Renormalized perturbation theory of magnetic instabilities in the two-dimensional Hubbard model at small doping

We consider magnetic instabilities in the two-dimensional Hubbard model at small doping. We find that the renormalization of the effective interaction prevents an immediate instability of a commensurate antiferromagnetic state upon doping. At increased doping levels, our calculations indicate the occurrence of an instability in the channel of transverse spin fluctuations. This instability is known to lead to a spiral magnetic phase. We also consider a dynamical spin susceptibility near the instability and find that conventional spin waves play no role in the transition. Instead, the incommensurate instability is governed by collective fermionic excitations coupled to the spin background.