Theoretical temperature and grain‐size dependence of domain state in X = 0.6 titanomagnetite

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Abstract
Domain state calculations have been made for x = 0.6 titanomagnetite (TM60) as a function of grain size (a), temperature (T), stress (σ), and exchange constant (A), based on the equilibrium domain models of Amar and Kittel. Grains were assumed to be rectangular parallelepipeds, containing a simple array of uniformly spaced domains separated by planar, 180° Bloch walls, in zero magnetic field. To investigate the effects of residual stress upon domain number N, the domain wall energy was given in terms of either magnetocrystalline or uniaxial stress anisotropy. The effects of temperature upon N were modeled through the thermal variation of the material constants of TM60 which described magnetostatic (saturation magnetization) and domain wall (magnetocrystalline, magnetostriction, and exchange) energies. Calculations confirmed that both the Amar and Kittel models yielded very similar results at room temperature, regardless of whether stress or magnetocrystalline anisotropy was dominant. Rapid divergence between the two models occurred only close to the Curie temperature. Thus, significant discrepancies which have been noted between the predicted number of domains and the observed number of domains are not due to a lack of refinement in previous models, but must reflect uncertainties of a more fundamental nature. Systematic failure of particles to achieve absolute energy minimum states may not be sufficient by itself to explain this discrepancy. Higher levels of residual stress or lower values of the exchange constant, or both, may be necessary in order to reconcile theory with observation. The thermal models predicted that N will either increase or decrease, with heating, according to whether the wall energy falls more or less rapidly than the magnetostatic energy with temperature. Furthermore, the thermal dependence of N should be accounted for in models of thermoremanent magnetization. A simple model for calculating domain blocking temperatures (Tdb) was developed and predicted that (1) particles governed by magnetocrystalline anisotropy had Tdb values which were truncated well below the Curie temperature, while those particles governed by stress anisotropy had much higher Tdb values and (2) in all cases, very large multidomain grains had distributed Tdb values, while particles in the two‐ and three‐domain range, had higher and more discrete Tdb values. Domain calculations also confirmed that TM60 particles should exhibit less thermal sensitivity in their domain structure when controlled by stress anisotropy than when controlled by magnetocrystalline anisotropy. This may help to explain recent domain observations on natural TM60, which suggested that few domain state changes occurred with heating. The model results also predicted that the exchange constant in TM60 should vary with temperature approximately as Ms1−3.