152504-2
Soulantica et al.
Appl. Phys. Lett. 95, 152504 ͑2009͒
1
50
00
150
100
50
150 2K - //.
150 300 K - //
2
K / Random.
300K / Random
9
0 nm
90 nm
1
100
50
100
90 nm
5 nm
90 nm
45 nm
45 nm
4
5 nm
4
Sim. 10°
Sim. 20°
5
0
SW
50
0
0
0
0
-
50
-50
-100
-150
-50
-100
-150
-50
-
100
150
-100
-150
-
-5
-4 -3 -2 -1
0
1
2
3
4
5
-5 -4 -3 -2 -1
0
1
2
3
4
5
-30 -20 -10
0
10
20
30
-30 -20 -10
0
10
20
30
µoH (T)
µoH (kOe)
H (kOe)
µoH (T)
FIG. 3. Magnetization curves for aligned Co NRs parallel to the magnetic
field, measured at 2 K ͑left͒ and 300 K ͑right͒. The curve labeled Sim. 10°
and Sim. 20° are the hysteresis magnetization simulated for a system
FIG. 1. Magnetization curves for randomly oriented Co NRs measured at
K ͑left͒ and 300 K ͑right͒. The curve labeled SW is the hysteresis mag-
netization calculated for a system of independent uniaxial nano-objects with
2
1
3
3
of interacting uniaxial nano-objects with
a
uniaxial anisotropy of
a uniaxial anisotropy of 10 erg/cm , in the framework of the SW model.
3
1
012 erg/cm , making an angle of 10° and 20° respect to the magnetic field.
disordered samples ͑NL and NS͒ at 2 and 300 K. It evidences
where the dipolar interactions are less effective. M has half
wide hysteresis with H up to 8.3 kOe ͑10 kOe͒ and 4.9 kOe
R
C
the value of M ͑48%–52% exactly at 2 K͒, which is ex-
͑
4.9 kOe͒ at T=2 and 300 K, respectively, for the NS ͑NL͒
S
pected for a system of non- or low interacting randomly ori-
ented nano-objects with a uniaxial anisotropy. The shape of
the hysteresis loops is very near the ideal one, which can be
calculated in the framework of SW model and considering a
sample. The value of M , normalized with respect to the total
S
mass of Co, is equal to 156 ͑145͒ emu/g for NS ͑NL͒, very
close to the value for bulk Co. M is equal to Ϸ0.5 MS,
R
which enable us to confirm that the Co NRs are well dis-
persed and randomly oriented in tetracosane. Moreover, the
solvent does not affect the surface magnetism.
6
3
uniaxial anisotropy of 13ϫ10 erg/cm ͑see Fig. 1͒. Indeed,
since the NRs are monocrystalline with a large aspect ratio
and diameters of the same order of magnitude as the ex-
change length in Co materials ͑7 nm͒, the deviations from
the coherent rotation are expected to be small. The discrep-
ancy is due to the presence of a dipolar interaction field,
which leads to a small decrease in HC, as compared to the
noninteracting case. However, the large HK along the NR
compared to the dipolar field dominates and defines the co-
In a subsequent step, the two samples NS and NL have
been oriented under magnetic field, in situ, in the magneto-
meter. For this, each sample is warmed up just above the
melting point of tetracosane ͑330 K͒. Keeping the tempera-
ture constant, a magnetic field of 50 kOe is applied in order
to orientate physically the NRs. Finally, keeping the mag-
netic field, the sample was cooled down to complete solidi-
electron microscopy ͑TEM͒ micrograph shown on Fig. 2,
made on a fragment of the solid oriented samples, the Co
NRs are found to be nearly parallel to each other. As shown
on Fig. 3, the NR alignment has significantly improved the
square shape of the hysteresis loop, the remnant magnetiza-
ercive field. The effective anisotropy ͑K ͒ acting on an iso-
eff
lated NR is given by the sum of the magnetocrystalline ͑KU͒
and shape ͑K ͒ contributions, since both have exactly the
f
same uniaxial symmetry. We estimated Keff from the coercive
field H as K =H M /2ϫ0.48 in the ideal case of negli-
C
eff
C
S
gible dipolar interactions. We then calculated the shape con-
2
tion reaching now a value up to 0.91M for NS. For, NL, the
S
tribution from K =1/2͑N −N
ʈ
͒M where N and N are the
ʈ
f
Ќ
S
Ќ
orientation procedure seems to be less efficient, since M is
R
demagnetization factors perpendicular and parallel to the NR
only 0.84M . Furthermore, H is increased up to 10.0 kOe
S
C
long axis, respectively. Since M remains practically con-
S
͑
11.75 kOe͒ at T=2 K and 6.2 kOe ͑6.5 kOe͒ at T=300 K,
stant up to 300 K, this contribution is temperature indepen-
for NS ͑NL͒, respectively. These values are the largest ever
6
3
dent and we estimate it in the range of 6ϫ10 erg/cm for
measured on elemental FM nano-objects.
the two samples. Thus, the evolution of K ͑from 12–13
eff
Interpreting the magnetization process in this system of
self-assembled NRs is far from being simple. The switching
mechanism is a complex combination of the intra-NR rever-
sal mode and the collective behavior mediated by dipolar
interactions. We first consider the randomly oriented case
6
3
6
3
ϫ10 erg/cm at 2 K, down to 7–8ϫ10 erg/cm at 300
K͒ reflects the temperature induced reduction of K . Its value
U
6
3
is in the same range than bulk Co ͑6–7ϫ10 erg/cm ͒ at 2
3
K, but decreases faster with T, down to 1–2ϫ10 erg/cm
6
3
at 300 K instead of 4ϫ10 erg/cm for the bulk.
Upon aligning the NRs and according to the SW model,
one expects a doubling of H , up to 2K /M =17–19 kOe
C
eff
S
6
−3
for K ϳ12–13ϫ10 erg/cm . However, the enhance-
eff
NS
ment is only in the range of 20%–25% well below the ex-
pected 100%. Nevertheless, careful analysis of the TEM mi-
crographs reveals that the magnetic alignment is imperfect,
and since the packing of the NRs has become dense, dipolar
interactions may play a more important role. In order to
evaluate more precisely the role of these two parameters, i.e.,
dipolar interactions and misorientations, we calculated nu-
merically the low temperature hysteresis loops for a sub-
system of ͑Ϸ50͒ densely packed NRs organized side by side,
with a mean separating distance of 2 nm. For simplicity,
NL
FIG. 2. TEM observations of the solidified samples after magnetic align-
ment of the NRs for NS ͑left͒ and NL ͑right͒.
single domain NRs with all spins pointing along the same
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