An effective spin-orbital Hamiltonian for the double perovskite Sr$_2$FeW O$_6$: Derivation of the phase diagram

TL;DR

This paper derives an effective spin-orbital Hamiltonian for Sr$_2$FeWO$_6$, explaining its magnetic and orbital ground states, and matches experimental antiferromagnetic order through theoretical modeling.

Contribution

The paper introduces a superexchange theory and derives a novel effective Hamiltonian for double perovskites, capturing the magnetic and orbital ordering phenomena.

Findings

Ground state is antiferromagnetic, matching experiments.

Order type is 111 ferromagnetic planes stacked antiferromagnetically.

Orbital order energy scale is an order of magnitude less than spin order.

Abstract

We formulate a superexchange theory of insulating double-perovskite compounds such as Sr$_2$FeWO$_6$. An effective spin-orbital Hamiltonian is derived in the strong coupling limit of Hubbard model for d-electrons on Fe and W ions. The relevant degrees of freedom are the spins S=2 and the three-fold orbital degeneracy of Fe$^{2+}$-ions. W-sites are integrated out by means of a fourth-order perturbative expansion. The magnetically and orbitally ordered ground states of the effective Hamiltonia n are discussed as a function of the model parameters. We show that for realistic values of such parameters the ground state is antiferromagnetic, as experimentally observed. The order found is of type-II, consisting of \{111\} ferromagnetic planes stac ked antiferromagnetically. The orbital order energy scale found is one order of magnitude less than the spi n one.