Longitudinal spin excitations and magnetic anisotropy in antiferromagnetically ordered BaFe$_2$As$_2$*

In the iron-based superconductors, there is an outstanding debate on the microscopic origin of the magnetism, whether it arises from local moments or itinerant electrons with Fermi-surface nesting. To answer this question, we performed a spin-polarized inelastic neutron scattering study of spin waves in the antiferromagnetically ordered state of BaFe$_2$As$_2$. Three distinct excitation components are identified, with spins fluctuating along the $c$-axis, perpendicular to the ordering direction in the $ab$-plane, and parallel to the ordering direction. While the first two ``transverse'' components can be described by a linear spin-wave theory with magnetic anisotropy and inter-layer coupling, the third ``longitudinal'' component is generically incompatible with the local moment picture. It points towards a contribution of itinerant electrons to the magnetism already in the parent compound of this family of Fe-based superconductors. (arXiv:1309.7553)