Biomedical Engineering Reference
In-Depth Information
for the different possible crystal structures, and therefore depends on the particle
size and matrix material. Cobalt nanoparticles generated by high- pressure sput-
tering have been shown [124] to undergo a transition from hcp to fcc below about
300 Å. The bulk equilibrium phase at room temperature is hcp-Co, whereas fcc-Co
is a high-temperature phase that is stable above 695 K. Kitakami
et al
. [124] argued
that the hcp-Co to fcc-Co transition as a function of size is due to the lower surface
energy of the fcc-Co phase. In support of the size effect hypothesis, these authors
showed that annealing above the bulk phase transition temperature and slow
cooling does not convert the nanoparticles to hcp-Co. As the moment of the two
Co phases differs by only about 2%, the principal effect on the magnetic behavior
should be a much smaller magnetocrystalline anisotropy for the fcc-Co phase. This
would be an important consideration when using Co nanoparticles in a permanent
magnet material or recording media, as the anisotropy fi elds for fcc-Co and hcp-Co
are approximately 500 Oe and 10 kOe, respectively. Michels
et al.
reported mixed
phases of hcp-Co and fcc-Co nanocubes with an average cube-edge of approxi-
mately 50 nm [125], whereas others have shown that when the Co particle size is
<
20 nm, only fcc-Co phase were found [65, 82, 83, 126-128]. These results further
support the size-dependent crystalline structure effects.
16.4.2.2
Size-Dependent Magnetic Domain Structure and the Reversal
of Co Nanoparticles
It is known that the magnetization behavior of a magnetic material is highly size-
dependent. When a large magnetic particle, which contains mobile domain walls,
is subjected to a magnetic fi eld, its domain walls will move to minimize the free
energy of the system and the magnetization reversal proceeds via domain- wall
displacement. For domain motion, the switching fi eld
H
SW
is angle - dependent and
follows the following equation:
H
SW
=
H
0
/cos(
H
is the applied fi eld
angle respective to the direction of magnetization). When the size of the particle
decreases below a critical size
θ
H
) (where
θ
d
c
, the domain wall disappears and the particles
become single domain due to the fact that the energy cost to produce a domain
wall is greater than the corresponding reduction in the magnetostatic energy. The
critical size depends on the saturated magnetization, anisotropy energy and
exchange interaction between the individual spins, which can be estimated by
−
(
−
12
(
AK
M
)
36
A
M
d
a
⎡
⎢
⎤
⎥
u
c
d
=
18
(large
K
u
) and
d
=
ln
1
(small
K
u
) (
K
u
is the
c
c
2
2
μ
μ
0
S
0
S
anisotropy constant,
M
S
is saturated magnetization, and
A
is the exchange
coupling constant). For smaller anisotropy FCC-Co particles (
K
u
1 0
4
J m
− 3
),
the critical size of the single domain is 30 nm, while for the larger anisotropy
HCP-Co particles (
K
u
∼
7
×
1 0
5
J m
− 3
), the critical size is 65 nm. Therefore,
the magnetic nanoparticles normally investigated are single-domain in nature.
The magnetic reversal of such particles with a single domain had been described
by the Stoner-Wohlfarth (S-W) model in a very simple theory, namely the
uniform rotation model. When investigating experimentally the magnetic reversal
of magnetic nanoparticles, the angle dependence of magnetic reversal are often
used.
∼
4.5
×
