  Antiferromagnetism is relevant to high temperature (high-Tc)
superconductivity because copper oxide and iron arsenide high-Tc
superconductors arise from electron- or hole-doping of their antiferromagnetic
(AF) ordered parent compounds. There are two broad classes of explanation for
the phenomenon of antiferromagnetism: in the local moment picture, appropriate
for the insulating copper oxides, AF interactions are well described by a
Heisenberg Hamiltonian; while in the itinerant model, suitable for metallic
chromium, AF order arises from quasiparticle excitations of a nested Fermi
surface. There has been contradictory evidence regarding the microscopic origin
of the AF order in iron arsenide materials, with some favoring a localized
picture while others supporting an itinerant point of view. More importantly,
there has not even been agreement about the simplest effective ground state
Hamiltonian necessary to describe the AF order. Here we report inelastic
neutron scattering mapping of spin-wave excitations in CaFe2As2, a parent
compound of the iron arsenide family of superconductors. We find that the spin
waves in the entire Brillouin zone can be described by an effective
three-dimensional local moment Heisenberg Hamiltonian, but the large in-plane
anisotropy cannot. Therefore, magnetism in the parent compounds of iron
arsenide superconductors is neither purely local nor purely itinerant; rather
it is a complicated mix of the two.
