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CeCo(In$_{0.990}$Hg$_{0.010}$)$_{5}$ is a charge doped variant of the$d$-wave CoCoIn$_{5}$ superconductor with coexistent antiferromagnetic andsuperconducting transitions occurring at T$_{N}$= 3.4 K and T$_{c}$=1.4 K,respectively. We use neutron diffraction and spectroscopy to show that themagnetic resonant fluctuations present in the parent superconducting phase arereplaced by collinear $c$-axis magnetic order with three-dimensional Isingcritical fluctuations. No low energy transverse spin fluctuations areobservable in this doping-induced antiferromagnetic phase and the dynamicresonant spectral weight predominately shifts to the elastic channel. Static($\tau$ $>$ 0.2 ns) collinear Ising order is proximate to superconductivity inCeCoIn$_{5}$ and is stabilized through hole doping with Hg.

From Ising resonant fluctuations to static uniaxial order in antiferromagnetic and weakly superconducting CeCo(In$_{1-x}$Hg$_{x}$)$_{5}$ ($x$=0.01)