  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.
