Two-dimensional magnetic interactions in LaFeAsO

Inelastic neutron scattering measurements demonstrate that the magnetic interactions in antiferromagnetic LaFeAsO are two dimensional. Spin-wave velocities within the Fe layer and the magnitude of the spin gap are similar to the $A$Fe${}_{2}$As${}_{2}$ based materials. However, the ratio of interlayer and intralayer exchange is found to be less than $\ensuremath{\sim}{10}^{\ensuremath{-}4}$ in LaFeAsO, very similar to the cuprates, and $\ensuremath{\sim}$100 times smaller than that found in $A$Fe${}_{2}$As${}_{2}$ compounds. The results suggest that the effective dimensionality of the magnetic system is highly variable in the parent compounds of the iron arsenides and weak three-dimensional interactions may limit the maximum attainable superconducting ${T}_{c}$.