8.1 Magnetic Materials 149
two sublattices cancels out. This is different in the case of ferrimagnetic compounds, where the magnetic moment of these two sublattices is different.
All ferrimagnetic oxides contain iron. They consist either of iron ions with different valency or besides the iron ions a second metal oxide. Typical examples are
Fe O Fe O Fe O
3 4
2
2
3
3
=
⋅
+
+
for an iron compound or MgFe 2 O 4 = MgO⋅Fe 2 O 3 as ternary
iron compound. A special case in this context is maghemite, γFe 2 O 3 . This compound is ferrimagnetic, because the second sublattice is partly occupied by vacancies. Therefore, the exact formula would be Fe O
Fe
O
8
3
12
40 3
3
8 3 20
+
+
(
)⋅(
)
, where
stands for vacancies replacing the second type of ions.
The temperature range where ferromagnetism and ferrimagnetism exist is
limited. The temperature where ferromagnetic or ferromagnetic materials transform into paramagnetic material is called the Curie temperature. In the case of
antiferromagnetic materials this temperature is the Néel temperature. Above
these critical temperatures, the thermal energy destroys the magnetic coupling
of the spins.
Looking at a ferromagnetic (which stands here and also later for ferrimagnetic)
single crystal, for energetic reasons, one observes a subdivision into magnetic
domains of different magnetic orientation. Depending on the material, the size
of the domains is in the range of a few hundred nanometers up to a tenth of a
millimeter. Inbetween the magnetic domains, one finds a quasicontinuous transition between the two orientation. The transition range, called a Bloch wall, usually
has a thickness of a hundred or more atoms. This situation, where a Bloch wall
connects two magnetic domains with opposite direction of magnetization is
depicted in Figure 8.3. Besides this 180 ° Bloch wall, as depicted in Figure 8.3, 90 °
walls are also possible. (To simplify the figure, in the graph the Bloch wall consists
of only three lattice planes, which is far from reality.)
Putting a ferromagnetic material into an external magnetic field, one measures
the magnetization curve. An example of such a magnetization curve, labeled with
Figure 8.3 Two magnetic domains of a ferromagnet connected with a Bloch wall. The
orientation difference of the domains is 180 °. In this simplified illustration, the Bloch wall
consists of three lattice planes.
Domain 1
Domain 2
Bloch wall
two sublattices cancels out. This is different in the case of ferrimagnetic compounds, where the magnetic moment of these two sublattices is different.
All ferrimagnetic oxides contain iron. They consist either of iron ions with different valency or besides the iron ions a second metal oxide. Typical examples are
Fe O Fe O Fe O
3 4
2
2
3
3
=
⋅
+
+
for an iron compound or MgFe 2 O 4 = MgO⋅Fe 2 O 3 as ternary
iron compound. A special case in this context is maghemite, γFe 2 O 3 . This compound is ferrimagnetic, because the second sublattice is partly occupied by vacancies. Therefore, the exact formula would be Fe O
Fe
O
8
3
12
40 3
3
8 3 20
+
+
(
)⋅(
)
, where
stands for vacancies replacing the second type of ions.
The temperature range where ferromagnetism and ferrimagnetism exist is
limited. The temperature where ferromagnetic or ferromagnetic materials transform into paramagnetic material is called the Curie temperature. In the case of
antiferromagnetic materials this temperature is the Néel temperature. Above
these critical temperatures, the thermal energy destroys the magnetic coupling
of the spins.
Looking at a ferromagnetic (which stands here and also later for ferrimagnetic)
single crystal, for energetic reasons, one observes a subdivision into magnetic
domains of different magnetic orientation. Depending on the material, the size
of the domains is in the range of a few hundred nanometers up to a tenth of a
millimeter. Inbetween the magnetic domains, one finds a quasicontinuous transition between the two orientation. The transition range, called a Bloch wall, usually
has a thickness of a hundred or more atoms. This situation, where a Bloch wall
connects two magnetic domains with opposite direction of magnetization is
depicted in Figure 8.3. Besides this 180 ° Bloch wall, as depicted in Figure 8.3, 90 °
walls are also possible. (To simplify the figure, in the graph the Bloch wall consists
of only three lattice planes, which is far from reality.)
Putting a ferromagnetic material into an external magnetic field, one measures
the magnetization curve. An example of such a magnetization curve, labeled with
Figure 8.3 Two magnetic domains of a ferromagnet connected with a Bloch wall. The
orientation difference of the domains is 180 °. In this simplified illustration, the Bloch wall
consists of three lattice planes.
Domain 1
Domain 2
Bloch wall