Magnetic properties of densely packed arrays of Ni nanowires
as a function of their diameter and lattice parameter
M. Va
´
zquez,
a)
K. Pirota, M. Herna
´
ndez-Ve
´
lez, V. M. Prida, D. Navas, R. Sanz,
and F. Batalla
´
n
Instituto de Ciencia de Materiales de Madrid, CSIC 28049 Madrid, Spain
J. Vela
´
zquez
CAI-XRD, Fac. C. Quı
´
micas, Univ. Complutense, 28040 Madrid, Spain
共Presented on 6 January 2004兲
High-quality densely packed hexagonal arrays of Ni nanowires have been prepared by filling
self-ordered nanopores in alumina membranes. Nanowires with different diameter d 共18–83 nm兲
and lattice parameter D 共65 and 105 nm兲 have been studied by atomic force, high resolution
scanning electron microscopies, Rutherford backscattering, and vibrating sample magnetometer
techniques. Axial loops coercivity and remanence decrease with increasing ratio diameter to lattice
parameter, r, until nanowires start to interconnect locally. Additionally, hysteresis of in-plane loops
increases with packing factor. In order to interpret the experimental results, multipolar magnetostatic
interactions among nanowires with increasing ratio r are considered. © 2004 American Institute of
Physics. 关DOI: 10.1063/1.1687539兴
I. INTRODUCTION: PREPARATION AND STRUCTURE
CHARACTERIZATION OF Ni NANOWIRE
ARRAYS
Studies on highly ordered arrays of magnetic nanowires
are recently attracting a growing interest. This ordering, to-
gether with the intrinsic nature of the nanomagnets, gives
rise to outstanding cooperative properties different from bulk
and even from film systems.
1,2
Arrays of magnetic nanowires
can be produced, among other techniques,
3
using nanoporous
alumina membranes as templates. Highly ordered hexagonal
symmetry is induced by the self-ordering process of nano-
pore formation. Arrays of nanowires typically 20–200 nm in
diameter, around 1000 nm long and separated 30–200 nm
are very suitable systems for micromagnetic studies and for
potential technological applications.
Studies on general magnetic behavior have been re-
ported on arrays of nanowires of Fe, Ni, Co, and their
alloys.
4–6
Individual Ni and Fe nanowires are taken in a first
approximation to be single-domain with longitudinal magne-
tization mainly due to shape anisotropy. Magnetization rever-
sal by curling rotational model combined with nucleation-
propagation processes for nanowires with diameter in the
range of around 50–400 nm has been proposed for indi-
vidual nearly noninteracting nanowires. In the case when the
wire diameter d is smaller than the exchange correlation
length 共for Fe, Co, and Ni it lies in the order of 10–50 nm兲,
magnetization should reverse at unison by coherent rotation.
Nevertheless, some discrepancies have been found regarding
those expectations. The determination of actual closure struc-
tures at the ends and of the nonaxial components of magne-
tization seem to be rather important to acquire deeper knowl-
edge of the reversal process. Finally, magnetostatic
interactions between nanowires should play a determinant
role, specially in the case of densely packed arrays.
A first objective of this work has been the controlled
production of densely packed highly ordered nanowire ar-
rays. As discussed previously,
7,8
a deep understanding of
how strongly nanowires are magnetically coupled is quite
important since it would determine, for example, the size of
magnetic bits of information for magnetic storage. Here, we
study in further detail the importance of magnetostatic inter-
actions in the arrays, introducing the influence on the mag-
netic behavior of geometrical characteristics particularly for
the case when nanowire diameter d reaches values compa-
rable to interwire distance D.
Nanoporous alumina membranes with hexagonal order-
ing have been prepared by a two-step anodization process.
6,9
Nanopores form by self-assembling process, and parameters
of first anodization determine the ordering degree of final
pore arrays and the interpore distance. The time of the sec-
ond anodization process determines the length of nanopores,
and their diameter can be finer controlled by subsequent
treatment in phosphoric acid. For the present work, diameter
of nanowires, as determined by AFM and HRSEM tech-
niques, ranges between 18 and 33 nm for interwire distance
of 65 nm employing sulphuric acid as electrolytic bath, and
between 35 and 83 nm diameter for interwire distance of 105
nm using oxalic acid as bath. Treatments in phosphoric acid
to increase the pore diameter in both series of membranes
lasted until 30 and 20 min, respectively. For longer treat-
ments, the arrays deteriorate as nanopores start to intercon-
nect locally.
Nanopores are afterwards filled with Ni by electrodepo-
sition with alternating pulse voltage technique. Figure 1
shows a HRSEM image showing a surface polydomain
structure. Long range order of nanowires is deduced from the
fast Fourier transform 共see inset兲 which has been taken from
a very large area of the real image 共about 24
m
2
). The
a兲
Electronic mail: mvazquez@icmm.csic.es
JOURNAL OF APPLIED PHYSICS VOLUME 95, NUMBER 11 1 JUNE 2004
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control of nanopore filling is performed by Rutherford back-
scattering technique, RBS.
10
Figure 2共a兲 shows the RBS ex-
perimental results. The observed sharp peak denotes a Ni
excess on the surface of the sample 共which is later removed
by careful polishing兲. The Ni filling of the pores is observed
just to the left side of that peak. Figure 2共b兲 shows the atomic
composition profile analyzed from the surface to the bottom
of the sample. This figure confirms the Ni overflow on the
membrane surface, as well as a continuously increasing Ni
content when approaching the bottom. In a first approach we
consider that the increasing yield to lower energies 关up to
channel 782, see Fig. 2共a兲兴 could be due to a partial lack of
fully filling of some nanopores. A complete interpretation of
this kind of spectra is introduced elsewhere.
10
The final op-
timization of the geometrical quality of the array includes a
polishing of the membrane surface to remove the Ni over-
flowing and an ion-beam etching of its bottom after alumi-
num substrate removing, to eliminate the dendrites accumu-
lated during the pores formation.
II. MAGNETIC BEHAVIOR AND ITS ANALYSIS
Magnetic characteristics of the nanowire arrays have
been measured by VSM magnetometer at room temperature.
From the longitudinal and in-plane hysteresis loops magnetic
parameters such as remanence, coercivity, or susceptibility
are evaluated. The existence of an effective longitudinal
magnetic anisotropy 共parallel to the nanowire axis兲 can be
checked by comparing longitudinal and transverse 共in-plane
of the membrane兲 hysteresis loops. For example, from the
loops for an hexagonal array of Ni nanowires 35 nm in di-
ameter and 105 nm in lattice parameter, an effective axial
magnetic anisotropy is deduced with anisotropy field of
around 2.5 kOe. That allows us to consider in a first approxi-
mation individual nanowires in such array to be nearly single
domains.
Figure 3共a兲 shows the longitudinal hysteresis loops for
nanowires ranging in diameter between 35 and 83 nm in an
array with lattice parameter of 105 nm. The dependence of
coercivity and remanence of the loops on the ratio of nano-
wire diameter to lattice parameter, r⫽ d/D, is shown in Fig.
3共b兲. As it can be observed, both magnitudes decrease with
increasing ratio r. A similar behavior is observed for the
series of nanowires with 65 nm lattice parameter ranging in
diameter between 18 and 33 nm.
In order to interpret this behavior, let us analyze the
influence of the increasing diameter of the nanowires. As the
diameter increases, nanowires effectively approach each
other since the interwire distance is kept constant, and con-
sequently they start to get magnetostatically coupled.
8,11
Magnetostatic interactions favor an antiparallel distribution
of magnetization in neighboring nanowires. For nanowires
initially magnetized in the same direction, the increase of
magnetostatic interaction results in the magnetization rever-
sal of N nanowires. Assuming that the reversal of an indi-
vidual nanowire produces a decrease of magnetostatic energy
E
v
that equals the magnetic anisotropy barrier ⌬E, the mac-
roscopic coercivity will be:
11
H
C
⫽
2K
0
M
S
冋
1⫺
冉
N
兩
E
v
兩
K
冊
1/2
册
, 共1兲
where 2K/
0
M
s
denotes the intrinsic coercivity due to the
magnetoelastic or magnetocrystalline anisotropies, K, and
E
v
the magnetostatic interaction between two nanowires.
Such interaction has been derived considering each nanowire
to be homogeneously magnetized, due to their uniaxial mag-
netic anisotropy, with magnetic charges at both ends,
⫽ /M/. This interaction energy, including multipolar compo-
nents, has an expression E
v
⫽ (
0
/8
)M
1
M
2
(D/L)r
2
关
1
⫺
关
1⫹ (L/D)
2
兴
⫺ 1/2
兴
共valid for d/LⰆ 1, L being the length of
the nanowires and M
i
the axial component of magnetization
in each nanowire.
8,12
兲 Thus, according to Eq. 共1兲, a linear
reduction of coercivity with the parameter r is expected.
Nevertheless, as observed in Fig. 3共b兲, the evolution of co-
ercivity loses linearity for the larger value of r seemingly as
a consequence of a modification of the reversal mode due to
an effective change of the magnetization easy axis from axial
FIG. 1. Real surface HRSEM image of a nanoporous alumina membrane.
The inset shows the FFT calculated of a large (24
m
2
) area of the
nanoporous membrane image.
FIG. 2. 共a兲 Experimental 共4087 keV radiation兲 RBS spectrum in a mem-
brane with Ni overflow on its surface. 共b兲 Profile of atomic composition in
% calculated from the spectrum in 共a兲.
FIG. 3. 共a兲 Longitudinal hysteresis loops as a function of the nanowire
diameter for Ni nanowires separated 105 nm having diameters in the range
from 35 to 83 nm. 共b兲 Dependence of coercivity 共filled symbols兲 and rema-
nence 共unfilled symbols兲 as a function of the ratio d/D for the series of
membranes prepared in oxalic and sulphuric acids.
6643J. Appl. Phys., Vol. 95, No. 11, Part 2, 1 June 2004 Va
´
zquez
et al.
Downloaded 26 Feb 2010 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
to in plane of the membrane. Although derived in a different
way,
13
a similar behavior is expected considering the depen-
dence of the effective shape anisotropy with the packing den-
sity, H
Sh
⫽ M
s
关
1-(
/3
1/2
)r
2
兴
.
Additional information is supplied from in-plane hyster-
esis measured for all the nanowire arrays of the series men-
tioned above. The shape of the loops shown in Fig. 4 evolves
with the ratio r indicating that the magnetization easy axis
gradually rotates towards an in-plane direction. Particularly,
coercivity remains almost constant 共around 180 Oe兲 with the
increasing diameter but for the most dense array 共260 Oe兲.
It should be mentioned that a final increase of longitudi-
nal coercivity and remanence has been observed for the case
when long treatment in phosphoric acid makes nanopores to
locally interconnect giving rise finally to collapse into a con-
tinuous film. For low density of nanowires, individual
nanowires can be approached to be single-domain structured
due to shape anisotropy. In this case, the magnetostatic inter-
action, being relatively weak, simply determines a reduction
in remanence and coercivity. As the ratio r⫽ d/D becomes
large enough, the effective easy axis rotates from axial to
transverse direction in the plane of the membrane. In this
case, the nearly single domain structure of nanowires con-
verts to multidomain and finally the magnetization process is
modified. Similar effects have been analyzed in cylindrical
dots.
11
III. CONCLUSIONS
Densely packed arrays of Ni nanowires embedded in po-
rous alumina membranes have been prepared and structurally
characterized. Their high ordering degree with hexagonal
symmetry of nanopores and their filling have been carefully
studied. We report on the magnetic behavior of arrays of Ni
nanowires for various diameter: and lattice parameter of the
hexagonal symmetry array. It is experimentally found that
both coercivity and remanence decrease with diameter to lat-
tice parameter ratio. Results are discussed considering the
increasing multipolar magnetostatic interactions within the
array as the ratio r increases.
ACKNOWLEDGMENTS
The authors wish to thank Dr. K. Nielsch, Dr. F. Paszti,
and Dr. A. Climent for analysis of results. The work was
supported by the Autonomous Community of Madrid under
Project No. CAM2002-0405.
1
D. Appell, Nature 共London兲 419,553共2002兲.
2
See, J. Magn. Magn. Mater. 249 共2002兲.
3
J. I. Martı
´
n, J. Nogue
´
s, K. Liu, J. L. Vicent, and I. K. Schuller, J. Magn.
Magn. Mater. 256, 449 共2003兲.
4
D. J. Sellmyer, M. Zheng, and R. Skomski, J. Phys.: Condens. Matter 13,
R433 共2001兲.
5
P. M. Paulus, F. Luis, M. Kro
¨
ll, G. Schmid, and L. J. de Jongh, J. Magn.
Magn. Mater. 224, 180 共2001兲.
6
K. Nielsch, R. B. Wehrspohn, J. Barthel, J. Kirschner, S. F. Fischer, H.
Kronmu
¨
ller, T. Schweinbo
¨
ck, D. Weiss, and U. Go
¨
sele, J. Magn. Magn.
Mater. 249, 234 共2002兲.
7
M. Va
´
zquez, K. Nielsch, P. Vargas, J. Vela
´
zquez, D. Navas, K. R. Pirota,
M. Herna
´
ndez-Ve
´
lez, E. Vogel, J. Cartes, R. B. Wehrspohn, and U. Go
¨
s-
ele, Physica B 343, 395 共2004兲.
8
J. Vela
´
zquez, K. R. Pirota, and M. Va
´
zquez, IEEE Trans. Magn. 39,3049
共2003兲.
9
K. R. Pirota, D. Navas, M. Herna
´
ndez-Ve
´
lez, K. Nielsch, and M. Va´zquez,
J. Alloys Compd. 共to be published兲.
10
M. Va
´
zquez et al., Invited at SMM’03 Conf., Du
¨
sseldorf, 2003, M.
Herna
´
ndez-Ve
´
lez et al. 共unpublished兲.
11
K. Yu. Guslienko, Phys. Lett. A 278, 293 共2001兲; W. Scholz, K. Y. Gus-
lienko, V. Novosad, D. Suess, T. Schrefl, R. W. Chantrell, and J. Fidler, J.
Magn. Magn. Mater. 266, 155 共2003兲.
12
J. Vela
´
zquez, D. Laroze, P. Vargas, and M. Va
´
zquez 共unpublished兲.
13
A. Encinas-Oropesa, M. Demand, L. Piraux, I. Huynen, and U. Ebels,
Phys. Rev. B 63, 104415 共2001兲.
FIG. 4. Transverse hysteresis loops as a function of the nanowire diameter
for Ni nanowires separated 105 nm having diameters in the range from 35 to
83 nm.
6644 J. Appl. Phys., Vol. 95, No. 11, Part 2, 1 June 2004 Va
´
zquez
et al.
Downloaded 26 Feb 2010 to 161.111.180.191. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp
