3 Collective Magnetic Behaviour
75
0
2.5
5
7.5
10
H (kOe)
-1
-0.5
0
0.5
1
M/M
RS
0
2.5
5
7.5
10
H (kOe)
0
2.5
5
7.5
10
H (kOe)
IRM
DCD
M
REF6
REF8
RCP8
a
b
c
Fig. 3.9 m IRM (H), m DCD (H) and δM(H) at T = 5 K for a non-interacting 6 nm particles b noninteracting 8 nm particles and c compact 8 nm particles [22]
M IRM /M RS , and m DCD (H) = M DCD (H)/M RS are used to calculate δM = m DCD -(1–
2m IRM ). For a non-interacting system of ideal superspins δM = 0 at all fields, whereas
for systems with interparticle interaction and/or non-ideal particle moments δM(H)
= 0 at low fields [21]. The field dependences of IRM, DCD and δM of REF6, REF8
and RCP8 at 5 K are shown in Fig. 3.9 a–c. REF6 shows the expected behaviour
of a non-interacting system of magnetic nanoparticles being switched according to
the Stoner–Wohlfarth model, i.e. δM(H) ≈ 0 at all fields. For REF8 on the other
hand, δM(H) = 0 at low fields. The different behaviour of REF6 and REF8 reflects
non-ideal behaviour of the 8 nm particles [22]; these particles exhibit finite exchange
bias after field cooling, whereas the 6 nm particles do not. Figure 3.9c shows the
very strong influence that interparticle interaction and collective behaviour of the
compact 8 nm particle system (RCP8) has on the field dependence of δM.
At higher temperatures, thermal relaxation implies that the measures M IRM , M DCD
and δM become time dependent: i.e. dependent on the duration of the magnetic field
pulse (how long time H r has been applied), the observation time of the measurement
of the remanence and for an interacting system the wait time before the magnetic
field is applied after zero-field cooling. This implies that also these time parameters
need to be controlled when this kind of measurements is made at temperatures where
significant magnetic relaxation occurs. The crucial influence that thermal relaxation
has on the hysteresis behaviour of (super)spin and glasses is evidenced by first-order
reversal curves (FORC) simulations of an Edwards-Anderson Ising spin glass at T =
0 and T = 0.3 T g , where finite temperature smoothens all sharp features of the FORC
diagram (in accord with experimental results) and effectively wipes out the reversal
field memory effect characteristic of 3D Ising spin glasses at T = 0 K [23]. FORC
diagrams and magnetic hysteresis of Heisenberg spin glasses are on the other hand
dominated by an induced excess moment that exhibits field-dependent exchange bias
[24, 25]. FORC diagrams of RCP8 at low temperature are very different from those
of the weakly interacting system (which primarily are controlled by the particle size
distribution) but also very different from FORCs of atomic spin glasses [22].
75
0
2.5
5
7.5
10
H (kOe)
-1
-0.5
0
0.5
1
M/M
RS
0
2.5
5
7.5
10
H (kOe)
0
2.5
5
7.5
10
H (kOe)
IRM
DCD
M
REF6
REF8
RCP8
a
b
c
Fig. 3.9 m IRM (H), m DCD (H) and δM(H) at T = 5 K for a non-interacting 6 nm particles b noninteracting 8 nm particles and c compact 8 nm particles [22]
M IRM /M RS , and m DCD (H) = M DCD (H)/M RS are used to calculate δM = m DCD -(1–
2m IRM ). For a non-interacting system of ideal superspins δM = 0 at all fields, whereas
for systems with interparticle interaction and/or non-ideal particle moments δM(H)
= 0 at low fields [21]. The field dependences of IRM, DCD and δM of REF6, REF8
and RCP8 at 5 K are shown in Fig. 3.9 a–c. REF6 shows the expected behaviour
of a non-interacting system of magnetic nanoparticles being switched according to
the Stoner–Wohlfarth model, i.e. δM(H) ≈ 0 at all fields. For REF8 on the other
hand, δM(H) = 0 at low fields. The different behaviour of REF6 and REF8 reflects
non-ideal behaviour of the 8 nm particles [22]; these particles exhibit finite exchange
bias after field cooling, whereas the 6 nm particles do not. Figure 3.9c shows the
very strong influence that interparticle interaction and collective behaviour of the
compact 8 nm particle system (RCP8) has on the field dependence of δM.
At higher temperatures, thermal relaxation implies that the measures M IRM , M DCD
and δM become time dependent: i.e. dependent on the duration of the magnetic field
pulse (how long time H r has been applied), the observation time of the measurement
of the remanence and for an interacting system the wait time before the magnetic
field is applied after zero-field cooling. This implies that also these time parameters
need to be controlled when this kind of measurements is made at temperatures where
significant magnetic relaxation occurs. The crucial influence that thermal relaxation
has on the hysteresis behaviour of (super)spin and glasses is evidenced by first-order
reversal curves (FORC) simulations of an Edwards-Anderson Ising spin glass at T =
0 and T = 0.3 T g , where finite temperature smoothens all sharp features of the FORC
diagram (in accord with experimental results) and effectively wipes out the reversal
field memory effect characteristic of 3D Ising spin glasses at T = 0 K [23]. FORC
diagrams and magnetic hysteresis of Heisenberg spin glasses are on the other hand
dominated by an induced excess moment that exhibits field-dependent exchange bias
[24, 25]. FORC diagrams of RCP8 at low temperature are very different from those
of the weakly interacting system (which primarily are controlled by the particle size
distribution) but also very different from FORCs of atomic spin glasses [22].