152 8 Magnetic Nanomaterials, Superparamagnetism
domains, coercivity or remanence are independent of the particle size, as changing
the direction of magnetization is eased by the movement of Bloch walls. Things
are different once the particles do not contain Bloch walls. In this case, remanence
and coercivity increase drastically. This is the range where magnetization curves
look like the one in Figure 8.5. This is the range of magnetic properties, which
are sought for magnetic data storage. Further reduction of the grain size leads to
an unexpected sudden reduction of the coercivity to zero. This phenomenon is
thus very special, as the particle size of this decrease depends on the time constant
of determination. The property observed in the range where coercivity and remanence are nil is called superparamegnetism.
8.2
Fundamentals of Superparamagnetism
Superparamagnetism is a phenomenon based on thermal instability. Assuming a
spherical magnetic particle, fixed against rotation, situated in an external magnetic
field, allows superparamagnetism to be described. Furthermore, it is assumed that
the magnetic axis of this particle is exactly in the direction of the external field. If
the direction of the magnetic field is changed, the direction of the magnetization
of the specimen will also change. However, one has to overcome the energy of
magnetic anisotropy. In the case of superparamagnetism, thermal energy helps to
change the direction of the magnetization. The energy of anisotropy is given by
Kv, where the quantity K stands for the constant of magnetic anisotropy and v for
the volume of the particle. This energy must be seen in relation to the thermal
energy kT, where k stands for the Boltzmann constant and T for the temperature.
If the condition
kT Kv
≥
(8.1)
is fulfilled, the thermal energy is larger than the energy of magnetic anisotropy.
In this case, the direction of magnetization fluctuates thermally. This has the
important consequence that the magnetization of the specimen may follow any
change of an external magnetic field without needing extra energy. The direction
of the magnetization may be changed without any losses! Certainly, superparamagnetism is possible only when the volume of the particles is very small. Superparamagnetism is found only in connection to very small particles, nanoparticles,
generally, with sizes below 10 nm. From Eq. (8.1) one may derive for the temperatures where superparamagnetism occurs
T
Kv
k
≥
.
(8.2a)
The lowest temperature, where superparamagnetism is observed, the “blocking
temperature” T B is given by
T
Kv
k
B =
.
(8.2b)
domains, coercivity or remanence are independent of the particle size, as changing
the direction of magnetization is eased by the movement of Bloch walls. Things
are different once the particles do not contain Bloch walls. In this case, remanence
and coercivity increase drastically. This is the range where magnetization curves
look like the one in Figure 8.5. This is the range of magnetic properties, which
are sought for magnetic data storage. Further reduction of the grain size leads to
an unexpected sudden reduction of the coercivity to zero. This phenomenon is
thus very special, as the particle size of this decrease depends on the time constant
of determination. The property observed in the range where coercivity and remanence are nil is called superparamegnetism.
8.2
Fundamentals of Superparamagnetism
Superparamagnetism is a phenomenon based on thermal instability. Assuming a
spherical magnetic particle, fixed against rotation, situated in an external magnetic
field, allows superparamagnetism to be described. Furthermore, it is assumed that
the magnetic axis of this particle is exactly in the direction of the external field. If
the direction of the magnetic field is changed, the direction of the magnetization
of the specimen will also change. However, one has to overcome the energy of
magnetic anisotropy. In the case of superparamagnetism, thermal energy helps to
change the direction of the magnetization. The energy of anisotropy is given by
Kv, where the quantity K stands for the constant of magnetic anisotropy and v for
the volume of the particle. This energy must be seen in relation to the thermal
energy kT, where k stands for the Boltzmann constant and T for the temperature.
If the condition
kT Kv
≥
(8.1)
is fulfilled, the thermal energy is larger than the energy of magnetic anisotropy.
In this case, the direction of magnetization fluctuates thermally. This has the
important consequence that the magnetization of the specimen may follow any
change of an external magnetic field without needing extra energy. The direction
of the magnetization may be changed without any losses! Certainly, superparamagnetism is possible only when the volume of the particles is very small. Superparamagnetism is found only in connection to very small particles, nanoparticles,
generally, with sizes below 10 nm. From Eq. (8.1) one may derive for the temperatures where superparamagnetism occurs
T
Kv
k
≥
.
(8.2a)
The lowest temperature, where superparamagnetism is observed, the “blocking
temperature” T B is given by
T
Kv
k
B =
.
(8.2b)