Revisiting Goodenough-Kanamori rules in a new series of double perovskites LaSr$_{1-x}$Ca$_x$NiReO$_6$

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.