Bilinear exchange

The biquadratic exchange applies side by side with the bilinear exchange, hence... 

Fig. 10.13. Temperature variation of the magnetic susceptibility (a) and the effective magnetic moment (b) for the SA = SB = 5/2 dimen solid—bilinear exchange with J/hc = —100 K long dashed—biquadratic exchange with additional j = — 1 K medium dashed—biquadratic exchange with additional j = +1 K.

The second-order van Vleck coefficients are omitted in the first approximation. The corresponding temperature behaviour is plotted in Fig. 10.16 it can be seen that the ground state alters, depending on the competition of the antiferromagnetic nature of the isotropic (bilinear) exchange and the ferromagnetic nature of the double exchange. 

Such a transformation may have some advantages. The isotropic (bilinear) exchange matrix in the molecular-state basis adopts a block-diagonal form only the matrix elements corresponding to the same spin are non-zero... 

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