Indeterminacy of the Analytic Method for Calculating Molecular Field Coefficients in Ferrimagnets

Abstract

It is demonstrated that instead of yielding unique values of α and β for yttrium iron garnet (YIG) and lithium ferrite, the analytic method of calculating molecular field coefficients in ferrimagnets yields only one of many possible (α, β) pairs from a linearly related set. The magnitudes of the internal magnetic fields, total magnetic moment, and the two sublattice magnetic moments, computed from any of the possible coefficients, remain relatively unchanged even though (α, β) and n are extremely sensitive to the input parameters and number of experimental data points. It is shown how this manifold of (α, β) pairs can exist, how the pairs can be linearly related, and how an analytic expression for this dependency can be derived, using low-temperature data. A procedure for testing whether the coefficients for other ferrimagnets can be uniquely determined is discussed. ``Best'' values of (α, β), obtained by minimizing a least-squares percentage error, not only fall along a straight line but are in good agreement with those usually generated by the analytic method. The use of the ``linearity'' test in the X-Y graph as a criterion for judging the appropriateness of the selected value of the Curie point is shown to be invalid.