Localized and itinerant magnetic excitations in CaFe$_{2}$As$_{2}$

Elementary magnetic excitations in the striped phase of CaFe$_{2}$As$_{2}$ are studied with linear-response density-functional theory. Itinerant, Stoner-like elementary excitations are found to coexist with the usual antiferromagnetic spin waves observed in neutron experiments. When the Fe moment $M$ exceed 1.1$\mu_{B}$, spin waves are dominant; while as $M$ decreases below 1$\mu_{B}$ there is a rather sharp transition to itinerant behavior, with spin waves being damped by Stoner excitations of several types. An unusual low energy excitation was found, whose origin can be traced to excitations within a narrow Fe $d$ band of \emph{xy} and \emph{yz} symmetry. This band lies above the Fermi level when $M$ is 1.1$\mu_{B}$, and passes through it as $M$ decreases. The more conventional spin waves are associated with transitions from a different band of $d$ states, at lower energy. This establishes that independent localized and itinerant elementary excitations coexist in CaFe$_{2}$As$_{2}$, and are present even below the N{\'e}el temperature.