3 Collective Magnetic Behaviour
69
different particles occurs. The inset shows the measured low-field ZFC magnetization
(χ = M/H) of the dilute 8 nm assembly (REF8) and the calculated behaviour for a
corresponding monodispersed 8 nm maghemite assembly (Debye AC susceptibility;
t obs = 10 s). Also drawn in Fig. 3.3 is the evolution of the relaxation time of the
system assuming a compact nanoparticle system with dipolar interaction yielding T g
= 140 K. The individual particle relaxation time that corresponds to the volume of
the particles and critical slowing down (τ crit = τ p t
−zν , t = (T-T g )/T g [9] and zν =
10 the dynamic critical exponent) have been used to calculate the evolution of the
critical relaxation time (τ crit ) of the dense particle assemblies (red curves; 7.5, 8 and
8.5 nm particles).
3.1.4 Model Behaviour Contra Collective Phenomena
A model superparamagnetic or superspin glass system would consist of monodispersed particles. However, such a system does not exist and the blocking behaviour
of a non-interacting system of magnetic nanoparticles is always significantly broadened compared to a model calculation using the mean volume (see inset Fig. 3.3).
The relaxation times of a model superspin glass approaching the glass temperature
obey critical slowing down [10–13]. In spite of the inevitable size distribution of the
nanoparticles, critical slowing down is observed in compact nanoparticle systems,
with similar sharpness as that observed in archetypal atomic spin glasses [14]. On
the other hand, nanoparticle systems with broader size distributions exhibit typical
characteristics of collective dynamics in glassy magnetic systems such as ageing and
memory phenomena although critical slowing down indicating a phase transition is
not observed [15].
Figure 3.4 illustrates the correspondence between the ageing/memory behaviour
of an archetypal spin glass (Cu(Mn)) [16] and a strongly interacting magnetic
nanoparticle assembly (RCP8) showing superspin glass behaviour [6]. The main
frames show low-field ZFC magnetization (M/H) versus temperature curves; a reference curve (red) where the system has been continuously cooled to a low temperature
where the magnetic field is applied and the magnetization recorded on increasing
temperature, and a memory curve (blue) where the sample has been kept at a halt
temperature a wait time t w during cooling. The memory curve shows a dip at the halt
temperature as a memory of the halt [17]. The insets show ZFC magnetic relaxation
at the halt temperatures using two different wait times (0 (red curves), and 3000 or
10,000 s (blue), respectively) at constant temperature before the magnetic field is
applied. At an observation time of 100 s, the magnetization is lower when the system
has been kept at constant temperature a longer wait time, this is in accord with the dip
in the M versus T memory curves. The fact that the reference and memory M versus T
curves coalesce at lower temperatures reflects the rejuvenation phenomenon (chaotic
nature); the response of the (super)spin glass at lower temperatures is unaffected by
the halt.
69
different particles occurs. The inset shows the measured low-field ZFC magnetization
(χ = M/H) of the dilute 8 nm assembly (REF8) and the calculated behaviour for a
corresponding monodispersed 8 nm maghemite assembly (Debye AC susceptibility;
t obs = 10 s). Also drawn in Fig. 3.3 is the evolution of the relaxation time of the
system assuming a compact nanoparticle system with dipolar interaction yielding T g
= 140 K. The individual particle relaxation time that corresponds to the volume of
the particles and critical slowing down (τ crit = τ p t
−zν , t = (T-T g )/T g [9] and zν =
10 the dynamic critical exponent) have been used to calculate the evolution of the
critical relaxation time (τ crit ) of the dense particle assemblies (red curves; 7.5, 8 and
8.5 nm particles).
3.1.4 Model Behaviour Contra Collective Phenomena
A model superparamagnetic or superspin glass system would consist of monodispersed particles. However, such a system does not exist and the blocking behaviour
of a non-interacting system of magnetic nanoparticles is always significantly broadened compared to a model calculation using the mean volume (see inset Fig. 3.3).
The relaxation times of a model superspin glass approaching the glass temperature
obey critical slowing down [10–13]. In spite of the inevitable size distribution of the
nanoparticles, critical slowing down is observed in compact nanoparticle systems,
with similar sharpness as that observed in archetypal atomic spin glasses [14]. On
the other hand, nanoparticle systems with broader size distributions exhibit typical
characteristics of collective dynamics in glassy magnetic systems such as ageing and
memory phenomena although critical slowing down indicating a phase transition is
not observed [15].
Figure 3.4 illustrates the correspondence between the ageing/memory behaviour
of an archetypal spin glass (Cu(Mn)) [16] and a strongly interacting magnetic
nanoparticle assembly (RCP8) showing superspin glass behaviour [6]. The main
frames show low-field ZFC magnetization (M/H) versus temperature curves; a reference curve (red) where the system has been continuously cooled to a low temperature
where the magnetic field is applied and the magnetization recorded on increasing
temperature, and a memory curve (blue) where the sample has been kept at a halt
temperature a wait time t w during cooling. The memory curve shows a dip at the halt
temperature as a memory of the halt [17]. The insets show ZFC magnetic relaxation
at the halt temperatures using two different wait times (0 (red curves), and 3000 or
10,000 s (blue), respectively) at constant temperature before the magnetic field is
applied. At an observation time of 100 s, the magnetization is lower when the system
has been kept at constant temperature a longer wait time, this is in accord with the dip
in the M versus T memory curves. The fact that the reference and memory M versus T
curves coalesce at lower temperatures reflects the rejuvenation phenomenon (chaotic
nature); the response of the (super)spin glass at lower temperatures is unaffected by
the halt.