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The magnetism of rare-earth intermetallics using computer algebra: application to PrAl2 and NdAl2

The magnetism of rare-earth intermetallic compounds is investigated with a model Hamiltonian containing crystal field and exchange terms. An algebraic analysis of the characteristic polynomial associated with the model is made and it is shown that, for Pr3+ (J=4) and Nd3+ (J=9/2), in the case of cubic symmetry, the ninth- and tenth-degree polynomials are decomposed into simple factors. From these factors, analytical expressions for the crystal field eigenvalues, the magnetic moments and the critical temperatures are derived. The results are applied to PrAl2 and NdAl2; exchange parameters and effective g factors are easily obtained from crystal field, Tc and low-temperature magnetic moments data.