32 CHAPTER 4. THE MAGNETICALLY ORDERED STATEfield dependence of the magnetization behaves as shown by curve (a) in Fig. 4.3.3. The
slope of the first part of this curve is given by and can be used to obtain
an experimental value of the intersublattice-coupling constant according to Eq. 4.3.27.
In the discussion given above, we have assumed that the mutually antiparallel sublattice
moments are free to orient themselves along any direction in the crystal. In other words,
they can align themselves perpendicular to any direction in which the field is applied.
In most cases, however, the mutually antiparallel sublattice moments adopt a specific
crystallographic direction in zero applied field. For this so-called easy direction, the mag
netocrystalline anisotropy energy K (which will be discussed in more detail in Chapter 11)
adopts its lowest value, K = 0. The field dependence of the magnetization will then show
a behavior represented by curve (a) in Fig. 4.3.3 only if H is applied perpendicular to this
easy direction.
Quite a different behavior will be observed when H is applied along the common easy
direction of the two sublattice moments (indicated by D in Fig. 4.3.3). In this direction,
the magnetocrystalline energy has its lowest value (K = 0), and the free energy is given
by By contrast, if the sublattice moments would adopt a direction
perpendicular to the field direction and hence perpendicular to the easy direction (i.e., the
so-called hard direction), the free energy would be given by For
comparatively low applied fields, one has and both sublattice moments will
retain the easy moment direction. However, may become eventually the lowest energy
state because Both sublattice moments will therefore adopt a direction (almost)
parallel to the applied field. The critical field at which this happens is given by the
equation