  We measured specific heat and resistivity of heavy fermion CeCoIn5 between
the superconducting critical field $H_{c2} = 5 T$ and 9 T, with field in the
[001] direction, and at temperatures down to 50mK. At 5T the data show Non
Fermi Liquid behavior down to the lowest temperatures. At field above 8T the
data exhibit crossover from the Fermi liquid to a Non Fermi Liquid behavior. We
analyzed the scaling properties of the specific heat, and compared both
resistivity and the specific heat with the predictions of a spin-fluctuation
theory. Our analysis leads us to suggest that the NFL behavior is due to
incipient antiferromagnetism (AF) in CeCoIn5, with the quantum critical point
in the vicinity of the $H_{c2}$. Below $H_{c2}$ the AF phase which competes
with the paramagnetic ground state is superseded by the superconducting
transition.
