Biquadratic spin exchange

The spin-spin interaction is not necessarily restricted to quadratic terms in the spin operators. Higher-order terms could be considered, among which the (isotropic) biquadratic exchange reads... 

The biquadratic exchange coupling constants adopt rather small values the experimental data show that exchange coupling constants obey j/J 0.05. The separation of the energy levels, however, alters significantly as the deviation from the Lande interval rule is dramatic for higher spin values [19]... 

Several kinds of exchange interactions, which couple the magnetic centres, are distinguished the (bilinear) isotropic, asymmetric, antisymmetric, biquadratic and double exchange. Various fine-structure Hamiltonian terms enter the spin-spin coupling tensor D these were derived from the relativistic Dirac and Breit equation. 

The different 5i and S2 operators are again replaced by the sum of the one-electron operators 5(1)+5(2) and 5(3) 4-5(4) and the effect of the nine operators on the seven different determinants can be evaluated. Using the results summarized in Table3.3, the effect of the biquadratic exchange operator on the spin functions listed in Eq. 3.69 is easily established ... 

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