Spin fluctuations in a metallic antiferromagnet

The magnon energy and amplitude renormalization due to intraband particle-hole excitations are studied in a metallic antiferromagnet. The change in sign of the intraband contribution with $\omega$ results in significant differences between static and dynamical behaviours. For electron doping, while the coherent magnon peak looses spectral weight and is shifted to higher energy with doping, the low-energy incoherent part becomes increasingly prominent as it narrows in width and shifts to lower energy. Implications for spin dynamics in the electron-doped cuprate $\rm Nd_{2-x} Ce_x Cu O_4$ are discussed. Due to an exact cancellation of two logarithmically divergent spin-fluctuation processes, the AF order parameter is unaffected to leading order. For hole doping, short wavelength transverse perturbations ($q > q^* \sim \sqrt{x}$) are found to be stable, implying short-range AF order with a spin correlation length $\xi/a \sim 1/\sqrt{x}$.