74
R. Mathieu and P. Nordblad
0
50
100 150 200 250 300 350
T (K)
0
0.2
0.4
0.6
0.8
1
M/M
max ZFC
RCP9
RCP11
65% mixed
Fig. 3.8 Left panel: Normalized ZFC/FC magnetization versus temperature for compacted samples
of 9 nm particles (RCP9), 11.5 nm particles (RCP11), and a mixture of 9 and 11.5 nm particles with
65% mixing fraction; H = 5 Oe. Right panel: T max of the compacted mixed samples (RCP) versus
concentration of large particles and T B of the dilute 9 and 11.5 nm samples (REF9 and REF11,
respectively). The inset shows the particle size distribution of the 9 and the 11.5 nm assemblies.
The magnetization curves were not corrected for demagnetization effects [19, 20]
as T max with particle volume. T max (and T g ) exceeds T B by a factor of 4 or more for
all samples.
All the discussed compacted samples have similar and quite narrow particle
size distributions and exhibit well-behaved critical slowing down indicating superspin glass transitions [14]. Figure 3.8 shows ZFC and FC magnetization curves for
compacted samples of 9 nm (RCP9) and 11.5 nm (RCP11) maghemite particles, as
well as for a sample consisting of a mixture of 9 and 11.5 nm particles (65% mixing
fraction). The volume (2V ) of the 11.5 nm particles is about twice the volume (V ) of
the 9 nm particles. The size distributions of the two particle systems are shown as an
inset in the right panel of Fig. 3.8. The evolution of the measured T max with increasing
fraction of larger particles is shown in the main frame of the right panel in Fig. 3.8.
T max increases linearly with the mixing fraction (mean particle size). Analyses of
the frequency dependence of the freezing temperatures indicate that the assemblies
of mixed particle sizes obey critical slowing down at all different mixing fractions
from 0 to 100% of larger particles [19]. In all cases, the SSG temperature exceeds
the blocking temperature of the dilute reference sample of the largest particles (2V )
by at least a factor of three.
At low temperatures, where the particle moments are thermally blocked on the
time scale of magnetization measurements, interparticle interaction can be revealed
from a comparison between the field dependence of the isothermal remanent magnetization IRM(H) and the direct current demagnetization DCD(H) [21]. IRM is
measured starting from a zero-field-cooled sample, applying a field pulse and then
measuring the remanent magnetization M IRM in zero field. DCD is measured starting
from a high negative field (−H s ) that saturates the remanent magnetization (M RS ),
applying a reversal field (H r ≥ 0), then removing this field and measuring the remanence M DCD in zero field. The relative values of these remanences: m IRM (H) =
R. Mathieu and P. Nordblad
0
50
100 150 200 250 300 350
T (K)
0
0.2
0.4
0.6
0.8
1
M/M
max ZFC
RCP9
RCP11
65% mixed
Fig. 3.8 Left panel: Normalized ZFC/FC magnetization versus temperature for compacted samples
of 9 nm particles (RCP9), 11.5 nm particles (RCP11), and a mixture of 9 and 11.5 nm particles with
65% mixing fraction; H = 5 Oe. Right panel: T max of the compacted mixed samples (RCP) versus
concentration of large particles and T B of the dilute 9 and 11.5 nm samples (REF9 and REF11,
respectively). The inset shows the particle size distribution of the 9 and the 11.5 nm assemblies.
The magnetization curves were not corrected for demagnetization effects [19, 20]
as T max with particle volume. T max (and T g ) exceeds T B by a factor of 4 or more for
all samples.
All the discussed compacted samples have similar and quite narrow particle
size distributions and exhibit well-behaved critical slowing down indicating superspin glass transitions [14]. Figure 3.8 shows ZFC and FC magnetization curves for
compacted samples of 9 nm (RCP9) and 11.5 nm (RCP11) maghemite particles, as
well as for a sample consisting of a mixture of 9 and 11.5 nm particles (65% mixing
fraction). The volume (2V ) of the 11.5 nm particles is about twice the volume (V ) of
the 9 nm particles. The size distributions of the two particle systems are shown as an
inset in the right panel of Fig. 3.8. The evolution of the measured T max with increasing
fraction of larger particles is shown in the main frame of the right panel in Fig. 3.8.
T max increases linearly with the mixing fraction (mean particle size). Analyses of
the frequency dependence of the freezing temperatures indicate that the assemblies
of mixed particle sizes obey critical slowing down at all different mixing fractions
from 0 to 100% of larger particles [19]. In all cases, the SSG temperature exceeds
the blocking temperature of the dilute reference sample of the largest particles (2V )
by at least a factor of three.
At low temperatures, where the particle moments are thermally blocked on the
time scale of magnetization measurements, interparticle interaction can be revealed
from a comparison between the field dependence of the isothermal remanent magnetization IRM(H) and the direct current demagnetization DCD(H) [21]. IRM is
measured starting from a zero-field-cooled sample, applying a field pulse and then
measuring the remanent magnetization M IRM in zero field. DCD is measured starting
from a high negative field (−H s ) that saturates the remanent magnetization (M RS ),
applying a reversal field (H r ≥ 0), then removing this field and measuring the remanence M DCD in zero field. The relative values of these remanences: m IRM (H) =