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We formulate a superexchange theory of insulating double-perovskite compoundssuch as Sr$_2$FeWO$_6$. An effective spin-orbital Hamiltonian is derived in thestrong coupling limit of Hubbard model for d-electrons on Fe and W ions. Therelevant degrees of freedom are the spins S=2 and the three-fold orbitaldegeneracy of Fe$^{2+}$-ions. W-sites are integrated out by means of afourth-order perturbative expansion. The magnetically and orbitally orderedground states of the effective Hamiltonia n are discussed as a function of themodel parameters. We show that for realistic values of such parameters theground state is antiferromagnetic, as experimentally observed. The order foundis of type-II, consisting of \{111\} ferromagnetic planes stac kedantiferromagnetically. The orbital order energy scale found is one order ofmagnitude less than the spi n one.Comment: 12 pages, 4 figure

physical review. b, condensed matter

Effective spin-orbital Hamiltonian for the double perovskite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">FeWO</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>:</mml:mo></mml:math>Derivation of the phase diagram

Effective spin-orbital Hamiltonian for the double perovskiteSr2FeWO6:Derivation of the phase diagram