The coupling between magnetic and cation ordering: A macroscopic approach
Harrison, Richard J.; Putnis, Andrew
European Journal of Mineralogy Volume 9 Number 6 (1997), p. 1115 - 1130
published: Dec 2, 1997
manuscript accepted: May 12, 1997
manuscript received: Mar 19, 1997
ArtNo. ESP147050906001, Price: 29.00 €
Abstract A macroscopic model of magnetic and cation ordering is derived, and applied to the minerals magnetite (Fe3O4), magnesioferrite (MgFe2O4), and the magnetite-spinel solid solution (Fe3O4)3MgAl2O4)1-x For pure Fe3O4 and MgFe2O4, the change in free energy due to the process of non-convergent cation ordering, relative to the fully disordered state, is given by a Landau potential of the form, where Q is the macroscopic cation order parameter, and h, a, Tc and c are constants. An analysis of the available cation distribution data suggests that the equilibrium ordering behaviour of Fe3O4 and MgFe2O4 is very similar, and yields absolute values for the Landau coefficients h = -1673 J/mole, a = 34.8 J/mole.K, Tc = 790 K, and c = 493393 J/mole. The free energy change due to magnetic ordering in these minerals (in an external magnetic field), relative to the paramagnetic state, is given by a Landau potential of the form. where Q is the macroscopic magnetic order parameter (linearly related to the net magnetization), and hm, am, bm and cm are constants for a given composition and magnetic field. The two ordering processes are shown to be strongly coupled. The lowest-order permitted coupling term is of the form λQQm2, where λ is the coupling constant. The observed behaviour of these minerals is shown to follow closely the predictions of the model. In cases where the kinetics of cation ordering are much slower than the rate of magnetic ordering, coupling leads to a linear renormalization of the Curie temperature as a function of the degree of order. This effect allows the magnitude of the coupling constant for MgFe2O4 to be determined as λ = 9690 J/mole. In cases where the rates of cation and magnetic ordering are similar, coupling leads to enhanced degrees of order at low temperatures. This significantly affects the magnitude and shape of the specific heat capacity anomaly associated with magnetic ordering, and the Cp anomaly in Fe3O4 is shown to be reproduced when coupling to the non-convergent cation ordering process is taken into account. The possible implications of coupling between magnetic and cation ordering in natural minerals are discussed.