Spin Dynamics of a Canted Antiferromagnet in a Magnetic Field

The spin dynamics of a canted antiferromagnet with a quadratic spin-wave dispersion near ${\bf q} =0$ possesses a unique signature. When the anisotropy gap is negligible, the spin-wave stiffness $D_{sw}({\bf q},B) = (\omega_{\bf q}-B)/q^2$ depends on whether the limit of zero field or zero wavevector is taken first. Consequently, $D_{sw} $ is a strong function of magnetic field at a fixed wavevector. Even in the presence of a sizeable anisotropy gap, the field dependence of the extrapolated ${\bf q} = 0$ gap energy $\Delta_0(B)$ distinguishes a canted antiferromagnet from a phase-separated mixture containing both ferromagnetic and antiferromagnetic regions. For a ferromagnet, $d\Delta_0 /dB =1$ whereas for a canted antiferromagnet, $d\Delta_0/dB > 1$. Calculations performed for a generalized Villain model with additional anisotropy terms are used to demonstrate these ideas. These results are used to demonstrate that the ``ferromagnetic'' regions in Pr manganites are actually canted.