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J. Richardi et al.
(χ
) components of the AC susceptibility versus temperature, are measured in
a range of AC frequencies varying by 2 decades in magnitude (Fig. 8.14a, b).
Both the χ
and χ
components show a clear frequency dependence, where the
temperature at which the maximum susceptibility is observed (T peak ) increases
with increasing frequency. T peak is defined as the temperature at which the relaxation time of the system, τ, is equal to the observation time, t, which is related to
the measurement frequency by t = 1/ω, where ω = 2πf . In order to differentiate
between superparamagnetic and superspin glass behaviors, which display both
the same frequency dependence in an AC measurement, the change in T peak with
frequency has to be quantitatively analyzed and hence extract a value of τ 0 . For
a superparamagnet, characterized by negligible dipolar interactions between the
magnetic moments, the frequency dependence should follow an Arrhenius law
τ = τ 0 e
Ea
k b T where is the angular inverse attempt frequency, E a is the anisotropy
energy, and k B is the Boltzmann constant. By plotting log 10 τ versus 1/T peak and
fitting the data to a straight line, the value of τ 0 can be extracted and in this
case we find τ 0 = 10
–31 s [75]. This unphysically small value indicates that
this system cannot be described by simple energy barrier blocking and thermal
activation. Actually and analogously to a spin glass, the magnetic response is
also influenced by interparticle interaction we have to take into account. In spin
glass systems, the dynamic behavior shows a critical slowing down, and hence,
the characteristic relaxation time diverges to a finite static glass temperature T g ,
according to a critical power law τ = τ * (T peak /T g
−1 )
−zν , where τ * is the relaxation time of an individual NP moment and zν is a critical exponent. T g is taken
as the maximum in the DC ZFC magnetization curve. Fitting the data yields τ *
= 10
–9±3 s and zν = 12 ± 2. This value of τ * is in good agreement with values
found for spin glasses, and zν, although slightly high, is also compatible within
error to that expected for spin glasses [76–78].
Spin glass and superspin glass materials are known to show aging and memory
effects, which can be demonstrated by a simple DC magnetization experiment. The
sample is zero field cooled from above T g to a temperature T s typically equal to 0.7
T g where a waiting time of t w = 104 s is imposed before continuing cooling down
to low temperature. A small field is then applied and the magnetization is measured
on heating. A deviation from the reference ZFC curve (with no stop during cooling)
is observed at T s , which is known as a “memory dip,” so-called as the system has
“remembered” the relaxation toward a zero magnetization value (aging) that occurred
during the cooling process.
The results of these AC and DC susceptibility investigations provide strong
evidence for superspin glass behavior in long-range ordered fcc supercrystals made
of low anisotropy 8 nm fcc-Co polycrystals.
J. Richardi et al.
(χ
) components of the AC susceptibility versus temperature, are measured in
a range of AC frequencies varying by 2 decades in magnitude (Fig. 8.14a, b).
Both the χ
and χ
components show a clear frequency dependence, where the
temperature at which the maximum susceptibility is observed (T peak ) increases
with increasing frequency. T peak is defined as the temperature at which the relaxation time of the system, τ, is equal to the observation time, t, which is related to
the measurement frequency by t = 1/ω, where ω = 2πf . In order to differentiate
between superparamagnetic and superspin glass behaviors, which display both
the same frequency dependence in an AC measurement, the change in T peak with
frequency has to be quantitatively analyzed and hence extract a value of τ 0 . For
a superparamagnet, characterized by negligible dipolar interactions between the
magnetic moments, the frequency dependence should follow an Arrhenius law
τ = τ 0 e
Ea
k b T where is the angular inverse attempt frequency, E a is the anisotropy
energy, and k B is the Boltzmann constant. By plotting log 10 τ versus 1/T peak and
fitting the data to a straight line, the value of τ 0 can be extracted and in this
case we find τ 0 = 10
–31 s [75]. This unphysically small value indicates that
this system cannot be described by simple energy barrier blocking and thermal
activation. Actually and analogously to a spin glass, the magnetic response is
also influenced by interparticle interaction we have to take into account. In spin
glass systems, the dynamic behavior shows a critical slowing down, and hence,
the characteristic relaxation time diverges to a finite static glass temperature T g ,
according to a critical power law τ = τ * (T peak /T g
−1 )
−zν , where τ * is the relaxation time of an individual NP moment and zν is a critical exponent. T g is taken
as the maximum in the DC ZFC magnetization curve. Fitting the data yields τ *
= 10
–9±3 s and zν = 12 ± 2. This value of τ * is in good agreement with values
found for spin glasses, and zν, although slightly high, is also compatible within
error to that expected for spin glasses [76–78].
Spin glass and superspin glass materials are known to show aging and memory
effects, which can be demonstrated by a simple DC magnetization experiment. The
sample is zero field cooled from above T g to a temperature T s typically equal to 0.7
T g where a waiting time of t w = 104 s is imposed before continuing cooling down
to low temperature. A small field is then applied and the magnetization is measured
on heating. A deviation from the reference ZFC curve (with no stop during cooling)
is observed at T s , which is known as a “memory dip,” so-called as the system has
“remembered” the relaxation toward a zero magnetization value (aging) that occurred
during the cooling process.
The results of these AC and DC susceptibility investigations provide strong
evidence for superspin glass behavior in long-range ordered fcc supercrystals made
of low anisotropy 8 nm fcc-Co polycrystals.