Field dependence of forced magnetostriction in cubic ferro-, ferri and antiferromagnets

The theoretical low-temperature field and temperature dependence of the forced magnetostriction of ferro-, ferri- and antiferromagnets has been explicitly derived in the spin-wave approximation. The magnetoelastic hamiltonian is cast in terms of operator equivalents for the crystal-field and exchange interactions, and the problem essentially reduces to finding the field dependence of thermal averages of the operator equivalents. In the case of ferromagnets, if the anisotropy is small compared with the applied field, the forced magnetostriction may be expanses as lambda = lambda 0 (T)+ lambda 1 (T)H 1 2/+ lambda 2 (T)H+ lambda 3 (T)H 2 + lambda 4 (T)H 3 2/+..., whereas if the anisotropy is large, lambda = lambda 0 (T)+ lambda 1 (T)H+... In ferri- and antiferromagnets the additivity of the sublattice magnetostrictions is confirmed. For ferrimagnets, in a broad class of approximations, the field dependence is of the same form as for ferromagnets. For antiferromagnets the low-temperature analysis shows that lambda = lambda 0 (T)+ lambda 1 (T)H 2 + lambda 2 (T)H 4 + lambda 3 (T)H 6 +..., similar to the Callens' high-temperature result.