Biomedical Engineering Reference
In-Depth Information
(a)
(b)
Mr
Ms
Hc
Dsp
Dc
Dsd
Particle Diameter
(D)
Magnetic Field
Magnetic Field
Figure 12.1
(a) Important parameters in a magnetic
hysteresis loop: saturation magnetization (
M
s
), remanent
magnetization (
M
r
) and coercive fi eld (
H
c
). Inset: Evolution of
the magnetic domain structure along the fi rst magnetization
curve; (b) Schematic illustration of the dependence of
H
c
on
particle size.
cally in Figure 12.1b. Below a certain critical particle diameter (
D
sd
), a magnetic
multidomain structure is not energetically favored and particles with dimension
below this size will therefore consist of a single magnetic domain. Typical
D
sd
values for magnetic iron oxides are 166 nm for
- Fe
2
O
3
and 128 nm for Fe
3
O
4
[2] .
Generally, the rotation of the spins (i.e., the reversal process) occurs at much
higher fi eld by incoherent rotation of the spins, and this leads to an increase of
coercivity with respect to a multidomain structure. For smaller particles, below a
given size (
D
c
) depending on the material, the rotation is coherent and this induces
a decrease in coercivity.
γ
12.2.2
Magnetic Anisotropy Energy
During the magnetization process, the work that is required to bring a ferromag-
netic body from the demagnetized to the saturated magnetic state is stored in the
body as magnetization potential energy, the magnetic anisotropy energy (
E
A
). The
magnetic anisotropy is extremely relevant in the physics of magnetic materials
because it is related, on one hand, to the intrinsic microscopic characteristics of
the material and, on the other hand, to its macroscopic characteristics [10]. In
a magnetically ordered solid, there are certain preferred orientations of the mag-
netization, called “easy axes”. These easy directions are given by the minima in
the magnetic anisotropy energy, which depend on the structure and chemical
