8.1 Magnetic Materials 151
only a minor influence on the magnetization curve, as long as the grains are large
enough to contain a few magnetic domains and Bloch walls. Therefore, one does
not expect any dependency on the grain size. On the other hand, changing the
direction of magnetization of one domain particles (see Figure 8.5) is, because of
the missing Bloch walls, difficult. These considerations are correct. They lead, in
connection with experimental results, to the diagram depicted in Figure 8.6. In this
graph, coercivity or remanence are plotted versus particle size.
Analyzing Figure 8.6 in detail, one realizes different ranges of particle sizes. As
explained above, as long as the particles are large enough to contain a few magnetic
Figure 8.5 Hypothetical magnetization curve of a single one-domain particle. The
magnetization remains constant until the external magnetic field is able to change the
direction of the magnetization without a Bloch wall.
-4
-2
0
2
4
magnetic field
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
magnetization
Figure 8.6 Dependency of the coercivity or remanence of the grain size. One realizes two
important ranges: Multi- and single-domain particles; the latter may be subdived into a range
with high coercivity and one with zero coercivity.
ParƟcles contain Bloch walls
MulƟdomain parƟcles
1
10
100
1000
10000
grain size [a.u.]
0
0.2
0.4
0.6
0.8
1
Range of superparamagneƟsm
Single-domain parƟcles
τ appl1
τ appl2
τ appl1 < τ appl2
kT Kv
<
coercivity or remanence [a.u.]