PRESENT STATUS OF FERROMAGNETIC THEORY 73 



common metals, and single grains (i.e., single crystals) have been 

 prepared which are so large that experiments may be performed and 

 data collected on just one such crystal. 



The structure of a single crystal of iron may be represented by a 

 cube with an atom at each corner and one in the center, the whole 

 crystal made up of such cubes packed together face to face. It is 

 found experimentally that in the direction of an edge of this cube 

 (called by the crystallographers a [100] direction) the magnetization 

 curve labeled 100 in Fig. 7 is obtained.^^ In the two other principal 

 directions, the direction of a face diagonal and that of a cube diagonal, 

 the other magnetization curves are obtained, as shown. The difference 

 in the initial parts of the magnetization curves is negligible, the effects 

 being large only above half saturation. 



The structure of nickel may be represented also by an assemblage of 

 cubes, but the atoms are arranged in a different manner, being at the 

 corners of the cubes and the centers of the cube faces (Fig. 7). The 

 magnetization curves for nickel corresponding to the same three 

 principal directions are shown also in Fig. 7, and it may be seen that 

 the curves are reversed in order from those of iron. In iron the [100] 

 direction is said to be the direction of easy magnetization and the [111] 

 the direction of most difficult magnetization, whereas the reverse is 

 true in nickel. It might be said that the electrostatic exchange forces 

 align the spins parallel to each other and that the crystal forces deter- 

 mine the particular crystal direction along which they shall be aligned. 

 The forces of exchange are so powerful that they are able to align the 

 spins of a group of atoms, a situation that in the absence of such 

 exchange forces could be accomplished at room temperature only by 

 an applied field of 10,000,000 oersteds. On the other hand, the crystal 

 forces are so feeble that it takes only 1,000 oersteds to redirect the spins 

 of an entire group of atoms from any direction to any other direction. 

 The ratio between these two equivalent fields is thus 10^ divided by 

 10^ or 10*. 



As a result of the forces of exchange and the magnetic crystal forces 

 in a single crystal of iron, for example, the situation is as represented in 

 Fig. 8. Even when the crystal is apparently unmagnetized, or de- 

 magnetized, there are small regions, called domains, that are mag- 

 netized to saturation in one of the six equivalent directions of the 

 crystal axes. Actually, the domains vary considerably in size and 

 shape, but are represented conveniently as squares. Each of the six 

 directions is equally stable and equally probable when no field is 

 applied. The initial effect of applying a magnetic field is to change the 

 direction of magnetization from one stable position to another, thus 



