Spin-Wave Theory of MnF2 in the Random Phase Approximation

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Abstract
In order to extend the validity of ferromagnetic spin‐wave theory to higher temperatures, Englert used the random phase approximation (RPA), in which the spin‐wave interactions are represented by a model in which the number of spin‐wave excitations are related self‐consistently to the magnetization through a sum rule. We have applied RPA to the two‐sublattice antiferromagnet of arbitrary spin and range of exchange interaction, and have found a formal correspondence to the Green's function theory of ferromagnetism of Tahir‐Kheli and ter Haar. Using this approximation, the sublattice magnetization is computed self‐consistently for parameters appropriate to MnF2 and compared over a wide temperature range to the sublattice magnetization predicted by the NMR experiments of several investigators. We find that the theory represents the significant features of the sublattice magnetization at low temperatures, and exhibits features peculiar to the temperature dependence of the anisotropy in that the magnetization is double valued in the region of the Néel point.