  The magnetic structure of Ca$_2$MnReO$_6$ double perovskite is investigated
by neutron powder diffraction and bulk magnetization, showing dominant
non-collinear Mn magnetic moments [$4.35(7)$ $\mu_B$] that are orthogonally
aligned with the small Re moments [$0.22(4)$ $\mu_B$]. $Ab$-initio electronic
structure calculations show that the strong spin-orbit coupling for Re $5d$
electrons combined with a relatively modest on-site Coulomb repulsion
($U_{eff}^{Re} \gtrsim 0.6$ eV) is sufficient to render this material
insulating. This is a rare example of spin-orbit assisted Mott insulator
outside the realm of iridates, with remarkable magnetic properties.
