Neutron scattering measurements were performed to investigate magneticexcitations in a single-crystal sample of the ternary iron arsenide BaFe2As2, aparent compound of a recently discovered family of Fe-based superconductors. Inthe ordered state, we observe low energy spin-wave excitations with a gapenergy of 9.8(4) meV. The in-plane spin-wave velocity v_ab and out-of-planespin-wave velocity v_c measured at 12 meV are 280(150) and 57(7) meV A,respectively. At high energy, we observe anisotropic scattering centered at theantiferromagnetic wave vectors. This scattering indicates two-dimensional spindynamics, which possibly exist inside the Stoner continuum. At T_N=136(1) K,the gap closes, and quasi-elastic scattering is observed above T_N, indicativeof short-range spin fluctuations. In the paramagnetic state, the scatteringintensity along the L direction becomes "rodlike," characteristic ofuncorrelated out-of-plane spins, attesting to the two-dimensionality of thesystem.
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