418
M. Reissner
space. The system can jump between different spin configurations by overcoming the
barriers between the valleys. Due to the different heights of the separating barriers,
different relaxation times are present. This leads to dynamic behaviour. A hierarchical
distribution of time scales should be present, which could explain the experimentally observed relaxation behaviour and irreversibilities. All the theories based on the
Edwards-Anderson model assume a thermodynamic phase transition into a ground
state. In such case the transition temperature should be independent from experiment
always the same. This is in contradiction to many experiments and also to the fact
that above the ordering temperature the expected pure paramagnetism is not present,
but lots of magnetic correlations are verified to exist up to temperatures several times
higher than T f . In 1974 Tholence and Tournier [136] and later Wohlfarth [137] proposed that the spin glass transition is not a true thermodynamic phase transition, but
is very similar to blocking of single domain particles in rock materials. For this Néel
has developed the theory of superparamagnetism. A short range order couples the
spins into clusters. Because temperature counteracts the formation of such clusters,
the size of the clusters increases with decreasing temperature. At high temperatures
the clusters are free to rotate. They jump between easy axis directions, which are
separated by energy barriers caused by anisotropy effects. This can be described
in the Néel theory by τ 0 , an intrinsic relaxation time in the range of ∼ 10
−9 s and
E a = KV the anisotropy energy with K the anisotropy constant and V the particle
volume. For a particular measurement, which is characterized by a typical measuring
time τ m , clusters appear frozen, if their relaxation time τ is longer than τ m . With
decreasing temperature, volume of clusters increase and therefore the rotation frequencies decrease, and at a distinct temperature the clusters become blocked. In case
of a cluster size distribution, clusters of different size will block at different temperatures. Coming from high temperatures the largest cluster will be blocked first.
Within this picture the measured zero-field cooled and field-cooled curves (Fig. 8.37)
are well understood. At high temperatures all clusters are free to rotate. All τ values
are shorter than τ m and the measured magnetization is zero. In lowering the temperature the cluster gradually freeze in random directions. Thus at low temperature
the measured magnetization is still zero. In applying a small measuring field and
by increasing the temperature (ZFC curve) the magnetization increases, because—
starting with the smallest ones—more and more clusters are freed, due to the thermal
energy kT and rotate in direction of the applied field. The increase of magnetization
stops when the largest clusters are rotated in direction of the applied field. With
further increase of temperature the thermal energy destroys successively the alignment and magnetic signal decreases like in a paramagnet thus forming the observed
cusp. If temperature now decreases (FC curve), due to reduction of thermal energy,
clusters begin again to rotate in direction of applied field, starting with the smallest ones and ending with the largest ones. Magnetization increases until it reaches
maximum again. With further decrease of temperature the magnetization stays constant, because all clusters are now frozen in direction of the applied field. Therefore
the temperature where the cusp appears is called the freezing temperature T f . In
this model all the irreversibilities and time dependences obtained in experiment can
be explained. It also explains, why the value T f is different for different measuring
M. Reissner
space. The system can jump between different spin configurations by overcoming the
barriers between the valleys. Due to the different heights of the separating barriers,
different relaxation times are present. This leads to dynamic behaviour. A hierarchical
distribution of time scales should be present, which could explain the experimentally observed relaxation behaviour and irreversibilities. All the theories based on the
Edwards-Anderson model assume a thermodynamic phase transition into a ground
state. In such case the transition temperature should be independent from experiment
always the same. This is in contradiction to many experiments and also to the fact
that above the ordering temperature the expected pure paramagnetism is not present,
but lots of magnetic correlations are verified to exist up to temperatures several times
higher than T f . In 1974 Tholence and Tournier [136] and later Wohlfarth [137] proposed that the spin glass transition is not a true thermodynamic phase transition, but
is very similar to blocking of single domain particles in rock materials. For this Néel
has developed the theory of superparamagnetism. A short range order couples the
spins into clusters. Because temperature counteracts the formation of such clusters,
the size of the clusters increases with decreasing temperature. At high temperatures
the clusters are free to rotate. They jump between easy axis directions, which are
separated by energy barriers caused by anisotropy effects. This can be described
in the Néel theory by τ 0 , an intrinsic relaxation time in the range of ∼ 10
−9 s and
E a = KV the anisotropy energy with K the anisotropy constant and V the particle
volume. For a particular measurement, which is characterized by a typical measuring
time τ m , clusters appear frozen, if their relaxation time τ is longer than τ m . With
decreasing temperature, volume of clusters increase and therefore the rotation frequencies decrease, and at a distinct temperature the clusters become blocked. In case
of a cluster size distribution, clusters of different size will block at different temperatures. Coming from high temperatures the largest cluster will be blocked first.
Within this picture the measured zero-field cooled and field-cooled curves (Fig. 8.37)
are well understood. At high temperatures all clusters are free to rotate. All τ values
are shorter than τ m and the measured magnetization is zero. In lowering the temperature the cluster gradually freeze in random directions. Thus at low temperature
the measured magnetization is still zero. In applying a small measuring field and
by increasing the temperature (ZFC curve) the magnetization increases, because—
starting with the smallest ones—more and more clusters are freed, due to the thermal
energy kT and rotate in direction of the applied field. The increase of magnetization
stops when the largest clusters are rotated in direction of the applied field. With
further increase of temperature the thermal energy destroys successively the alignment and magnetic signal decreases like in a paramagnet thus forming the observed
cusp. If temperature now decreases (FC curve), due to reduction of thermal energy,
clusters begin again to rotate in direction of applied field, starting with the smallest ones and ending with the largest ones. Magnetization increases until it reaches
maximum again. With further decrease of temperature the magnetization stays constant, because all clusters are now frozen in direction of the applied field. Therefore
the temperature where the cusp appears is called the freezing temperature T f . In
this model all the irreversibilities and time dependences obtained in experiment can
be explained. It also explains, why the value T f is different for different measuring