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 ${\omega }^{2\mathrm{/}3}$. This non-Fermi liquid behavior originates in the coupling of fermions to the longitudinal spin susceptibility ${\chi }_{\parallel }(q,\mathrm{\Omega })$ in which the order-induced ``gap’’ in the spectrum at $q=0$ dissolves into the Landau damping term at $v_{F}q>\mathrm{\Omega }$. The transverse spin fluctuations obey $z=1$ scaling characteristic of spin waves, but remain overdamped in a finite range near the critical point.