniaxial magnetocrystalline anisotropy term $K {sin}^2\theta$. In one type of these antiferromagnets, the D vector is perpendicular to the easy axis. This is presumably the case in the orthoferrites. For this case, we have calculated the resonance frequency as a function of an external field applied parallel to the easy axis. In the second type of these antiferromagnets the D vector lies parallel to the easy axis. This is the situation in hematite below the Morin temperature. For this case, we have calculated the resonance frequency as a function of an external field applied in the plane perpendicular to the easy axis. In both cases we obtained two resonance modes, and the lower mode was found to have a frequency $W_{-}=0\mathrm{}$ for a characteristic critical field, at which the antiferromagnetic axis becomes perpendicular to the easy axis.