Collective magnetic excitations of $C_4$ symmetric magnetic states in iron-based superconductors

We study the collective magnetic excitations of the recently discovered $C_4$ symmetric spin-density wave states of iron-based superconductors with particular emphasis on their orbital character based on an itinerant multiorbital approach. This is important since the $C_4$ symmetric spin-density wave states exist only at moderate interaction strengths where damping effects from a coupling to the continuum of particle-hole excitations strongly modifies the shape of the excitation spectra compared to predictions based on a local moment picture. We uncover a distinct orbital polarization inherent to magnetic excitations in $C_4$ symmetric states, which provide a route to identify the different commensurate magnetic states appearing in the continuously updated phase diagram of the iron-pnictide family.