ARTICLE IN PRESS
C. Rocha et al. / Journal of Magnetism and Magnetic Materials 320 (2008) e275–e278
e276
account a mean field proportional to the total magnetiza-
tion and a log-normal distribution of local interaction
fields, with mean zero.
The XRD results (not shown here by reason of space)
corroborate the MFM results and confirm the presence of
polycrystalline Ni in the samples. The diffractogram
showed also strong peaks of Al substrate absence of
Al O peaks suggesting that it is amorphous. The (1 1 1) Ni
3
2
. Experimental details
2
peak was not observed because it coincides with the strong
2 0 0) Al peak. For the fcc structure, the (1 1 1) peak should
(
The samples were synthesized by the following proce-
be the strongest, so we cannot conclude that [2 2 0] is the
preferential direction of growth. The grain size in the
direction [2 2 0] was calculated by Scherrer formula,
resulting in approximately 17 nm.
dure. Aluminum foils (99.997%) were cleaned in solution
of acetone and electropolished in H PO +H SO +H O
solution (4:4:2 weight), at 20 V dc. The first anodization
3
4
2
4
2
was carried out at ꢁ4 1C, in a bath of C H O (0.3 M) by
2
2
4
For the magnetic characterization, we obtained M (H )
r
1
h, at 20 V dc. The initial Al O membrane was removed in
2
p
3
and M (H ) from measurements of remanence curves
d
acidic 0.2 M CrO +0.4 M H PO solution at 50 1C during
p
3
3
4
(described elsewhere [7]) at 300 K. The coercivity was
4
0 min. The second anodization was carried out in the same
H ¼ 562 Oe. In Fig. 2a, we compare the behavior of
conditions during 40 min. The nanowires of Ni were
deposited inside the porous membrane by an ac electro-
deposition at 20 V, 100 Hz and using an electrolyte
containing NiSO ꢂ 6H O (0.1 M), and 45 g/L H BO , for
C
remanent (irreversible) magnetizations during the initial
magnetization process and the demagnetization from
saturation. At equal values of field, the later is always
larger than the first, due to the magnetic ordering created in
4
2
3
3
2
min. The structural characterization was done by Atomic
saturated state. We plotted MrevðMirrÞ curves in Fig. 2b
Hp
Force Microscopy (AFM), Magnetic Force Microscopy
MFM) and X-ray Diffractometry (XRD) with Cu-Ka
for several values of H . Remarkably, the form of these
p
(
˚
curves is very different from known materials that reverse
by coherent rotation (straight lines) or nucleation and
unpinning of reversal domains (parabolic curves) [3]. This
suggests that these curves could be associated with some
non-uniform reversal mode, once the single-domain
magnetic grains must be of the same size as the grain size
results from XRD analysis.
radiation (l=1.5418 A). The magnetic measurements were
TM
carried out at 300 K, in a Quantum Design
with magnetic field perpendicularly applied to the mem-
brane surface.
7T-SQUID,
3
. Structural and magnetic characterization
AFM and MFM micrographs were obtained after the
electrodeposition and a subsequent field application in
order to align any magnetic domains perpendicularly to the
surface. In Fig. 1, we show AFM (left) and MFM (right)
images with 1 mm scan size. We can clearly observe a highly
oriented hcp pore growth pattern and the conformation
between surface topology and magnetic domains with
perpendicular orientation. From these images, we esti-
mated the mean diameter of pores, which turns out to be
about 42 nm for anodization voltage of 20 V.
4. Discussion
We reproduced qualitatively the experimental results
through a numerical micromagnetic model. We applied
an interacting Stoner–Wohlfarth model developed by
Crew [5,6]. In the Stoner–Wohlfarth model, the free
energy density of a uniaxial single-domain particle of
volume V, in the presence of magnetic field H is given by
2
E=V ¼ Keff sin ðC ꢀ yÞ ꢀ M H cos C, where K is the
S
eff
Fig. 1. AFM (left) and MFM (right) micrographs for the sample studied.
Rocha
