Superexchange Anisotropic

Moriya (451) has extended the Anderson formalism for superexchange to include spin-orbit coupling in the perturbation Hamiltonian that appears in the transfer integral bij of equation 100. To first order, this leads to a second-order perturbation in the energy of the form 

D L two-fold axis if the two-fold rotation axis is perpendicular to AB at C. 

Ordering of Two Valence Stales Among Ions of the Same Atom on the Same Sublattice 

Such ordering optimizes the Mudclung energy. The classic illustration of this effect is found in the spinel Fe3+[Fc2+Fc3+]04. Ordering of the B-site Fe2+ and Fe3+ ions into alternate (001) B-site layers below 119°K distorts the crystal to orthorhombic symmetry (248,637,639). 

Although Fe304 is cited as the classical example of this effect, it should be noted that the transition temperature is about four times smaller than is predicted from electrostatic considerations. Also the room-temperature Hall mobilities of the charge carriers are 0.5 cm2/V-sec (719), which might be thought to represent narrow-band conductivity. (In Fe304 there arc 3.5 t2g electrons per B-site cation, so that if R Rc, and upper H-site t2g band, which is split from a lower t2g band by intraatomic exchange via the localized eg electrons, would be one-sixth filled.) However, intermediate mobil- 

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Moriya, T. 1960. Anisotropic superexchange interaction and weak ferromagnetism. Physical Review 120 91-98. 

So far, only isotropic or symmetric exchange coupling has been discussed. Moriya proposed that anisotropic superexchange results when the effects of spin-orbit coupling... 

Moriya derives the following anisotropic superexchange interaction by extending the Anderson theory to include the spin-orbit coupling,... 

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