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The biquadratic term was used in this manner first in [31, 32]; it has appeared in other contexts, however. For systems with S > 1/2, the term does not necessarily represent fluctuation effects if it appears in the Landau or mean-field energies, as in [40, 41]. It has appeared, even in S = 1/2 systems, in the microscopic analysis of effects due to quantum fluctuations, thermal fluctuations, dilution, and magnetoelastic coupling [42-49], as noted also in [12]: there exists however no microscopic derivation of the term as representing fluctuation effects for an arbitrary spin configuration. In [42-49], the analysis was limited to the LSW level, and the ground state was either known beforehand or selected from known candidates; an unpublished manuscript [46] used the term phenomenologically to estimate wall energies above a known ground state, the coefficient being fitted to numerical LSW results. In contrast, in [31, 32] the term includes fluctuation effects beyond the LSW level, explicitly the reconstruction of the IC ground state. As discussed in the appendix, reference [50] on the stacked TAFM did not consider the term explicitly; it noted however that some effects of fluctuations (explicitly the collinear phase) can be mimicked by allowing some Landau coefficients to depart from the mean-field values, thereby intentionally breaking the classical TAFM degeneracy.
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