The spin fluctuation spectra from nonsuperconducting Cu-substituted, and superconducting Co-substituted, BaFe2As2 are compared quantitatively by inelastic neutron scattering measurements and are found to be indistinguishable. Whereas diffraction studies show the appearance of incommensurate spin-density wave order in Co and Ni substituted samples, the magnetic phase diagram for Cu substitution does not display incommensurate order, demonstrating that simple electron counting based on rigid-band concepts is invalid. These results, supported by theoretical calculations, suggest that substitutional impurity effects in the Fe plane play a significant role in controlling magnetism and the appearance of superconductivity, with Cu distinguished by enhanced impurity scattering and split-band behavior. PACS numbers: 74.70.Xa, 75.30.Fv, 75.30.Kz The role of chemical substitution and its effects on structure, magnetism and superconductivity have become central issues in studies of the iron-pnictide superconductors. [1][2][3][4] This is particularly true for transition-metal (M ) substitution on Fe sites, resulting, nominally, in electron doping of the FeAs layers. When low concentrations of Co, [5,6] Ni, [7,8] Rh,[9, 10] Pt [11] and Pd [9,10] replace Fe, the structural transition temperature (T S ) and the antiferromagnetic (AFM) transition temperature (T N ) are both suppressed to lower values and split with T S > T N . [5-7, 9, 12-14] When the structural and magnetic transitions are suppressed to sufficiently low temperatures, superconductivity emerges below T c and coexists with antiferromagnetism over some range of concentration. Moreover, for Co, Rh and Ni substitutions in BaFe 2 As 2 , neutron diffraction measurements manifest a distinct suppression of the magnetic order parameter in the superconducting regime (T < T c ), which clearly indicates competition between AFM order and superconductivity. [13][14][15][16][17] Cu substitution in BaFe 2 As 2 , in contrast, suppresses the magnetic and structural transitions, but does not support superconductivity [2,8] except, perhaps, below 2 K over a very narrow range in composition.[18] This dichotomy between Co and Ni substitutions and that of Cu is also realized in quaternary fluoroarsenides.[19] However, for Co/Cu co-substitutions in BaFe 2 As 2 , at a fixed non-superconducting Co concentration, the addition of Cu first promotes and then suppresses T c .[18] It has been suggested that previously neglected impurity effects play an important role in this behavior. [8,20] The effects of impurity scattering are also neglected in a simple rigid-band picture for M substitutions, which, at least for Co substitution in BaFe 2 As 2 , seems to adequately account for the evolution of angleresolved photoemission spectroscopy (ARPES) [21], Hall effect, and thermoelectric power (TEP) measurements with concentration.[22] The rigid-band model has also been used successfully to model the suppression of the AFM transition temperature and ordered moment in Ba(Fe 1−x Co x ) 2 As 2 for "u...