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. 2015 Mar 25;6:6677. doi: 10.1038/ncomms7677

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(a) Energy gain of FM compared with AFM state (see Methods) per 20-atom formula unit, ΔE, as a function of the moment on the d⁰ sites, m_d0. Inset: band gap Δ versus m_d0. The different points correspond to various perturbations of the superlattice, including varying the A- and R-cation species, the on-site Coulomb repulsion U and the volume of the cell. (b) Simplified spin exchange diagram between nearest neighbour d¹ sites (Ti₁ and Ti₃) via a d⁰-site (Ti₂). The curved arrows represent inter-site spin hopping through oxygen ions, and the dashed box represents intra-site spin-exchange via Hund’s rules, in the case of d_xz–d_yz orbital ordering due to AFD motions, or Pauli's exclusion principle, in the case of d_xy orbital ordering in the absence of AFD motions.