Non-Fermi-liquid behavior in itinerant antiferromagnets

We consider a two-dimensional itinerant antiferromagnet near a quantum-critical point. We show that, contrary to conventional wisdom, fermionic excitations in the ordered state are not the usual Fermi-liquid quasiparticles. Instead, down to very low frequencies, the fermionic self-energy varies as omega(2/3). This non-Fermi-liquid behavior originates in the coupling of fermions to the longitudinal spin susceptibility chi(parallel to)(q,Omega) in which the order-induced gap in the spectrum at q=0 dissolves into the Landau damping term at v(F)q>Omega. The transverse spin fluctuations obey the z=1 scaling characteristic of spin waves, but remain overdamped in a finite range near the critical point.