Neutron scattering measurements were performed to investigate magnetic excitations in a single-crystal sample of the ternary iron arsenide BaFe2As2, a parent compound of a recently discovered family of Fe-based superconductors. In the ordered state, we observe low energy spin-wave excitations with a gap energy of 9.8(4) meV. The in-plane spin-wave velocity v_ab and out-of-plane spin-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 the antiferromagnetic wave vectors. This scattering indicates two-dimensional spin dynamics, 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, indicative of short-range spin fluctuations. In the paramagnetic state, the scattering intensity along the L direction becomes rodlike, characteristic of uncorrelated out-of-plane spins, attesting to the two-dimensionality of the system.
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