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A method based on the Gaussian approximation is presented for calculating the magnetic neutron scattering from short-range-ordered magnetic systems. Scattering profiles are calculated for three highly frustrated systems: the rhombohedral-, kagome$aa----, and pyrochlore-lattice antiferromagnets. The results are compared with those obtained from conventional Monte Carlo techniques and with recent experimental results for ${FeF}₃$ and ${Tb}₂Mo₂{O}₇$. For the rhombohedral lattice, the calculations predict two-dimensional peaks even in the presence of strong interplanar interactions and provide an explanation for the lack of observed wide-angle magnetic neutron scattering in LiNiO₂. Scattering consistent with short-range order is predicted for the pyrochlore- and kagom\'e-lattice antiferromagnets down to very low temperatures. The Monte Carlo method is most successful for treating truly short-range-ordered systems and low-dimensional systems. The Gaussian approximation method gave similar results for these systems and was also found to be useful for three-dimensional systems with quasi-low-dimensional order where the Monte Carlo method was impractical.
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J. N. Reimers (1992) studied this question.
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