Chemistry Reference
In-Depth Information
χ
=
C
/(
T
−
T
c
)
. Below
T
c
the magnetisation
M
varies in mean field theory
1
/
2
(see problem 7.4). Experimentally it is found that
as
M
(
T
)
∼
(
T
c
−
T
)
χ
)
−
γ
and
M
)
β
, where
varies more typically near
T
c
as
(
T
−
T
c
(
T
)
as
(
T
c
−
T
γ
∼
0.33. The discrepancy again arises because mean field
theory fails to take sufficient account of the short range order in a ferro-
magnet, assuming that because the mean magnetic moment
1.33 and
β
∼
is zero,
there are effectively no correlations between neighbouring moments. In
practice, moments tend to be aligned locally near
T
c
, but the direction of
the local moment fluctuates strongly through the sample.
m
7.8 Ferromagnetic domains
Despite the existence of spontaneous magnetisation below the Curie tem-
perature, it is well known that ferromagnets (such as steel needles) can
apparently lose their magnetisation. This is due to the formation of
domains, whereby themagnetisationpoints indifferent directions indiffer-
ent parts of the sample. Application of an external magnetic field can cause
the domain walls to move, as illustrated in fig. 7.9, leading to a net mag-
netisation of the sample. This is how a steel needle becomes magnetised
when a bar magnet is passed along the needle.
Why are domains formed in a magnetic material? Because they reduce
the overall energy of the system. If a sample has only one domain, there
will be a large external magnetic field
B
associated with its macroscopic
magnetisation, with the energy stored per unit volume in the external field
given by
2
HB
B
2
=
/
µ
0
in free space. With many domains, the external
field
B
is significantly reduced, thereby reducing the overall energy.
Although the boundaries between domains are shown as sharp lines in
fig. 7.9, there is in fact a narrow transition region, known as a Bloch wall,
between neighbouring domains, across which the magnetisation direc-
tion changes smoothly, as illustrated earlier in fig. 7.8, when discussing
spin waves. Two competing effects determine the width,
w
, of the domain
2
(a)
(b)
(c)
Figure 7.9
(a) Schematic domain structure for a ferromagnet in zero applied field,
where the domain pattern is tending to minimise the magnetostatic energy.
Application of an external field
H
can lead first to reversible domain wall
motion (b) and then (c) to irreversible elimination of domains.
