Spin Wave Spectra for Canted Antiferromagnets and Ferromagnets

The magnetic resonance conditions and the spin wave spectra are found for canted antiferromagnetic and ferromagnetic lattices, where the cant is produced by magnetocrystalline anisotropy fields which are non-collinear. The sublattices are thereby caused to cant towards each other in antiferromagnets and away from each other in ferromagnets. The cant of the antiferromagnetic sublattices may produce a net moment (weak ferromagnetism) but does not alter appreciably the usual antiferromagnetic spin wave spectrum in the presence of anisotropy. The static susceptibility parallel (${\ensuremath{\chi}}_{\mathrm{II}}$) and at right angles (${\ensuremath{\chi}}_{\ensuremath{\perp}}$) to the vector difference of the anisotropy fields is calculated, and is shown to be altered from the noncanted result. It is shown that in antiferromagnets with no apparent weak ferromagnetism, canted sublattices may still be present, and can be detected by a nonzero ratio of ${\ensuremath{\chi}}_{\mathrm{II}}$ to ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ at 0\ifmmode^\circ\else\textdegree\fi{}K. The ferromagnetic spin wave spectrum shows a sudden change from the normal spectrum as soon as one introduces the noncollinear anisotropy fields. An optical branch is formed and a high-frequency k=0 magnetic resonance is expected. This resonance is a consequence of the two-sublattice character of the canted ferromagnet and may be termed an exchange resonance.