Chemistry Reference
In-Depth Information
aggressive chemical treatments, the natural minerals which contain nano and
microsized particles or inclusions with different cationic species. Indeed, these
materials under investigation consist of out-of equilibrium granular structure with
a distribution of size and different chemical composition because the processes are
a priori non homogeneous. The modelling of corresponding Mössbauer spectra
would consequently give an approximate description of physical features resulting
from a mixture of static and dynamic phenomena.
4.3 From Magnetism to Nanomagnetism
The characteristics of magnetic materials result from the cooperative contribution
of magnetic domains characterized by their individual magnetization which
exhibits different orientations (see review and topics [
10
-
15
,
20
-
23
]). The splitting
into magnetic domains separated by domain walls originates from the magneto-
static energy acting as a driving force. Coercive field, saturation and remnant
magnetization are the three main characteristics obtained from the hysteresis loop
which allows thus to qualify the class of magnetic materials as soft, semi-hard or
hard magnets according its magnetic stiffness and to understand the mechanism of
magnetization reversal. Calculations earlier proposed by Frenkel and Doefman
[
24
] gave rise to establish typical dimensions for magnetic domains in ferro-
magnetic crystalline materials with a minimum magnetic domain size, roughly
estimated at about 100 nm. The main question arises when the size of the material,
typically nanoparticles, becomes similar or lower than the minimum magnetic
domain size. Indeed, there exists a critical size of magnetic particles below which
the magnetic wall formation becomes unstable: it can be first estimated from a
simple approach by comparing the energy of single domain and multidomain
particle at equilibrium and at zero K, i.e. the magnetostatic energy and the
interfacial wall energy. It can be expressed as
NVM
s
=
2
¼
cV
2
=
3
ð
4
:
2
Þ
where N represents the smallest demagnetizing field factor, V the volume of the
particle and c is the interfacial wall energy per surface unit. One can finally
establish the critical length as l
c
* c/M
2
, assuming the coefficient 2/N related to
the particle shape, equal to unity. By substituting the Bloch wall energy expression
c = 4HAK, one can also write l
c
* d
e
HQ where Q = K/M
2
and d
e
* HA/M
s
are the quality factor and the exchange length, respectively, while A, K and M
2
represent the exchange, magnetic effective anisotropy and dipolar energies. When
the size of the particle does not exceed l
c
, it behaves as a single domain magnet.
It is clear that the morphology of the nanoparticles strongly influences its
magnetic energy and consequently the critical size which has to be estimated from
more rigorous calculations. When considering spherical magnetic particles with
uniaxial anisotropy, the magnetic energy is given by E
a
= KVsin
2
h, where h is the
