Spin Dynamics of a Canted Antiferromagnet in a Magnetic Field

The spin dynamics of a canted antiferromagnet with a quadratic spin-wave dispersion near $\text{vq}=0$ is shown to possess a unique signature. When the anisotropy gap is negligible, the spin-wave stiffness $\dsw (\vq, B) = (\omega_{\vq}-B)/q^2$ depends on whether the limit of zero field or zero wavevector is taken first. Consequently, $\text{dsw}$ is a strong function of magnetic field at a fixed wavevector. Even in the presence of a sizeable anisotropy gap, the field dependence of both $\text{dsw}$ and the gap energy distinguishes a canted antiferromagnet from a phase-separated mixture containing both ferromagnetic and antiferromagnetic regions.