MAGNETIZATION IN CRYSTALS — DILLON 



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(a) 



(c) 



Figure 7. — The magnetization in the magnetic garnets prefers to lie along the body diag- 

 onals of the cube which represents the symmetry of the lattice. This figure shows how 

 these body diagonals are disposed relative to any one of the principal planes of the sym- 

 metry cube. 



partial list of the symmetry elements of the cube and of the garnet 

 structure. Figure 6 indicates the fourfold, threefold, and twofold 

 axes of a cube. 



On examination of the magnetic properties of a single crystal, it is 

 invariably found that the magnetization prefers to lie along certain 

 crystal directions. In iron, a cubic ciystal, for instance, these pre- 

 ferred directions are parallel to the edges of the cube. In yttrium iron 

 garnet, the preferred directions are the body diagonals of the cube; 

 that is, the threefold axes. There are four body diagonals, and the 

 magnetization can point either way along each of these; thus there 

 are eight so-called easy directions. To pull the magnetization out of 

 the easy directions requires the expenditure of work. With any crys- 

 tallographic direction we can associate an energy, thus defining an 

 energy surface. This is called the magnetocrystalline anisotropy 

 energy. If any part of the volume of a crystal has its magnetization 

 along some other than easy direction, there is a contribution to the 

 anisotropy energy and thus to the total magnetic energy. Figure 7 

 shows the three so-called principal planes of a cubic crystal with the 

 body diagonals drawn in. In (a) the plane perpendicular to the four- 

 fold axis contains no easy directions; they lie some 35° above and be- 

 low it. In (b) we see that there are two easy axes in the plane per- 

 pendicular to the twofold axis. They make an angle of about 70° 

 with each other. Finally, the plane perpendicular to the threefold 

 axis has one easy axis normal to it, and three others about 20° out of 

 the plane. 



Plate 5 shows a crystal fragment of gadolinium iron garnet in which 

 the magnetization in various domains lies along almost all of the pos- 

 sible body diagonals. The plane of the crystal is perpendicular to the 

 threefold axis, as in figure 7(c) . The line drawing shows the orienta- 

 tion of some of the domains. 



