Characterizing magnetic interactions in Ni nanowires by FORC analysis

Article abstract of DOI:10.1016/j.jmmm.2008.02.060

Polycrystalline Ni nanowires with different diameters were electrodeposited in nanoporous anodized alumina membranes. First-Order Reversal Curves (FORCs) were measured and FORC distributions were calculated. They clearly showed an asymmetric behavior with a strong maximum at negative interaction fields, evidencing the dominant demagnetizing interactions which depend on the geometry of the nanowires.

Full text of DOI:10.1016/j.jmmm.2008.02.060

ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) e279–e282
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Characterizing magnetic interactions in Ni nanowires by FORC analysis
Ã
T.R.F. Peixoto, D.R. Cornejo
´
Instituto de Fısica, Universidade de Sa˜o Paulo, 05508-900 Sa˜o Paulo, SP, Brazil
Available online 21 February 2008
Abstract
Polycrystalline Ni nanowires with different diameters were electrodeposited in nanoporous anodized alumina membranes. First-Order
Reversal Curves (FORCs) were measured and FORC distributions were calculated. They clearly showed an asymmetric behavior with a
strong maximum at negative interaction fields, evidencing the dominant demagnetizing interactions which depend on the geometry of the
nanowires.
r 2008 Elsevier B.V. All rights reserved.
PACS: 75.60.Ej; 75.60.Jk; 75.75.+a
Keywords: Magnetic nanowire; FORC; Demagnetization process; Electrodeposition
1. Introduction
r can be compared to the statistical distribution of particles
from the Preisach model [12], which describes the field-
induced reversal of an ensemble of single-domain particles.
Thus, the FORC diagram provides a detailed characte-
rization of the hysteretic response of a system because it
evidences dominant magnetic interactions, magnetic after-
effects and the annihilation of memory during the
demagnetization process.
Self-organized arrays of ferromagnetic nanowires show
potential feasibility for applications in perpendicular
magnetic recording media and high-sensitivity magnetic
sensors [1], and are well suited for both experimental and
theoretical study of magnetism at nanoscale [1–4]. These
systems can be easily synthesized through the method of
two-step anodization [5] and subsequent chemical electro-
deposition [2,3].
One phenomenological approach that has been topic of
renewed interest in magnetic systems is the First-Order
Reversal Curves (FORC) analysis [6–11]. FORCs can be
experimentally obtained as follows: (a) first, one has to
saturate the sample with a field Hmax; (b) then, set the field
H to a return value HroHmax; (c) then, increase H back to
Hmax, measuring the magnetization; and (d) and repeat
steps (b) and (c) for decreasing values of Hr, while
In this work, a set of samples of Ni nanowires grown in
the nanoporous anodized alumina membranes were mag-
netically characterized by FORC analysis.
2. Experimental details
Thin (0.2 mm) Al foils with 99.997% purity were pre-
treated in vacuum at 600 1C for 2 h; washed in acetone;
electropolished in
a H2SO4+H3PO4+H2O solution;
etched in a 3 M NaOH solution and rinsed in deionized
water. Later, the foils were anodized in a constant voltage
cell containing an aqueous solution of 0.3 M oxalic acid
(H2C2O4), at 4 1C, using a graphite electrode as cathode.
The first anodization was carried out for 1 h and the second
for 40 min. Several samples were prepared with anodization
voltage Van varying between 15 and 30 V. The electro-
depositions were carried out in a solution of 0.1 M
NiSO4 ꢂ 6H2O+45 g/LH3BO3, at 55 1C, for 2 min, under
20 V, at 100 Hz.
HrXꢀHmax
.
The FORC distribution is, then, defined by rðHr; HÞ ꢁ
ꢀ0:5fq2MðHr; HÞ=qHrqHg and performed on the dataset
of the measured FORCs. The FORC diagram is a contour
plot of r on a 451 rotated coordinate system fHc ¼
ðH ꢀ HrÞ=2; Hb ¼ ðH þ HrÞ=2g. In these coordinates,
Ã
Corresponding author. Tel.: +55 11 30916885; fax: +55 11 30916984.
E-mail address: cornejo@if.usp.br (D.R. Cornejo).
0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2008.02.060

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T.R.F. Peixoto, D.R. Cornejo / Journal of Magnetism and Magnetic Materials 320 (2008) e279–e282
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The structural characterization was done by Scanning
Electron Microscopy (SEM) and X-ray Diffractometry
(XRD), with Cu Ka radiation. The magnetic characteriza-
tion was accomplished at 300 K in a 7T-SQUID, with
magnetic field applied perpendicularly to the membrane
surface.
3. Structural and magnetic characterization
SEM images of the samples were obtained and treated in
a suitable image processing software, from where we
calculated the mean diameter dm, the mean interpore
distance Dint and the density of pores. A linear dependence
of dm and Dint with Van was observed, with dm between 30
and 90 nm and Dint between 40 and 110 nm, in agreement
with the literature [13,14]. The mean density of pores varies
between 109 and 1010 pores/cm2. The shape of the pores
also varies with Van. Samples made at 30 and 40 V have a
more regularly oriented hcp patterns. Below Van=30 V, the
pore arrays are predominantly random, whereas above
40 V the pores tend to deform. It is well known that the
regularity of the pore array depends on voltage and
duration of the first anodization [15–17] and that for high
Van the pores tend to diverge from the circular shape [18].
On the other hand, the length of the pores depends solely
on the duration of the second anodization [13]. We
estimate that our samples have lengths between 5 and
15 mm, yielding an aspect ratio greater than 50.
The XRD patterns confirm the presence of polycrystal-
line Ni. The (1 1 1) peak of Ni was not detected due to its
coincidence with the strong (2 0 0) peak of Al. The grain
sizes of Ni were calculated for each crystallographic
direction and they were seen to increase with dm, in
the range of 10–22 nm, indicating that the geometry of the
pores regulates the grain size of Ni. In this range, the
crystallites must be exchanged-coupled single-domain
particles, with random orientation of easy axes [2]. Such
a magnetic structure can allow non-uniform modes of
magnetization reversal [19,20].
Fig. 1. (a) FORCs and (b) FORC diagram for the sample with
dm ¼ 38 nm.
The shape uniaxial anisotropy in our samples was
confirmed by measuring hysteresis loops in the directions
perpendicular and parallel to the wires. An outstanding
increase of coercive field HC and remanence (MR40.5MS),
in comparison to bulk Ni, was observed. It is in accordance
with Ref. [19]. To obtain the FORC distributions, approxi-
mately 20 FORCs with Hmax ¼ 3 kOe were measured for
each sample (see Fig. 1a). The FORC distributions were
calculated by the method described by Heslop and
Muxworthy [11], applying the ‘‘extended’’ FORC definition
[7], normalized by the saturation magnetization MS of each
sample and plotted in the {Hc, Hb} coordinates. Fig. 2b
displays typical results for the sample with dm ¼ 38 nm.
4. Results and discussion
In the classical Preisach model, a distribution of non-
interacting single-domain particles is considered, where
Fig. 2. FORC distribution of all samples at (a) Hb ¼ 0 and (b) Hc ¼ 0.

ARTICLE IN PRESS
T.R.F. Peixoto, D.R. Cornejo / Journal of Magnetism and Magnetic Materials 320 (2008) e279–e282
e281
each particle is characterized by a square elementary
hysteresis loop with width Hc and offset Hb. This
distribution P(Hc, Hb) has a definition very similar to that
of the FORC distribution [12]. This model only considers
magnetization process by irreversible flipping of particles
into the direction of the applied field. When particles with
zero width are considered, a secondary peak appears at
Hc ¼ 0 (H ¼ Hr) and the main peak is shifted towards the
left [6]. Moreover, to have a physical meaning, P(Hc, Hb)
has to be positive-valued.
However, real systems exhibit a much more complex
magnetic response, resulting from magnetic interactions. In
the FORC analysis, the actual behavior of the material is
probed and those effects manifest themselves in the FORC
diagram, which is a real map of magnetic phenomena in a
material.
In our samples, the FORC distributions exhibited the
same two-branch structure observed by Pike et al. for a Ni
nanopillar array [9] and the splitting of the main
peak observed by Muxworthy et al. [8] and Dumas et al.
[22]. The most prominent peaks occurred for values of Hc
around the coercive field of each sample and for Hbo0.
This asymmetry is regarded as the effect of dipolar
inter-wire interactions [6]. The nanowire arrays are highly
dense, with high aspect ratio (450). It is expected that they
have a strong stray field at the surface, whose lines tend
to close into the neighboring wires [2]. Thus, each nanowire
experiences a demagnetizing effective interaction field.
We can also observe smaller sharp peaks for low values
of Hc. As any increase of magnetization in this region
is due to the rotation of low-coercivity particles, this
magnetization is predominantly reversible, yielding the
‘‘reversible ridge’’ near Hc ¼ 0 [7,9]. Negative r regions
can be also be observed in the diagram. In general,
they reflect the fact that in real systems r is not uniquely
determined by P(Hc, Hb) alone, but also depends on
the applied field and the magnetic history of the system
[6–9].
Fig. 3. (a) FORC distributions vs. Hb with Hc fixed at the main
irreversible peak and (b) mean local interaction field (Hint) and coercivity
vs. dm.
particles [6,8,22]. It represents the spread of the distri-
bution of bias fields Hb. So, the FWHM (Hint) was
measured for each sample and plotted in Fig. 3b, along
with the coercivity of each sample (HC), as functions of dm.
We can observe that both behaviors seem to be unison with
dm. It is showing that the intensity of the mean local
interaction field influences strongly the coercivity of the
sample.
5. Conclusions
From the FORC ‘‘fingerprints’’ obtained and based
on the extensive literature on the FORC analysis method
[2,7,8,10,21,22], we assert that our samples of Ni nano-
wire arrays do not reverse by coherent rotation alone.
A non-uniform reversal mode due to the coupling
among Ni grains also occurs, possibly curling [2,19].
Previous Mrev vs. Mirr curves analysis results for Fe
nanowires [20] also corroborate this statement. The
intensity of the mean local interaction field, determined
from the FORC distribution, influences the coercivity of
the sample.
Following Ref. [10], we show the behavior of r(Hc, Hb)
for (a) Hb ¼ 0 and (b) Hc ¼ 0 for three samples in Fig. 2. In
Fig. 2a, each sample exhibits a reversible peak at Hc ¼ 0
and an irreversible peak at Hc40. By comparing the
heights and the positions of the peaks, we can notice that
reversible processes are stronger in samples A and C than
in sample B. In sample C, these two peaks have almost the
same height. This sample has the largest mean diameter
and the most deformed pores, which can favor non-
uniform reversal modes and reversible components. In
Fig. 2b, we see the profile of the reversible ridges. The slight
asymmetry observed evidences the coupling between
reversible and irreversible components [7,9,20]. In
Fig. 3a, we plot r(Hb, Hc) vs. Hb, at the absolute maximum
of each FORC distribution, where the asymmetry towards
Hbo0 is stronger.
Realistic micromagnetic modeling can also bring com-
plementary knowledge about the magnetization reversal
mechanisms of magnetic nanowires. So, a more extensive
work regarding these approaches is under way.
Acknowledgments
We are thankful to Dr. Marcia Fantini for her support in
´
As several authors have pointed out, the vertical
FWHM of the FORC distribution can be regarded as a
measure of the mean local interaction field Hint among
the XRD characterization and Dr. David Heslop for
private communications. This work was supported by
CAPES, CNPq and FAPESP.

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