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arXiv · 1407.0811

A Poor Man's Derivation of Quantum Compass-Heisenberg Interaction: Superexchange Interaction in J-J Coupling Scheme

Hiroyasu Matsuura·Masao Ogata
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Abstract

The exchange interaction between 5d electrons in t$_{2g}$ orbitals is derived in the J-J coupling scheme which is the appropriate basis in the case of strong spin-orbit interaction. From simple calculations, it is found that ferromagnetic Ising interaction (quantum compass model) occurs due to a selection rule of hybridization between $\Gamma_7$ and $\Gamma_8$ orbitals, while antiferromagnetic Heisenberg interaction appears from hybridization between $\Gamma_7$ orbitals. It is also found that the ferromagnetic Ising interaction becomes small as the spin-orbit interaction increases. Thus, the sign of exchange interaction changes from ferromagnetic Ising to antiferromagnetic Heisenberg interaction as the spin-orbit interaction increases.

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Hiroyasu Matsuura, Masao Ogata. 2014-07-03. A Poor Man's Derivation of Quantum Compass-Heisenberg Interaction: Superexchange Interaction in J-J Coupling Scheme. https://doi.org/10.7566/jpsj.83.093701

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