superferromagnetic material is shown in Figure 8.6b, where the one important
essential for superferromagnetism is clearly apparent – that all the particles must be
of very similar size.
8.2
Superparamagnetic Materials
As mentioned above, superparamagnetic materials excel in zero remanence and
coercivity; moreover, superparamagnetism is limited to small nanoparticles.
In the case of a single isolated magnetic nanoparticle, the condition leading to
superparamagnetism, a typical thermal instability, is:
kT ! Kv
ð8:1Þ
where K is the constant of magnetic anisotropy (as shown in Table 8.1), v is the
volume of the particle, Kv is the energy of magnetic anisotropy and kT is the thermal
superparamagnetic
superferromagnetic
(a)
(b)
Figure 8.6 Superparamagnetic materials. (a)
Within a superparamagnetic particle, the
elementary magnetic dipoles are oriented in
parallel. While the magnetic interaction of the
particles is negligible, orientation of the
magnetic moment of the particles is random.
(b) Superferromagnetic material. Provided that
the superparamagnetic particles are of equal
size and their distance allows dipole–dipole
interaction (as in ferromagnetic materials),
magnetic coupling between the particles will
occur.
Table 8.1 Constant of magnetic anisotropy K 1 for different
ferrimagnetic materials (ferrites).
Ferrite
Constant of anisotropy (J m
À3 )
Fe 3 O 4
À11 Â 10
3
MnFe 2 O 4
À2.8 Â 10
3
CoFe 2 O 4
90 Â 10
3
NiFe 2 O 4
À6.2 Â 10
3
MgFe 2 O 4
À2.5 Â 10
3
8.2 Superparamagnetic Materials j171