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 …