ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 43

Fig. 1.16. The crystal-field split-
ting of the nine | 4 M J > states on
the hexagonal sites in dhcp Pr. The
wavefunctions are written in terms
of a basis |M J > corresponding to
quantization along the c -direction.
to account for a variety of experimental phenomena (Houmann et al.
1979).
If the lattice is strained, the crystal fields, and indeed all the other
magnetic interactions which we shall discuss, are modified. In conse-
quence, there is a magnetoelastic coupling between the moments and
the strain, which can have profound consequences for rare earth mag-
netism. Magnetoelastic effects are manifested in both single-ion and
two-ion terms in the Hamiltonian, though we shall mostly be concerned
with the former. The elastic energy is quadratic in the strain, measured
relative to the equilibrium configuration in the absence of magnetic in-
teractions. The magnetoelastic energy is linear in the strain and the
competition between the two effects may lead to some equilibrium strain
or magnetostriction . Because of their moderate elastic constants and the
large orbital component in their moments, the lanthanide metals display
the largest known magnetostrictions.
Following Callen and Callen (1965), it is convenient to develop the
theory in terms of the irreducible strains for hexagonal point-symmetry,