1. ARTICLE IN PRESS
Physica B 354 (2004) 195–197
www.elsevier.com/locate/physb
Self-organized nanowires: evidence of dipolar interactions
from ferromagnetic resonance measurements
C.A. Ramosa,Ã, E. Vasallo Brignetib, M. Vazquezc
´
a
Instituto Balseiro, Universidad Nacional de Cuyo and Centro Ato´mico Bariloche, Comisio Nacional de Eenrgıa Ato
´n ´ ´mica. Av. Ezequiel
´
Bustillo 9500,8400 San Carlos de Bariloche, Rıo Negro, Argentina
b
Pontificia Universidad Cato´lica de Peru Av. Universitaria cdra 18, San Miguel, Lima, Peru
´, ´
c
Instituto de Ciencia de Materiales, CSIC, 28049 Madrid. Spain
Abstract
We present ferromagnetic resonance (FMR) results on dense hexagonal arrays of Ni nanowires (NW) performed at
34 GHz. The measurements show that the angular variation of the resonance field follows an uniaxial anisotropy law, as
expected from the shape of the individual wires. However, the magnitude of the effective anisotropy clearly indicates
that the effect of dipolar interaction between the wires amounts to a decrease of nearly 20% of the single-wire
anisotropy, 2pM s : Also, the angular variation of the FMR linewidth indicates that the NW are very well aligned and
reflects anisotropy variations which correlate with the array long-range order.
r 2004 Elsevier B.V. All rights reserved.
PACS: 75.75.+a; 76.50.+g; 75.30.Gw
Keywords: Ni nanowires; Dipolar interactions; Ferromagnetic resonance; Sharpe anisotropy
1. Introduction wires can be electrodeposited into self-organized
porous alumina templates to create large areas or
The study of artificial arrays of magnetic ordered nanowires, typically with radii
nanostructures has steadily increased in the last r$10–30 nm, 1–10 mm length, and spacing between
decades, impelled by the need for new devices, the the wires $100 nm. The alumina pore array can be
technological capabilities to fabricate such struc- varied with the anodization characteristics allow-
tures, and the need to understand their behavior. ing to change slightly the pore-diameter, their
In particular, hexagonal arrays of metallic nano- separation, overall order and wire length. As a
consequence, we can study magnetic nanowire
ÃCorresponding author. Fax: +54 2944 445299. arrays subject to these variations. One of the most
E-mail address: cramos@cab.cnea.gov.ar (C.A. Ramos). important parameters to characterize the sample is
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2004.09.047

2. ARTICLE IN PRESS
196 C.A. Ramos et al. / Physica B 354 (2004) 195–197
its anisotropy field, H A : H A is usually estimated
from magnetization measurements or determined
from ferromagnetic resonance (FMR) data.
In this work, we present FMR measurements on
three samples of Ni NW arrays having wires of
typical size $30–40 nm with interwire-distances of
$90–110 nm and NW lengths of 0.66, 1.05 and
2.3 mm (named S1, S2 and S3, respectively) as
determined from magnetization measurements
assuming bulk magnetization (MS=485 emu/cm3)
and a filling factor ($0.10) estimated from atomic
force microscopy (AFM) scans on a 1 mm2 area.
Room temperature FMR experiments were
performed at 34.0 GHz.The FMR angular varia-
tion can be well described by
Fig. 2. Peak-to-peak line width as a function of the applied
ðo=gÞ2 ¼ ½H R cosðj À jH Þ þ H A cos2 ðjÞŠ field direction.
 ½H R cosðj À jH Þ þ H A cosð2jÞŠ; ð1Þ
where o ¼ 2pn; n ¼ 34 GHz; g ¼ gmB =_ is the
giromagnetic ratio, H R is the resonance field, j fit of H R to Eq. (1) give: HA=2.56(8), 2.46(4), and
is the angle between the magnetization equilibrium 2.09(20) kOe. These results indicate a systematic
direction (determined self-consistently at H R ) and decrease of H A on going from sample S1 to S3.
the easy axis, and jH is the applied field direction In Fig. 2, we plot the observed peak-to-peak line
measured from the easy axis. Fig. 1 shows the width, DH. As it is observed from Fig. 2 DH has
angular variation of H R as a function of jH and two maxima, one in the parallel direction and
the fit to Eq. (1) using H A and g as parameters. another in the perpendicular direction, with a
The results from the fit yield g=2.16(2), 2.19(1), minimum at intermediate angles.
and 2.15(3) for samples S1, S2 and S3, respectively.
These values are close to values reported pre-
viously [1]. The results from the angular variation 2. Discussion
The uniaxial anisotropy observed is mainly due
to the wire shape. However, the shape anisotropy
2pMS=3.05 kOe, is larger than the anisotropy
measured by $0.5–1.0 kOe. Dipolar interactions
between the wires oppose the shape anisotropy.
Assuming a regular array of nanowires saturated
along the easy axis we can calculate the magnitude
of the effective field produced by the neighbouring
wires at a central ‘‘test’’ wire. The calculated
magnetic field produced by the neighbouring
points opposite to the magnetization. At the centre
of this test wire the dipolar field can be approxi-
mated, within 1%, by the magnitude H d ¼
À4pM S f, where f is the filling factor. The filling
factor can be expressed in terms of the interwire
Fig. 1. Observed angular variation of the resonance field. The separation, S, and nanowire radius, r, as f ¼
p
lines are non-linear least-square fits using Eq. (1). 2pr2 = 3S2 : The dipolar field produced by the

3. ARTICLE IN PRESS
C.A. Ramos et al. / Physica B 354 (2004) 195–197 197
neighbours at the centre of this ‘‘test’’ wire is thus discarding any significant misalignment of the
independent of the nanowire length. Therefore, the wires, which is corroborated from SEM pictures
anisotropy field can be expressed as obtained from the sample edges, which indicate
H A ¼ 2pM S ð1 À 2f Þ: (2) extremely straight Al2O3 columns. Clearly, a better
determination of the filling factor is necessary in
Eq. (2) indicates that the effective anisotropy order to draw definite conclusions regarding the
changes only due to the saturation magnetization validity of Eq. (2). Secondly, the variation of H A
and the nanowire array filling factor. in terms of variations of the Ni wire size and inter-
The fact that this calculation does not approach, spacing would give an anisotropy variation due to
for f-1, the limit of a thin film (HA=À4pMS) is a local variations in the dipolar fields which would
consequence of the wires preserving its shape reflect in a larger DH having maxima in the
anisotropy (2pMS), and therefore implies that they parallel and perpendicular directions. This indeed
do not contact each other. Previously [2], we is found to be the case, as shown in Fig. 2.
quoted a mean-field result that leads to HA=2pMS Furthermore, we would expect a larger line width
(1–3f) [3], yet our calculations indicate that Eq. (2) in the more disordered arrangement (S1), which is
is the correct form for non-contacting nanowires. also found. Something puzzling, however, is that
Preliminary atomic force microscopy character- we would expect a larger DH along the parallel
ization indicate that the short-range hexagonal direction in all the cases, and roughly a half along
ordering changes. We find that S1 is the less- the perpendicular direction. The only sample that
ordered arrangement, S2 posses intermediate order has a smaller line width along the perpendicular
and S3 sample is the most ordered reaching direction is sample S3, which is the most ordered
1–10 mm2. Also the inter-wire separation changes arrangement, and the angle-dependent DH is
systematically as follows: S1=92714 nm, roughly 2:1, as expected.
S2=102710 nm, and S3=109710 nm.The wire In conclusion, FMR shows that dipolar inter-
diameters are more difficult to determine with this actions are important in determining the final
technique, yet it seems to increase along series, anisotropy field and its variation in nanowire
changing from 3177 to 3774 nm for samples S1 arrangements.
and S3, respectively. Both, wire size and inter-wire
separation increase on going from S1 to S3. The
filling factors calculated are 0.10370.03 and
0.10670.015 for the S1 and S3 samples, respec- Acknowledgements
tively. The average anisotropy field calculated
using these f values and Eq. (2) yield HA(calc) This work was partially supported by an
$2.4 kOe for both samples, close to the observed International CSIC-CONICET (Spain-Argentina)
HA. and by a ANPCyT PICT 2626 (2003) grants.
If in fact FMR can effectively distinguish the
subtle structural differences between the arrays
studied it could be used as a characterization tool. References
That this may be the case is reaffirmed by two
facts. Firstly, we observe a clear minimum in the [1] U. Ebels, J-L. Duvail, P. E. Wigen, L. Piraux, L.D. Buda,
three angular variations of DH which point to the K. Ounadjela. Phys. rev. B 64 (2001)144421 and references
fact that the wires are very well aligned. Indeed, if there in.
[2] C.A. Ramos, M. Vazquez., K. Nielsch, K. Pirota J. Rivas,
DH would be originated in a misalignment of the
´
R. Wherspohn, M. Tovar, R.D. Sanchez, U. Gosele, ¨
wires then this would traduce in a maximum at J. Mag. Mag. Mater 272–276 (2004) 1652.
intermediate angles at which dH=dj is largest, [3] A. Encinas, M. Demand, L. Vila, L. Piraux, App. Phys.
that is, near j ¼ 501: Just the opposite is observed, Lett. 81 (2002) 2032.