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For a decade and a half, CeCoIn$_5$ and related alloys have served as a richplayground to explore the interplay between magnetism and unconventionalsuperconductivity. Despite this extended study, the presence/absence ofmetamagnetism (MM) in this ternary system remains as an unresolved issue. Herewe show that the linear and non-linear magnetic response in CeMIn$_5$ (M = Rh,Ir and Co) can be understood within the context of the recently proposed singleenergy scale (SES) model of MM. New measurements of the third-ordersusceptibility, $\chi_3$, in CeCoIn$_5$ are presented and together with theknown systematics of the linear susceptibility in all three compounds, areshown to be consistent with the SES model. Predictions are made for the MMcritical field in CeCoIn$_5$ and the fifth-order susceptibility, $\chi_5$.

The CeMIn5 (M = Rh, Ir and Co) System and the Single Energy Scale Model of Metamagnetism