  Existence of non-ergodic ground states is considered as a precursor to a
first order long range magnetostructural transformation.
Mn$_3$Ga$_{0.45}$Sn$_{0.55}$C lies compositionally between two compounds,
Mn$_3$GaC and Mn$_3$SnC, undergoing first order magnetic transformation.
Mn$_3$Ga$_{0.45}$Sn$_{0.55}$C though crystallizes in single phase cubic
structure, exhibits more than one long range magnetic transitions. Using a
combination of magnetization, ac susceptibility, neutron diffraction and XAFS
techniques it is shown that, though Mn$_3$Ga$_{0.45}$Sn$_{0.55}$C exhibits long
range magnetic order, it presents a cluster glassy ground state due to
formation of magnetically ordered Ga rich and Sn rich clusters. The clusters
are big enough to present signatures of long range magnetic order but are
distributed in such way that it limits interactions between two clusters of the
same type leading to a frozen magnetic state at low temperatures. The main
reason for such a cluster glass state is the difference in local structure of
Mn atoms that find themselves in Ga rich and Sn rich clusters.
