  The magnetism of ordered and disordered La$_2$NiMnO$_6$ is explained using a
model involving double exchange and superexchange. The concept of majority spin
hybridization in the large coupling limit is used to explain the ferromagnetism
of La$_2$NiMnO$_6$ as compared to the ferrimagnetism of Sr$_{2}$FeMoO$_{6}$.
The ferromagnetic insulating ground state in the ordered phase is explained.
The essential role played by the Ni-Mn superexchange between the Ni $e_{g}$
electron spins and the Mn $t_{2g}$ core electron spins in realizing this ground
state, is outlined. In presence of antisite disorder, the model system is found
to exhibit a tendency of becoming a spin-glass at low temperatures, while it
continues to retain a ferromagnetic transition at higher temperatures, similar
to recent experimental observations [D. Choudhury .et.al., Phys. Rev. Lett.
108, 127201 (2012)]. This reentrant spin-glass or reentrant ferromagnetic
behaviour is explained in terms of the competition of the ferromagnetic double
exchange between the Ni $e_{g}$ and the Mn $e_{g}$ electrons, and the
ferromagnetic Ni-Mn superexchange, with the antiferromagnetic antisite Mn-Mn
superexchange.
