Spin fluctuations in a metallic antiferromagnet

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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 ω 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 Nd₂₋ₓ Ceₓ Cu O₄ 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* √x) are found to be stable, implying short-range AF order with a spin correlation length ξ/a 1/√x.