Magnetoelastic coupling associated with vacancy ordering and ferrimagnetism in natural pyrrhotite, Fe₇S₈

Magnetoelastic coupling associated with the hexagonal-monoclinic transition in a natural sample of the mineral pyrrhotite, Fe₇S₈, has been analysed in terms of separate coupling of spontaneous strains with two discrete order parameters,q_vfor Fe/vacancy ordering andq_mfor magnetic ordering. Coupling of the two order parameters separately with strain gives rise to two terms for coupling between them,λqm2qv2andλqm2qv8, and a pattern of evolution in whichq_vvaries continuously andq_mdiscontinuously through a single transition point. The transition is ferrimagnetic and ferroelastic but the relatively slow relaxation rate for Fe/vacancy ordering, in comparison with magnetic ordering, results in elastic and anelastic properties which are quite different from those observed in other ferroic or multiferroic materials with two instabilities. Instead of classical elastic softening, there is stiffening of the elastic constants which scales withqm2andqv2. Instead of the normal pattern of acoustic loss associated with the mobility and subsequent freezing for ferroelastic twin walls, the loss is consistently low throughout the temperature range 300 K-875 K.