Length dependence of coercivity in CoFe2 nanowire arrays with high aspect ratios

Article abstract of DOI:10.1016/j.jallcom.2010.06.086

CoFe₂ nanowires with high aspect ratios were electrodeposited into the anodic aluminum oxide (AAO) template. The coercivities and remanence measured along the longitudinal axis of the nanowires are found to increase with the length of nanowires. The magnetostatic interaction between the nanowires is responsible for the decrease of coercivity and remanence of an array of nanowires as compared to an isolated single nanowire. By considering the magnetostatic interaction between the nanowires, a simple model as a function of length is used to calculate the coercivity in an array of the nanowire and this model shows good agreement with experimental data.

Full text of DOI:10.1016/j.jallcom.2010.06.086

Journal of Alloys and Compounds 505 (2010) 609–612
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jallcom
Length dependence of coercivity in CoFe2 nanowire arrays with high aspect ratios
S.L. Lima, F. Xub, N.N. Phuocb, C.K. Onga,∗
a Physics Department, National University of Singapore, Singapore 117542, Singapore
b Temasek Laboratories, National University of Singapore, Singapore 117411, Singapore
a r t i c l e i n f o
a b s t r a c t
Article history:
CoFe2 nanowires with high aspect ratios were electrodeposited into the anodic aluminum oxide (AAO)
template. The coercivities and remanence measured along the longitudinal axis of the nanowires are
found to increase with the length of nanowires. The magnetostatic interaction between the nanowires
is responsible for the decrease of coercivity and remanence of an array of nanowires as compared to an
isolated single nanowire. By considering the magnetostatic interaction between the nanowires, a simple
model as a function of length is used to calculate the coercivity in an array of the nanowire and this model
shows good agreement with experimental data.
Received 4 December 2009
Received in revised form 10 June 2010
Accepted 12 June 2010
Available online 25 June 2010
Keywords:
CoFe2 nanowires
AAO template
Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.
Magnetostatic interaction
Coercivity
Length dependence
1. Introduction
magnetostatic interactions considered, previous works have well
interpreted the decreases of coercivity and remanence of nickel
Highly ordered arrays of magnetic nanowires have poten-
tial applications in new magnetic devices and particularly in
recording media [1,2]. The high ordering and intrinsic nature of
the nanomagnets give rise to outstanding cooperative properties
which are of fundamental and technological interest [3]. As a
result, the magnetic properties of magnetic nanowires have been
widely researched on. Electrodeposition of magnetic nanowires
into anodic aluminum oxide (AAO) template is one of the most
popular approaches to fabricate magnetic nanowires. This method
offers many advantages, such as low cost, high yield and fine control
over the length and diameter of the nanowires [4].
Studies on general magnetic behaviors have been reported on
nanowire arrays of Fe, Ni, Co and their alloys [5–7]. The mag-
netic properties of the nanowires are governed by two factors,
the magnetic nature of the individual nanowire and the magne-
tostatic interactions between the nanowires. The magnetic nature
of individual nanowire is influenced by the longitudinal uniaxial
shape, magnetocrystalline and magnetoelastic anisotropies. The
magnetostatic interaction originates from unbalanced magnetic
poles at both ends of individual wires generating stray fields that
couple with the magnetization of neighboring nanowires. Magne-
tostatic interactions can reduce the switching field of the nanowires
as compared to the non-interacting array of nanowires. With
nanowire arrays with the increase of diameter of the nanowires
while their interpore distance is kept constant [8,9].
In this paper, we investigate the length dependence of the coer-
civity of CoFe2 nanowire arrays which have the high aspect ratios
ranging from 200 to 1000. Few experimental works have been car-
ried on this issue in detail and in this range of aspect ratio [10,11].
The coercivity of the nanowires in this work cannot be explained
based on the assumption of non-interacting nanowires. The magne-
tostatic interaction between the nanowires is included to account
for the length dependence of the nanowire arrays. A simple model
based on the influence of the effective magnetostatic energy is used
to calculate the coercivity of the nanowires and the calculation with
this model shows a good agreement with experimental data.
2. Experiment
The AAO templates were prepared from aluminum foil by one-step anodization
technique. The aluminum foils were cleaned by ultrasonic in acetone and distilled
water before they were annealed in furnace for 6 h at 500 ◦C. Then, the annealed alu-
minum foils were electropolished at 20 V for 2 min in a solution consisting of ethanol
and perchloric acid at a ratio of 5:1. The electropolishing was carried out at temper-
ature of 5 ◦C. After this treatment, the aluminum foils were anodized at 25 V in 0.4 M
H2SO4 at 10 ◦C to form AAO template. The lengths of the AAO templates were varied
from 7 ␮m to 35 ␮m by using different anodizing time. The pore diameter and the
distance between two nearest pores of the AAO template were kept constant. The
AAO templates were immersed in 0.3 M H3PO4 for 15 min at 40 ◦C to widen the pore
and to thin down the barrier layer so that it was suitable for AC electrodeposition.
CoFe2 nanowires were deposited into AAO templates by AC electrodeposition. The
electrolyte used in the AC electrodeposition consisted of 0.073 M CoSO4, 0.0147 M
FeSO4, 0.6 M boric acid and 1 g/L of ascorbic acid. Deposition was carried out at room
temperature with an AC voltage of 16 V, 100 Hz using graphite rod as counter elec-
∗
Corresponding author. Tel.: +65 65162984; fax: +65 67776126.
E-mail address: phyongck@nus.edu.sg (C.K. Ong).
0925-8388/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2010.06.086

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S.L. Lim et al. / Journal of Alloys and Compounds 505 (2010) 609–612
Fig. 1. XRD pattern of the CoFe2 nanowires embedded in the AAO template with
the aluminum removed.
trode. The current of the deposition was monitored during the deposition. Initially,
the current fell sharply and then remained stable. The deposition of the nanowires
was stopped when there was an increase in the current, indicating that some of the
nanowires were growing out of the AAO template.
The microstructure of the AAO template and nanowires were observed by scan-
ning electron microscopy (SEM) and by transmission electron microscopy (TEM),
respectively. The length of AAO template was measured by cutting the AAO tem-
plate with a pair of scissor for the SEM side view of the template. In order to measure
the length of CoFe2 nanowires deposited in the AAO template, the AAO template was
first etched in a solution of 6 wt% H3PO4 and 1.8 wt% CrO3 at 40 ◦C until the tip of the
nanowires were exposed. Then the AAO template filled with CoFe2 nanowires was
cut with a pair of scissor for the SEM side view. To liberate the nanowires from the
templates for TEM studies, the AAO template was dissolved in 1 M NaOH. After this,
the solution was washed carefully with distilled water for several times, and then a
drop of suspension was dropped on a copper grid coated with carbon film for TEM
observation. The phase structure of the nanowires was investigated by X-ray diffrac-
tion (XRD) with Cu K␣ radiation and selected area electron diffraction (SAED) of
the TEM. Prior to the XRD measurement, the aluminum was removed from the AAO
template embedded with CoFe2 nanowires using CuCl2 solution. The magnetic prop-
erties of the nanowires were measured by vibrating sample magnetometer (VSM)
with the applied field parallel to the long axis of wires.
3. Results and discussions
The crystallographic structure of the CoFe2 nanowires was
examined using the XRD. Fig. 1 displays the typical XRD spectra
of the electrodeposited CoFe2 nanowires embedded in the AAO
template. CoFe2 nanowires exhibit body-centered cubic structure
with a preferred texture orientation of [1 1 0] along the long axis of
nanowires.
The SEM image of the AAO template is shown in Fig. 2(a). And it
shows that the average pore diameter pore is 32 nm and the inter-
pore distance (D) is 65 nm. The SEM top view of 21 ␮m long AAO
template deposited with CoFe2 nanowires which has been etched
in a solution of 6 wt% H3PO4 and 1.8 wt% CrO3 at 40 ◦C is presented
in Fig. 2(b). Clearly the tips of the nanowires are exposed from
etching of the AAO template. The corresponding SEM side view of
the same AAO template filled with CoFe2 nanowires is shown in
Fig. 2(c). Fig. 2(c) shows that the length of the nanowires is about
20.5 ␮m which is close to the length of the AAO template in which
the nanowires is deposited. Fig. 2(d) shows the enlarged view of Fig.
2(c). Fig. 3 shows the TEM image of the CoFe2 nanowires freed from
the AAO template. The diameter of the CoFe2 nanowires (2R) is also
32 nm which is consistent with the average pore diameter of AAO
template. The polycrystalline structure of the CoFe2 nanowires was
confirmed by the multiple diffraction rings in the SAED of TEM.
Fig. 4(a) presents the magnetic hysteresis loops of the nanowire
arrays with the average nanowire length (L) varying from 7 ␮m
to 35 ␮m with the field applied parallel to the long axis of
nanowires. Fig. 4(b) shows the magnetic hysteresis loops of the
nanowire arrays with the field applied perpendicular to the long
Fig. 2. (a) SEM Picture of the top view of the AAO template fabricated. (b) The SEM
top view of 21 ␮m long AAO template deposited with CoFe2 nanowires which has
been etched in a solution of 6 wt% H3PO4 and 1.8 wt% CrO3 at 40 ◦C. (c) The corre-
sponding SEM side view of the same AAO template filled with CoFe2 nanowires. (d)
The enlarged SEM view of (c).

S.L. Lim et al. / Journal of Alloys and Compounds 505 (2010) 609–612
611
Fig. 5. Coercivity of the nanowires as a function of length. The red line represents
the LLG simulation result of the coercivity of an isolated nanowire. The green line
represents the coercivity in an array of CoFe2 nanowires calculated using Eq. (1).
The black dots are the experimental results of coercivity measured by VSM. (For
interpretation of the references to color in this figure legend, the reader is referred
to the web version of the article.).
Fig. 3. TEM picture of the CoFe2 nanowires freed from the AAO template with the
inset showing the SAED of the CoFe2 nanowires.
magnetization of CoFe2 nanowires (Ms) is 1930 emu/cm3 and the
exchange constant is 2.5 × 10−11 J/m. Since the CoFe2 nanowire has
a polycrystalline structure, the crystalline anisotropy energy is cho-
sen to be zero. The coercivity of a long wire with large radius can
also be predicted from curling mode [12], H0 = cA/ꢀ0MsR2 and is
calculated to be 3430 Oe. However, the coercivity of a long wire
from the simulation is 3025 Oe which is much lower than that pre-
dicted by the curling mode. Fig. 5 presents the experimental and
simulation results of length dependence of coercivity. Clearly, the
shape anisotropy of an isolated nanowire cannot account for the
trend of increasing coercivity with the length at high aspect ratio
ranging from 200 to 1000.
axis of nanowires. The comparison of these loops clearly shows
the increase of coercivity with the length. The magnetic prop-
erties of an isolated nanowire have been also studied with the
micromagnetism simulation based on the Landau–Lifshitz–Gilbert
equation. LLG Micromagnetics SimulatorTM is used to simulate the
hysteresis loop of an isolated CoFe2 nanowire with applied field
parallel to the long axis of nanowire. The cell size is chosen to be
8 nm × 8 nm × 8 nm and the damping factor is 0.3. The saturation
In order to interpret this behavior, magnetostatic interaction
between the nanowires must be taken into consideration when
the distance between two nearest nanowires is comparable to the
diameter of a nanowire. Stray field generated from each nanowire
in the array will couple with the magnetizations of other nanowires.
This magnetostatic interaction favors an anti-parallel distribution
of magnetization in neighboring nanowires [8,13]. In an array with
all the nanowires initially magnetized in the same direction, the
magnetostatic interaction between neighboring nanowires favors
the reversal of some of them. Assuming the reversal of an individual
nanowire produces a decrease of magnetostatic interaction εEint(D)
that equals to the magnetic anisotropy barrier ꢁE of a nanowire,
the macroscopic coercivity will be:
ꢀ
ꢂ
ꢁ
εEint(D)
K1V
Hc = H0 1 −
(1)
where V represents the volume of a single nanowire and H0 is the
coercivity of an isolated nanowire, Eint(D) represents the magneto-
static interaction between two nanowires separated by distance
D. Such interaction has been derived by assuming the homoge-
nous magnetization in the direction along long axis of the wire
ꢃ
and has the expression Eint = ꢀ0Ms2R2/2DL[1 − (1/ 1 + L2/D2)]V
if the R/L ꢀ 1 [14]. Assuming that the each magnetic nanowire
is single domain and has the uniaxial shape anisotropy, mag-
netic anisotropy barrier will be given as ꢁE = K1V(1 − H/H0)2,
with the uniaxial shape anisotropy K1 = ꢀ0MsH0/2 [15]. Finally,
Fig. 4. (a) Hysteresis loops of the CoFe2 nanowires with length L varying from 7 ␮m
to 35 ␮m. The external field is applied parallel to the long axis of the nanowires. (b)
Hysteresis loops of the CoFe2 nanowires with the external field applied perpendic-
ular to the long axis of the nanowires.
the macroscopic coercivity as a function of L can be expressed as
ꢃ
Hc = H [1 − εMsR2/H DL(1 − (1 + L2/D2)−1/2)]. Moreover, ε is a
0
0
fitting parameter that depends on the distribution magnetic wires

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S.L. Lim et al. / Journal of Alloys and Compounds 505 (2010) 609–612
in space and on the long distance correlation among the wires. In
Eq. (1), both H0 = 3025 Oe which is obtained from the LLG simu-
lation and ε = 80 are used. Since the magnetostatic energy Eint(D)
decreases with length of nanowires, the coercivity in the array of
CoFe2 nanowires increases with the length of nanowires. The cal-
culated coercivity is presented in Fig. 5. It can predict the trend
observed in the experimental data and shows relatively good agree-
ment with experimental data. At lower shape ratio range, Vázquez
et al. studied the effect of length on the coercivity and observed that
there was almost a linear relationship between the coercivity and
length [10]. On the contrary, in dot arrays where 2R > L, a different
behavior is observed in which case the coercivity decreases with
increasing length [16].
array of nanowires. For longer length of nanowires, the strength of
magnetostatic interaction becomes weaker and thus the coercivity
and remanence increase. A simple expression as a function of mag-
netostatic interaction is used to obtain the coercivity in an array
of CoFe2 nanowires and shows relatively good agreement with the
coercivity measured by the VSM.
Acknowledgment
This research was financially supported by Defense Science and
Technology Agency of Singapore. And the authors would like to
acknowledge Dr. D.H. Wang and Prof. S.G. Yang for the instruction
of sample preparations.
Not only the coercivity of the nanowires increases with the
length of nanowires, the remanence (Mr/Ms) is also observed
to increase with the length of the nanowires from Fig. 5. This
can be explained by the length dependence of the magneto-
static interaction between the nanowires. As the length of the
nanowires interaction increases, the magnetostatic interaction
decreases. Thus the anti-parallel configuration between the magne-
tization states of the nanowires becomes less favorable and fewer
nanowires have their magnetization flipped in the opposite direc-
tion in zero applied field.
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In conclusion, we have fabricated CoFe2 nanowires with high
aspect ratios to investigate the effect of length on the coercivity
and remanence. From the VSM measurements, the coercivity and
remanence increase with the length of the nanowires. In order to
account for such a phenomenon, the effect of magnetostatic inter-
action between the nanowires due to the coupling of stray field with
the magnetization of nanowires must be included. This magneto-
static interaction will reduce the coercivity and remanence in the
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