Spin excitations in the excitonic spin-density-wave state of the iron pnictides

Motivated by the iron pnictides, we examine the spin excitations in an itinerant antiferromagnet where a spin-density wave (SDW) originates from an excitonic instability of nested electronlike and holelike Fermi pockets. Using the random-phase approximation, we derive the Dyson equation for the transverse susceptibility in the excitonic SDW state. The Dyson equation is solved for two different two-band models, describing an antiferromagnetic insulator and metal, respectively. We determine the collective spin-wave dispersions and also consider the single-particle continua. The results for the excitonic models are compared with each other and also contrasted with the well-known SDW state of the Hubbard model. Despite the qualitatively different SDW states in the two excitonic models, their magnetic response shows many similarities. We conclude with a discussion of the relevance of the excitonic SDW scenario to the iron pnictides.