Abstract
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 \textit{A}Fe$_2$As$_2$ based materials. However, the ratio of interlayer and intralayer exchange is found to be less than $\sim 10^{-4}$ in LaFeAsO, very similar to the cuprates, and $\sim$ 100 times smaller than that found in \textit{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 3-D interactions may limit the maximum attainable superconducting $T_{c}$.
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