Page 285 - Electrical Properties of Materials

Domains and the hysteresis curve 267

case until only three easy directions are left, namely AB, AD, and AE, that
is those with components in the AG direction. This may be achieved with
very little magnetic field, but from then on (K in Fig. 11.5) the going gets
hard. In order to increase the magnetization further, the magnetic moments
need to change direction, which can only happen if the internal anisotropy
forces are successfully overcome. This requires more effort, hence the slope
of the magnetization curve changes, and saturation will only be achieved at
greater magnetic fields.
Is this explanation still correct for polycrystalline materials? Well, a poly-
crystalline material contains lots of single crystal grains, and the above
argument applies to each of the single crystals; thus the magnetization curve of
a polycrystalline material should look quite similar to that of a single-crystal
material in a difficult direction. As you know from secondary school, this is not
the case. Figure 11.5 does not tell the whole story. The magnetization curve of a
typical ferromagnetic material exhibits hysteresis, as shown in Fig. 11.7. Start-
ing with a completely demagnetized material, we move up the curve along 2,
3, 4, 5 as the magnetic field is increased. Reducing then the magnetic field, we
get back to point 6, which is identical with point 4, but further decrease takes
place along a different curve. At 7 there is no applied magnetic field, but B is
finite. Its value, B = B r , is the so-called remanent flux density. Reducing fur-
ther, the magnetic field B takes the values along 8, 9, 10. Returning from 10,
we find that 11 is identical with 9 and then proceed further along 12 and 13 to
reach finally 4.
The loop 4, 7, 8, 9, 12, 13, 4 is referred to as the hysteresis loop, already
discussed for ferroelectric materials. It clearly indicates that the magnetization
of iron is an irreversible phenomenon. Note that the value of H at 13
The paths 4, 5 and 9, 10 suggest that rotation from easy into difficult direc- is called the coercivity, denoted
tions is reversible, thus the causes of irreversibility should be sought in domain by H c . It represents the magnetic
movement. Because of the presence of all sorts of defects in a real material, the field needed for the flux density to
domain walls move in little jerks, causing the magnetization to increase in a vanish.
discontinuous manner (region 2, 3 magnified in Fig. 11.7). The walls get stuck
once in a while and then suddenly surge forward, setting up in the process some
eddy currents and sound waves, which consume energy. If energy is consumed,
the process cannot be reversible, and that is the reason for the existence of the
hysteresis loop.

B 5
6
7 4
3
B
r
2 H
8 c
1 13 H

12 Fig. 11.7
9
The magnetization curve of a typical
10
11
ferromagnetic material.