Theory of magnetism in La$_2$NiMnO$_6$

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.