Phase separated magnetic ground state in Mn$_3$Ga$_{0.45}$Sn$_{0.55}$C

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.