76
R. Mathieu and P. Nordblad
- 1
0
1
2
3
4
5
log 10 (t)
0.7
0.8
0.9
M/M
FC(T
h
)
0
2
4
log 10 (t)
0
0.05
0.1
M/M
FC(T
h )
300 s
3000 s
10000 s
t w = 0
ZFC
t w = 0
t h = 300 s
IRM
RCP8
T = 110 K
Fig. 3.10 Left: Equivalent field change sequence for a field pulse of duration t h . Right: M ZFC (t w ,
t)/M FC versus log(t) recorded in H = 0.5 Oe and calculated m IRM (t) for RCP8 (t w = 0)
At low fields, where the particle system obeys linear response to field applications,
M IRM reflects the relaxation function, p(t w , t) and the time dependence of M IRM (t)
obeys the principle of superposition. The relaxation function is directly measured
by the ZFC relaxation after the application of a weak magnetic field (h): p(t w , t) =
M ZFC (t w , t)/h [26], where t is the time elapsed after the field application and t w the
wait time at constant field before the magnetic field is applied. The right panel of
Fig. 3.10 shows zero-field-cooled magnetic relaxation, M ZFC (t, t w ) versus log (t), of
the compact 8 nm particle assembly (RCP8) measured at 110 K. The relaxation at
temperatures below T g (= 140 K) occurs over extended time scales stating from the
individual particle relaxation time (τ p ) and continuing well beyond any experimental
time scales.
The fact that there is a wait time dependence of the relaxation function implies that
the system experiences magnetic ageing, as already the memory behaviour suggested
(Fig. 3.4). The magnitude of the low-field IRM is controlled by the relaxation function
p(t w , t): and given by: M IRM (t) = hp(tw, t + t h )−hp(t w + t h , t) [26]. Where the
response function empirically is defined from the measured M ZFC (t w , t) curves. The
inset of the right panel of Fig. 3.10 shows the calculated m IRM (t) using the t w =
0 and t w = 300 s curves of the main panel and the field application sequence is
indicated in the left panel of Fig. 3.10: a positive field is applied at t = 0 and a
negative field change h (= 0.5 Oe) is made at time t h (= 300 s). The remanence,
m IRM [ = M IRM /M FC (T h )], that has been attained after the field has been cut to
zero can be frozen in by immediately cooling the sample to lower temperatures.
Figure 3.11 shows the temperature dependence of M IRM on cooling and heating
(red dots) and on heating after the sample has been quenched to low temperature
immediately after the field has been switched off (black dots) [27]. As can be seen
by the red curve there is a rapid decrease of the magnetization in the temperature
region close to the halt temperature (cf. the decay of m IRM (t) on a linear scale shown
in the inset of Fig. 3.11, the same m IRM data as shown on a logarithmic scale in
R. Mathieu and P. Nordblad
- 1
0
1
2
3
4
5
log 10 (t)
0.7
0.8
0.9
M/M
FC(T
h
)
0
2
4
log 10 (t)
0
0.05
0.1
M/M
FC(T
h )
300 s
3000 s
10000 s
t w = 0
ZFC
t w = 0
t h = 300 s
IRM
RCP8
T = 110 K
Fig. 3.10 Left: Equivalent field change sequence for a field pulse of duration t h . Right: M ZFC (t w ,
t)/M FC versus log(t) recorded in H = 0.5 Oe and calculated m IRM (t) for RCP8 (t w = 0)
At low fields, where the particle system obeys linear response to field applications,
M IRM reflects the relaxation function, p(t w , t) and the time dependence of M IRM (t)
obeys the principle of superposition. The relaxation function is directly measured
by the ZFC relaxation after the application of a weak magnetic field (h): p(t w , t) =
M ZFC (t w , t)/h [26], where t is the time elapsed after the field application and t w the
wait time at constant field before the magnetic field is applied. The right panel of
Fig. 3.10 shows zero-field-cooled magnetic relaxation, M ZFC (t, t w ) versus log (t), of
the compact 8 nm particle assembly (RCP8) measured at 110 K. The relaxation at
temperatures below T g (= 140 K) occurs over extended time scales stating from the
individual particle relaxation time (τ p ) and continuing well beyond any experimental
time scales.
The fact that there is a wait time dependence of the relaxation function implies that
the system experiences magnetic ageing, as already the memory behaviour suggested
(Fig. 3.4). The magnitude of the low-field IRM is controlled by the relaxation function
p(t w , t): and given by: M IRM (t) = hp(tw, t + t h )−hp(t w + t h , t) [26]. Where the
response function empirically is defined from the measured M ZFC (t w , t) curves. The
inset of the right panel of Fig. 3.10 shows the calculated m IRM (t) using the t w =
0 and t w = 300 s curves of the main panel and the field application sequence is
indicated in the left panel of Fig. 3.10: a positive field is applied at t = 0 and a
negative field change h (= 0.5 Oe) is made at time t h (= 300 s). The remanence,
m IRM [ = M IRM /M FC (T h )], that has been attained after the field has been cut to
zero can be frozen in by immediately cooling the sample to lower temperatures.
Figure 3.11 shows the temperature dependence of M IRM on cooling and heating
(red dots) and on heating after the sample has been quenched to low temperature
immediately after the field has been switched off (black dots) [27]. As can be seen
by the red curve there is a rapid decrease of the magnetization in the temperature
region close to the halt temperature (cf. the decay of m IRM (t) on a linear scale shown
in the inset of Fig. 3.11, the same m IRM data as shown on a logarithmic scale in