For cubic materials with a positive and a negative value of K 1 , respectively,
Figure 8.7a and b show polar plots of the energy of anisotropy as a function of
the orientation. In these plots, the energy of anisotropy is plotted radially versus the
orientation. For positive values of K 1 , there is a clear minimum in the directions
perpendicular to the face planes of the elementary cubes, whereas the maxima are in
the directions of the diagonal of the faces of the cube. In case of negative values of K 1
the easy direction is rotated for 45
.
In reality, although Eq. (8.3) describes a quite complex three-dimensional body,
the basic phenomenon is clarified in Figure 8.7a and b. In the case of magnetite,
Figure 8.7 Constant of magnetic anisotropy K 1
for different directions in the (001) plane of a
cubic material. (a) K 1 > 0. The hard directions
are along the diagonals of the cube; the soft
directions are along the edges. (b) K 1 < 0. The
hard directions are along the edges of the cube;
the soft directions are along the diagonals.
8.2 Superparamagnetic Materials j173
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