  We present the results of elastic and inelastic neutron scattering
measurements on non-superconducting
Ba(Fe${_{0.957}}$Cu${_{0.043}}$)${_2}$As${_2}$, a composition close to a
quantum critical point between AFM ordered and paramagnetic phases. By
comparing these results with the spin fluctuations in the low Cu composition as
well as the parent compound BaFe$_2$As$_2$ and superconducting
Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ compounds, we demonstrate that paramagnon-like
spin fluctuations are evident in the antiferromagnetically ordered state of
Ba(Fe$_{0.957}$Cu$_{0.043}$)$_2$As$_2$, which is distinct from the AFM-like
spin fluctuations in the superconducting compounds. Our observations suggest
that Cu substitution decouples the interaction between quasiparticles and the
spin fluctuations. We also show that the spin-spin correlation length,
${\xi(T)}$, increases rapidly as the temperature is lowered and find
${\omega/T}$ scaling behavior, the hallmark of quantum criticality, at an
antiferromagnetic quantum critical point.
