Spin excitations in Ba(Fe$_{0.957}$Cu$_{0.043})_{2}$As$_{2}$ single crystals near a putative antiferromagnetic quantum critical point*

We report on inelastic neutron scattering measurements of the spin excitations in the non-superconducting Ba(Fe$_{0.957}$Cu$_{0.043})_{2}$As$_{2}$ compound that orders antiferromagnetically at $T_{\mathrm{N}}=$26(5) K in the near vicinity of a putative antiferromagnetic quantum critical point. These results are compared to those of previous studies on low Cu doped BaFe$_{2}$As$_{2}$ and high Co doped BaFe$_{2}$As$_{2}$ compounds. While Co doping induces superconductivity and Cu doping does not, we find that the Cu-doped and Co-doped spectra are qualitatively similar so additional factors must be considered to explain why the Cu-doped compound is not a superconductor. In addition, we show a possible E/T scaling in this compound, which has been observed in many heavy fermion and cuprate superconductors at/near putative quantum critical points.