Chemistry Reference
In-Depth Information
where
K
is a mean or average anisotropy constant. The Bloch wall energy
per unit area,
E
Bloch
=
E
ex
+
E
an
, is then minimised when
E
ex
KNa
2
a
6
N
∂
E
Bloch
∂
∂
π
=
+
=
0
(7.39)
∂
N
N
that is, when
a
E
ex
6
K
=
=
π
w
Na
(7.40)
As the exchange energy,
E
ex
, is generally several orders ofmagnitude larger
than the anisotropy energy,
K
, we conclude that each Bloch wall will be
many layers thick: substituting appropriate values for Fe, one finds that
N
1000Å.
The total Blochwall energy per unit area can be estimated by substituting
the value of
w
≈
350, with the wall thickness then
∼
=
Na
from eq. (7.40) into eq. (7.39), giving
a
2
E
ex
K
3
E
Bloch
=
π
(7.41)
For a spherical particle of radius
R
, the energy to create a single Bloch wall
then scales as
R
2
, whereas the energy stored in the external field scales as
R
3
. Below a critical radius
R
c
, the energy to create a Bloch wall therefore
exceeds that stored in the external magnetic field, so that single domain
particles become preferred.
7.9 High-performance permanent magnets
The unique attraction of permanent magnets is that (barring the even-
tual development of a room temperature superconductor) they provide
magnetic flux with no continuing expenditure of energy. Indeed their fer-
romagnetism has its origin in resistanceless electric currents circulating on
the atomic scale. Furthermore, their ability to generate complex field pat-
terns with intense spatial variations is unrivalled by any electromagnetic
device. The surface current needed to generate a flux pattern similar to
that of a long cylindrical magnet with
1 T is 796 kA/m. Solenoids,
whether resisitive or superconducting, able to produce such fields would
have to be several centimetres in diameter to accommodate the necessary
ampere-turns.
Intrinsic magnetic properties set the limits on the potential development
of any particular material. These properties include the magnitudes of the
saturation magnetisation,
M
s
, and of the magnetocrystalline anisotropy
energy,
U
c
, and the existence or otherwise of a suitable easydirection. These
µ
0
M
=
