  The magnetic ground state in highly ordered double perovskites
LaSr$_{1-x}$Ca$_x$NiReO$_6$ ($x$ = 0.0, 0.5, 1.0) were studied in view of the
Goodenough-Kanamori rules of superexchange interactions. In LaSrNiReO$_6$, Ni
and Re sublattices are found to exhibit curious magnetic states, but do not
show any long range magnetic ordering. The magnetic transition at $\sim$ 255 K
is identified with the Re sublattic magnetic ordering. The sublattice
interactions are tuned by modifying the Ni-O-Re bond angles via changing the
lattice structure through Ca doping. Upon Ca doping, the Ni and Re sublattices
start to display a ferrimagnetically ordered state at low temperature. The
neutron powder diffraction reveals a canted alignment between the Ni and the Re
sublattices, while the individual sublattice is ferromagnetic. The transition
temperature of the ferrimagnetic phase increases monotonically with increasing
Ca concentration.
