Complex Susceptibility and Resonance Frequencies of Canted Antiferromagnets

Expressions for the complex susceptibility and resonance frequencies of the two-sublattice model for a canted antiferromagnet are derived. This work is an extension of the analysis given by Herrmann in that (1) the applied field is allowed to have an orientation in the $\mathrm{ac}$ plane, (2) the two sublattice moments are allowed to assume their equilibrium orientations wherever they may be in the $\mathrm{ac}$ plane, (3) phenomenological damping is included, and (4) a magnetocrystalline anisotropy energy term with fourfold symmetry is included. It is found that both the susceptibility and the resonance frequency exhibit an extremely sensitive dependence on the angular orientation of the applied field, when the field is near either the $a$ or the $c$ axis. For precise alignment of the field along an axis, resonance is found for arbitrarily low frequencies. However, the minimum frequency for resonance becomes 10 GHz if the field is 0.03° from the axis for material constants similar to those of TmFe${\mathrm{O}}_3$. Simple maxima in both parts of the complex susceptibility occur if the operating frequency is below the minimum resonance frequency in such an off-axis case. With the variety of behavior predicted by this analysis, the microwave absorption measurements in TmFe${\mathrm{O}}_3$ by LeCraw et al. can be plausibly interpreted within the framework of the two-sublattice model by postulating inhomogeneities in the orientation of the crystalline axes. The expressions developed in this paper are essential for relating the microwave measurements to material constants as measured by other techniques.