  Spin fluctuations in superconducting BaFe2(As1-xPx)2 (x=0.34, Tc = 29.5 K)
are studied using inelastic neutron scattering. Well-defined commensurate
magnetic signals are observed at ({\pi},0), which is consistent with the
nesting vector of the Fermi surface. Antiferromagnetic (AFM) spin fluctuations
in the normal state exhibit a three-dimensional character reminiscent of the
AFM order in nondoped BaFe2As2. A clear spin gap is observed in the
superconducting phase forming a peak whose energy is significantly dispersed
along the c-axis. The bandwidth of dispersion becomes larger with approaching
the AFM ordered phase universally in all superconducting BaFe2As2, indicating
that the dispersive feature is attributed to three-dimensional AFM
correlations. The results suggest a strong relationship between the magnetism
and superconductivity.
