We have investigated the effect of Cd substitution on the archetypal heavy fermion antiferromagnet CeIn$_3$ via magnetic susceptibility, specific heat and resistivity measurements. The suppression of the Neel temperature, T$_{N}$, with Cd doping is more pronounced than with Sn. Nevertheless, a doping induced quantum critical point does not appear to be achievable in this system. The magnetic entropy at $T_N$ and the temperature of the maximum in resistivity are also systematically suppressed with Cd, while the effective moment and the Curie-Weiss temperature in the paramagnetic state are not affected. These results suggest that Cd locally disrupts the AFM order on its neighboring Ce moments, without affecting the valence of Ce. Moreover, the temperature dependence of the specific heat below $T_N$ is not consistent with 3D magnons in pure as well as in Cd-doped CeIn$_3$, a point that has been missed in previous investigations of CeIn$_3$ and that has bearing on the type of quantum criticality in this system.
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