Biomedical Engineering Reference
In-Depth Information
the magnetic anisotropy energy barrier blocks any change in the magnetization
direction. As the temperature increases, some of the nanoparticles are able to
overcome their energy barrier, on the basis of their thermal activation energy,
k
B
T
.
Consequently, the magnetization direction of each thermally activated nanopar-
ticle begins to fl ip randomly faster than the measuring time of the magnetometer
[19]. The overall magnetization of the nanoparticles then decreases with increasing
temperature.
M
TRM
is related to the distribution of anisotropy energy barriers:
∞
∫
MMf
=
(
Δ
EdE
)
(12.5)
TRM
nr
a
Δ
Ec
where
M
nr
is the nonrelaxing component of the magnetization and
E
c
is a
critical value of energy, below which all the particles are blocked [19, 39]. The
relationship in Equation 12.5 shows that the derivative of
M
TRM
with respect to
temperature provides an estimate of the anisotropy energy barrier distribution.
Values of
f
(
Δ
Δ
E
a
), obtained from the
M
TRM
, are shown in Figure 12.2c (the continu-
ous line).
12.2.4
Magnetic Metal Oxides
Metal oxides represent the most common, and probably the richest, class of mate-
rials in terms of chemical, structural, and physical properties. For this reason, they
are well known for their interesting optical, electrical, electrochemical, mechanical
and magnetic properties. Such diversity originates from the more complex crystal
and electronic structure of metal oxides compared to other classes of materials.
The combination of such a variety of properties with the peculiar effects of low-
dimensionality make the nanostructured magnetic metal oxides suitable for
several applications [40] .
Among magnetic metal oxides, the compounds with spinel structure (
Me M
II III
2
)
represent probably the most important class, because the rich crystal chemistry of
spinels offers excellent opportunities for fi ne-tuning the magnetic properties.
These have a face-centered cubic (fcc) structure in which the oxygen atoms are
cubic close-packed. The structure contains two interstitial sites, occupied by metal
cations, with tetrahedral, (A) - site, and octahedral, [B] - site, oxygen coordination,
resulting in a different local symmetry. When the (A)-sites are occupied by Me
II
cations and the [B]-sites by Me
III
cations, the structure is referred to as normal
spinel, (Me
II
) [Me
III
]. However, if the A sites are completely occupied by Me
III
and
the B-sites are randomly occupied by Me
II
and Me
III
, then the structure is referred
to as inverse spinel, (Me
III
) [Me
III
Me
II
]. In general, the cationic distribution in
octahedral and tetrahedral sites is quantifi ed by the “inversion degree” (
O
), which
is defi ned as the fraction of divalent ions in octahedral sites [41-43]. In order to
simplify the interpretation of some experimental results (Mössbauer spectra in
γ
