Fig. 3: Examples of different types of domain states in magnetite and their behaviour, as acquired through our micromagnetic models.
On the left side, we have compiled the magnetisation (green diamonds) and the corresponding magnetic energy (black dots) for each of the 50 LEM models of a specific grain. These values are normalised by the respective maximum values (of either magnetisation/energy) among the fifty models. The stereographic projections within the plots display the direction of the magnetisation for all models by converting the magnetisation components in the x (Mx), y (My), and z (Mz) directions to declination \(({{{\rm{DEC}}}}=\arctan ({M}_{y}/{M}_{x}))\) and inclination \(({{{\rm{INC}}}}=\arctan ({M}_{z}/\sqrt{{M}_{x}^{2}+{M}_{y}^{2}}))\). The inclination is coloured according to its polarity (red for positive and blue for negative), and the triangles indicate the direction of the LEM state with the lowest energy (Min). On the right, the minimum free energy model of the corresponding grain is depicted, where the arrows indicate the direction of the magnetisation, and the vortex structures inside are the isosurface hued by the helicity. SD grains show (a, b) practically no difference between the models, whereas SV can exhibit a variety of possible domain states (c, d) with distinct magnetisation (and associated energies), especially when the morphology of the grain is highly irregular (e, f).
