Chemistry Reference
In-Depth Information
angle between the magnetization vector and an easy direction of magnetization.
But, it is important to emphasize that the critical diameter which is typically
ranged from 5 to 200 nm, does not depend exclusively on the shape of the particle
but also on its magnetic nature: from literature, it is found about 6 and 60 nm for
Fe and Fe
3
O
4
particles, respectively [
25
].
It is now important to better understand the magnetic behaviour of an assembly
of single domain nanoparticles. The instability of the creation of domain wall was
confirmed by the pioneering experiments of geomagnetism performed by Thellier
[
26
]. Indeed, when studying the magnetization of rocks and pottery to be corre-
lated to their cooling history, he found that the magnetization induced by cooling a
sample in a magnetic field was unexpectedly decayed with time, that can be
considered as the first experimental feature of super paramagnetic relaxation.
Then, Louis Néel reported that the magnetization of very small particles may be
reversed due to their thermal agitation when the anisotropy energy becomes of the
same order of magnitude as the thermal energy, i.e. the initial theory of super-
paramagnetism [
27
-
29
].
Indeed, the theory of Néel consists in considering the precession around the
uniaxial anisotropy field of the magnetization characteristics of a small ferro-
magnetic nanoparticle, possessing a magnetic anisotropy energy given by Eq.
4.1
.
One observes two energy minima corresponding to two antiparallel easy direc-
tions, and separated by an energy barrier (height KV). In this theory, the atomic
moments are assumed to be strongly coupled such that their rotation occurs in
unison and the precession is perturbed by lattice vibrations. In addition, the
average time between magnetization reversals also called the superparamagnetic
relaxation time s, can be calculated using the Boltzmann statistics: for KV
k
B
T,
the
relaxation
time
follows
approximately
an
Arrhenius
law
expressed
as
s = s
0
exp (KV/k
B
T). Prefactor s
0
is of the order of 10
-13
- 10
-9
s while k
B
corresponds to the Boltzmann's constant.
The superparamagnetic relaxation time of a ferromagnetic particle was also
derived by Brown [
30
] from the Langevin equation while the magnetic dynamics
of an assembly of non-interacting magnetic nanoparticles has been described by a
Fokker-Planck differential equation. Numerous models were also developed
assuming that the magnetization reversal follows coherent rotation (unison),
buckling or curling modes [
31
]. It is clear that the improvement of the synthesis
routes giving rise to controlled assemblies of magnetic nanoparticles allows
suitable experimental data to be obtained: consequently, further theories have been
refined including the role of external magnetic field on the magnetization reversal
and the symmetry of the anisotropy of the nanoparticles. During the last 15 years,
additional approach by means of computer simulations was also devoted to the
magnetic structure and the magnetic dynamics of ferromagnetic nanoparticles
using Langevin dynamics as a function of size, time at different temperatures. But
the theoretical and computer modelling of the magnetic behaviour has not been
completely achieved in the case of weakly and strongly interacting nanoparticles.
From the experimental point of view, the timescale characteristic of the applied
technique has to be compared to the relaxation time to investigate the dynamics of
