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Understanding ferromagnetism in Cr-based 3d-5d double perovskites

Ferromagnetism in Cr-based double perovskites is analyzed using effective model as well as simulation approach. Starting from a microscopic model proposed recently for this class of double perovskites, an effective spin-only model is derived in the limit of large exchange coupling at the B-site. Analytic expressions for the resultant exchange coupling is derived in certain limiting cases. The behaviour of this exchange is used to provide a plausible explanation for the enhanced ferromagnetic tendency as also the enigmatic increase in Curie temperature observed in Cr-based DP-s, in the series Sr$_{2}$CrWO$_{6}$,Sr$_{2}$CrReO$_{6}$ to Sr$_{2}$CrOsO$_{6}$. The superexchange between neighbouring B and B' sites is found to play a crucial role both in stabilizing ferromagnetism, especially in the latter two compounds, as well as increasing the T$_{c}$.