Field dependence of the elastic constantsc11 andc33 of paramagnetic rare earth metals

An earlier theory for the magnetic field dependence of the elastic constantsc11 andc33 of paramagnets of hcp structure is extended in three different ways. First, the effect of the principal axial crystal-field term$$\tilde B_2^0 \tilde O_{20} (J_i )$$ on the energy eigenstates of each magnetic ion is taken into account. Secondly, a field-dependent part of$$\tilde B_2^0 $$ having its origin in the homogeneous strains is shown to yield a contribution toc11 andc33 similar in form to the other contributions. Finally, a contribution toc11 andc33 coming from the part of the magnetoelastic interaction linear in the strains evaluated in second order perturbation theory is calculated. This second order contribution is large and may predominate over the other contributions in certain cases. All three effects lead to “correction terms” to the earlier theory varying as (1/T). This temperature variation is too weak, however, to explain the apparent temperature dependence of the magnetoelastic coupling constants measured by Salama, Melcher and Donoho for terbium and by Kale, Donoho, Pinatti and Ferreira for dysprosium. The unexpectedly strong temperature dependence deduced from their measurements is discussed in the light of the present extensions to the theory, suspicion falling on the susceptibility functionsχz(T) andχ⊥(T) that enter the analysis of the data.