  To study the mutual interaction between unconventional superconductivity and
magnetic order through an interface, we fabricate Kondo superlattices
consisting of alternating layers of heavy-fermion superconductor CeCoIn$_5$ and
antiferromagnetic (AFM) heavy-fermion metal CeIn$_3$. The strength of the AFM
fluctuations is tuned by applying hydrostatic pressure to
CeCoIn$_5(m)$/CeIn$_3(n)$ superlattices with $m$ and $n$ unit-cell-thick layers
of CeCoIn$_5$ and CeIn$_3$, respectively. Superconductivity in CeCoIn$_5$ and
AFM order in CeIn$_3$ coexist in spatially separated layers. At ambient
pressure, N\'{e}el temperature $T_N$ of the CeIn$_3$ block layers (BLs) of
CeCoIn$_5$(7)/CeIn$_3(n)$ shows little dependence on $n$, in contrast to
CeIn$_3(n)$/LaIn$_3$(4) superlattices where $T_N$ is strongly suppressed with
decreasing $n$. This suggests that each CeIn$_3$ BL is magnetically coupled by
the RKKY interaction through the adjacent CeCoIn$_5$ BL and a 3D magnetic state
is formed. With applying pressure to CeCoIn$_5$(7)/CeIn$_3$(13), $T_N$ of the
CeIn$_3$ BLs is suppressed up to 2.4 GPa, showing a similar pressure dependence
as CeIn$_3$ single crystals. An analysis of upper critical field reveals that
the superconductivity in the CeCoIn$_5$ BLs is barely influenced by the AFM
fluctuations in the CeIn$_3$ BLs, even when the CeIn$_3$ BLs are in the
vicinity of the AFM quantum critical point. This is in stark contrast to
CeCoIn$_5$/CeRhIn$_5$ superlattice where the superconductivity in the
CeCoIn$_5$ BLs is profoundly affected by AFM fluctuations in the CeRhIn$_5$
BLs. The present results show that although AFM fluctuations are injected into
the CeCoIn$_5$ BLs from the CeIn$_3$ BLs through the interface, they barely
affect the force which binds superconducting electron pairs. These results
demonstrate that 2D AFM fluctuations are essentially important for the pairing
interactions in CeCoIn$_5$.
