Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori Rules

Abstract:

We point out that large composite spin-orbital fluctuations in Mott insulators with t2g orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules.

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http://arxiv.org/pdf/cond-mat/0604417.pdf


Since the 1960’s the magnetism of correlated Mott insulators like transition-metal oxides has been understood by means of the Goodenough-Kanamori (GK) rules [1, 2]. These state that if there is large overlap between partly occupied orbitals at two magnetic ions, the superexchange interaction between them is strongly antiferromagnetic (AF) because of the Pauli principle, whereas overlap between partly occupied and unoccupied orbitals gives weakly ferromagnetic (FM) interaction due to Hund’s exchange [3]. In the archetypical case of 180◦ bonds through a single ligand ion this translates into a complementary interdependence between spin order and orbital order [4]: ferro orbital (FO) order supports strong AF spin order, while alternating orbital (AO) order supports weak FM spin order. The canonical example of this behavior is KCuF3, where weak FM (positive) spin correlations in the ab planes and strong AF (negative) correlations along the c axis are accompanied by AO order in the ab planes and FO order along the c axis.