Determination of Magnetic Ordering in Heisenberg Magnets from High-Temperature Expansions

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Abstract
We investigate the possibility of determining the type of magnetic ordering to be expected for a Heisenberg model by using high‐temperature expansion methods. (The latter have been addressed in the past only to questions about the model given the type of ordering.) We take as a criterion for the critical temperature Tc that the static correlation function 〈Si·Sj〉 becomes long range as the critical temperature is approached from above. This criterion is applied by looking for the ``generalized Fourier amplitude'' λα of 〈Si·Sj〉 that will diverge at a finite temperature. This ``generalized Fourier amplitude'' is essentially like the usual Fourier amplitude—for Bravais lattices it is precisely the latter, and it is suitably generalized for lattices with more than one spin per unit cell. In the special case where ferromagnetism is expected, the divergent λα is essentially the susceptibility. In general, the divergent λα is to be estimated by extrapolation from the first terms of its expansion in powers of T−1, in the spirit of the usual high‐temperature expansion methods. This approach has been applied to normal spinels with nearest neighbor AB and BB interactions. Our preliminary results suggest that the approach will give reasonably definitive answers to the question of the type of ordering to be expected. Furthermore, they suggest that correlation corrections to the predictions of molecular‐field theory can have a very large effect on the qualitative properties of the model, i.e., the type of ordering. The possible relevance of these results to the problems of CoCr2O4 and MnCr2O4 is mentioned.