Structural and magnetic properties of the 5$d^2$ double perovskites Sr$_2 B$ReO$_6$ ($B$ $=$ Y, In)

We have performed magnetic susceptibility, heat capacity, neutron powder diffraction, and muon spin relaxation experiments to investigate the magnetic ground states of the 5$d^2$ double perovskites Sr$_2$YReO$_6$ and Sr$_2$InReO$_6$. We find that Sr$_2$YReO$_6$ is a spin glass, while Sr$_2$InReO$_6$ hosts a non-magnetic singlet state. By making detailed comparisons with other 5$d^2$ double perovskites, we argue that a delicate interplay between spin-orbit coupling, non-cubic crystal fields, and exchange interactions plays a key role in the great variation of magnetic ground states observed for this family of materials.