Magnetic properties of arrays of electrodeposited nanowires

Article abstract of DOI:10.1016/S0304-8853(02)00531-0

The fabrication and magnetic properties of arrays of short nanowires are reviewed. The arrays consist of electrodeposited ferromagnetic cylinders with aspect ratios of up to 3 and diameters of 57-180 nm. Their hysteresis loops are characterized and their remanent states are related to the predictions of a three-dimensional micromagnetic model, which shows a transition from a single-domain 'flower' state to a lower-remanence 'vortex' state with increasing diameter. The shapes of the array hysteresis loops are governed by interactions between the particles. The switching fields of small Ni cylinders can be described using a dynamic micromagnetic model.

Full text of DOI:10.1016/S0304-8853(02)00531-0

Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
Magnetic properties of arrays of electrodeposited nanowires
a,
C.A. Ross *, M. Hwang , M. Shima , Henry I. Smith , M. Farhoud , T.A. Savas ,
a
a
b
b
c
d
d
d
e
W. Schwarzacher , J. Parrochon , W. Escoffier , H. Neal Bertram ,
f
F.B. Humphrey , M. Redjdal
f
a
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
b
c
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
d
H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK
e
University of California, San Diego, CMRR, 9500 Gilman Drive, La Jolla, CA 92093, USA
Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215, USA
f
Abstract
The fabrication and magnetic properties of arrays of short nanowires are reviewed. The arrays consist of
electrodeposited ferromagnetic cylinders with aspect ratios of up to 3 and diameters of 57–180 nm. Their hysteresis
loops are characterized and their remanent states are related to the predictions of a three-dimensional micromagnetic
model, which shows a transition from a single-domain ‘flower’ state to a lower-remanence ‘vortex’ state with increasing
diameter. The shapes of the array hysteresis loops are governed by interactions between the particles. The switching
fields of small Ni cylinders can be described using a dynamic micromagnetic model.
r 2002 Elsevier Science B.V. All rights reserved.
Keywords: Micromagnetics; Nanowires; Electrodeposition
1
. Introduction
because these may be useful as patterned recording
media [1–3]. In these arrays, both the magnetic
behavior of the individual elements and the
interactions between elements determine the hys-
teresis behavior of the array and its suitability for
data storage.
In this work, we will review the fabrication of
nanowire arrays and their magnetic properties.
Additional details have been presented elsewhere
[4,5]. The behavior of a range of nanowire arrays
agree well with predictions of remanent states and
switching fields based on two micromagnetic
models. Also, interactions between the particles
in the array are discussed; these affect the shapes
of the hysteresis loops. These results can be helpful
The last decade has seen considerable progress
in the lithographic patterning of small magnetic
structures. Simultaneously, increases in computa-
tional power have enabled three-dimensional
micromagnetic modelling to be carried out in
order to understand the remanent states and
reversal behavior of these structures. Of particular
interest is the behavior of closely spaced arrays of
magnetic ‘nanowires’ (prisms or cylinders) with
magnetization perpendicular to the sample plane,
*Corresponding author.
E-mail address: caross@mit.edu (C.A. Ross).
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 5 3 1 - 0

C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
201

202
C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
in the design of small magnetic elements for
patterned media and other applications.
the range 1:9oxo40 at% and 11oyo26 at% by
altering the composition of the electrolyte or the
current density [5]. The CoP was amorphous for
y > 15%: The Ni, Co and CoNi were polycrystal-
line with a grain size of approximately 10 nm. The
Co and CoNi were HCP with weak crystal-
lographic textures, while the Ni was FCC. The
only single-crystal samples were Ni-1 and Ni-2
from Table 1, which recrystallized during an
annealing process such that the [1 1 1] axis is
generally parallel to the length of the particles. The
Co and Ni were made using commercial electro-
lytes, and codeposition of impurities from the
electrolytes caused the saturation moment of the
Co and Ni samples to be smaller than that of the
pure metals. For the CoP and CoNi, saturation
moment increased with Co content.
2
. Sample fabrication
Large-area arrays of cylindrical particles were
fabricated using interference lithography com-
bined with electrodeposition [4–7]. The substrate
consists of a silicon wafer coated with a conductive
gold layer, upon which the template for electro-
deposition is formed. The template consists of a
polymer layer containing a square array of holes
with periodicity 100–200 nm and hole diameter of
5
7–180 nm. Magnetic material is electrodeposited
within the holes in the template, then the template
may be removed to leave an array of free-standing
cylinders with heights of up to 300 nm. Inter-
ference lithography is capable of patterning areas
of several square cm or greater with deep-
submicron features, and the samples are therefore
large enough for characterization by standard
magnetometry techniques.
3. Micromagnetic modelling
Remanent states of cylindrical particles were
calculated using a micromagnetic model based on
solution of the Landau–Lifschitz–Gilbert equa-
tions [6,8]. The particles are discretized into cubic
elements with sizes smaller than 0:5lex; where lex is
the exchange length given by OðAÞ=Ms: A is the
Table 1 summarizes the samples made during
this study. Most of the samples have aspect ratios
(
height/diameter) between 1 and 3. Samples were
made from Ni, Co, Co100ꢀxNix and Co100ꢀyPy
alloys using electrolytes summarized in Table 2.
The compositions of the two alloys were varied in
ꢀ
6
ꢀ1
exchange constant (taken as 10 erg cm ) and
Ms the saturation moment of the material.
Table 2
Composition of electrolytes used during sample electrodeposition
Electrolyte
Composition
pH
3.5
T (1C)
Current density
(
Voltage vs.
SCE
mA cmꢀ
)
3
Ni (commercial sulfamate)
Ni(SO
BO
3
3
NH
2
)
2
1.3 M
0.5 M
50
1–11
5.7
H
3
Co (commercial sulfamate)
CoNi (pyrophosphate)
Co(SO
BO
3
3
NH
2
)
2
1.3 M
0.7 M
3.5
10
30
30
H
3
CoSO
NiSO
4
50–170 mM
30–150 mM
1.0 M
ꢀ1.1
4
4 2 7
K P O
CoP (phosphate)
CoSO
CoCl
4
1.0 M
0.2 M
1.6
60
10–1000
2
H
H
3
PO
BO
3
12–120 mM
0.5 M
3
3

C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
203
Typically, the cylinder was discretized into 31
1.0
R=3
cubic elements across its diameter. Remanent
states were calculated for diameters of up to 6lex
and aspect ratios of up to 3.
R=2
R=1.5
0
0
0
.9
.8
.7
For particles with aspect ratios in the range 1–3,
two different remanent states were identified
depending on the diameter of the cylinder, shown
in Fig. 1. For small diameters, a ‘flower’ state is
observed in which the magnetization lies parallel
to the axis of the cylinder with a small radial tilt at
the top and bottom of the cylinder. The remanence
along the axis is very close to 1. As the diameter
increases, the magnetization begins to tilt in the
circumferential direction, starting at the ends of
the cylinder, to make a ‘vortex’ configuration. As
the vortex develops, the axial remanence decreases
gradually, but can still be quite high, especially for
high aspect ratio vortex-state cylinders. Fig. 2
shows the remanence as a function of cylinder
size. The transition between the flower and vortex
Flower
2
Vortex
4
1
3
5
6
7
8
Diameter/exchange length
Fig. 2. The axial remanence of cylindrical particles as
a
function of diameter, for three different aspect ratios of R ¼
1:5; 2 and 3. Above a diameter of 3:5l ; the vortex develops
and the remanence gradually decreases, more slowly at higher
aspect ratios.
ex
transition diameter increases if axial anisotropy is
present, but in the samples presented here,
magnetocrystalline anisotropy plays only a minor
role at room temperature because of the weak
crystallographic texture in the Co and CoNi, and
the low anisotropy in Ni. Similar flower–vortex
transitions have been calculated for cubic and
cuboidal particles [9,10].
states occurs at a diameter of 3:5l : This
ex
Further modelling showed that as the diameter
continues to increase, more complex multi-domain
states form and the remanence becomes close to
zero. Also, for aspect ratios below 1, in-plane
flower-state configurations become energetically
favorable. These cases are discussed elsewhere [4].
Switching fields of particles were calculated
using a dynamic micromagnetic model [11,12] in
order to compare with the measured coercivities of
the two smallest Ni samples, Ni-1 and Ni-2. In this
case the particle is modelled as a cylinder with a
rounded top, to better simulate the observed
shape, and is discretized into 5 cells across its
diameter and 12 cells in height. The model does
not account for thermally activated reversal, so
calculated switching fields should be compared
with data measured at low temperature. Since
samples Ni-1 and Ni-2 were single crystal, a cubic
anisotropy corresponding to the anisotropy of Ni
Fig. 1. Calculated magnetization patterns in cylinders. Arrows
represent magnetization vectors within the structure: (a) A
cylinder with aspect ratio 2.1 and diameter 3:6lex; showing a
flower state and (b) A cylinder with aspect ratio 2.1 and
diameter 6:1lex; showing a vortex state where the magnetization
has a circumferential component, especially near the ends of the
cylinder.
4
ꢀ3
at 4.2 K (K ¼ ꢀ120 ꢁ 10 erg cm , K ¼ 30ꢁ
1
2
4
ꢀ3
1
0 erg m ) was added to the model. This is
significant because the anisotropy of Ni increases
considerably and changes sign at low temper-
atures compared to its room-temperature

204
C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
value (K1 ¼ ꢀ4:5 ꢁ 10 erg cmꢀ3, K2 ¼ ꢀ2:3ꢁ
4
04 erg cm ), with the result that the [1 1 0]
ꢀ3
1
direction becomes the easy axis at low tempera-
tures.
4
. Experimental results
Magnetic force microscopy was used to image
the state of individual particles in the arrays. For
the smaller diameter particles, a clear dark or light
contrast was seen corresponding to each particle,
which is characteristic of an out-of-plane dipole
(
Figs. 3(a) and (b)). This was the case for the high
aspect ratio CoP and smaller diameter Ni samples.
The images suggest the presence of a flower state
or a high-remanence vortex state. The Ni samples
have diameters close to 3:5lex and are expected to
have flower-state magnetization, while the CoP
sample of Fig. 3(b) had an aspect ratio of 3 and a
diameter of 5:5lex and is expected to have a high-
remanence vortex state. Thus, in both the cases the
micromagnetic model predicts the existence of
high-remanence states, in agreement with the
observation. In contrast, the CoNi and Co
samples, which have much higher normalized
diameters of over 8l ; show no clear magnetic
ex
contrast (Fig. 3(c)), and neither did the largest Ni
sample with aspect ratio 1.4 and diameter 6lex:
For these geometries the model predicts low
remanence.
Vibrating sample magnetometry was used to
measure room-temperature hysteresis loops of the
arrays. Data are shown in Table 1 and Fig. 4. The
small diameter Ni particles showed high coercivity,
sheared hysteresis loops in the out-of-plane direc-
tion, and in-plane loops characteristic of a hard
axis. This is expected from an array of interacting
dipoles or magnetized prisms, in which magneto-
static interactions lead to shear in the out-of-plane
Fig. 3. Magnetic force microscope images of three arrays: (a)
Sample Ni-4; (b) sample CoP-5 and (c) sample Co-4. The first
two samples show contrast characteristic of out-of-plane
dipoles, whereas the third shows very little contrast. In each
case the rows of cylinders run at 451 to the edges of the images
and the scale bars are printed parallel to the rows.

C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
205
Fig. 4. Micrographs of four samples and the corresponding hysteresis loops. IP represents the loop measured with the field in plane
and OP represents the loop measured out of plane. The magnetizations are normalized to the saturation moment: (a) Sample Ni-6;
(b) Ni-4; (c) Ni-13 and (d) CoP-5.
hysteresis loop. The maximum interaction field in
a square array is given by 9Hi where Hi is the
nearest-neighbor interaction field [13]. The sam-
ples had coercivities of 220–710 Oe, which is
relatively high compared to the nearest-neighbor
interaction fields, and the hysteresis loop therefore
shows high remanence. However, if the interaction
field between nearest neighbors is large compared
to the coercivity, as was the case for samples such
as CoP-5 (Figs. 3(b) and 4(d)), then the interac-
tions are strong enough to demagnetize the array
leading to a low net remanence, even though the
individual particles still have high remanence as
seen by magnetic force microscopy.
Interactions between high-remanence particles
can be modelled by treating them as interacting
prisms with a Gaussian distribution of switching
fields [13–15]. This is a better approximation than

206
C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
treating the particles as ideal dipoles, since the
dipole calculation overestimates the interactions
between closely spaced particles. Excellent agree-
ment has been obtained between modelled and
measured hysteresis loops. The standard deviation
of switching fields for Ni cylinders is typically
around 100 Oe, which is assumed to be a result of
differences in the shapes, heights and microstruc-
tures of the particles [16].
0.36
Without anisotropy
With Cubic anisotropy
Measured at 10K
Measured at 300K
0.32
0.28
0.24
0.20
0.16
0
.12
.08
0
Larger-diameter particles had hysteresis loops
with low remanence and coercivity in both in-
plane and out-of-plane directions. The saturation
field in the out-of-plane direction is larger if the
particles are shorter or if they are more closely
spaced. The coercivity of individual particles is low
because it is relatively easy to move a vortex or
domain wall through the particles, and the shape
of the hysteresis loops is therefore dominated by
interactions between the particles. Indeed, the
interactions can be so strong as to make the in-
plane direction the easier direction of magnetiza-
tion [17], as seen in Fig. 4(c).
0
.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Diameter/λex
Fig. 5. Calculated switching fields for Ni cylinders of aspect
ratio 2.4 with rounded tops, calculated without cubic aniso-
tropy (squares) and with cubic anisotropy (open circles). The
calculations use parameters for Ni at 4.2 K. Superposed are the
coercivities of samples Ni-1 and Ni-2 measured at different
temperatures.
measurements for the polycrystalline Ni samples
are in progress.
Switching fields of the smallest Ni samples,
Ni-1 and Ni-2, measured at both room tempera-
ture and 10 K, were compared with predictions of
the dynamic micromagnetic model for an aspect
ratio of 2.4. This aspect ratio was chosen because
the cylinders have a 5 nm oxide layer on their
surfaces which reduces their effective diameter.
The coercivity was calculated for cylinders with
diameters of 0:5lex to 4lex: Because these are
single-crystal samples, the model was run under
two conditions: with and without the low-tem-
perature cubic anisotropy of Ni. The results are
shown in Fig. 5, with the calculated data points
joined for clarity. The calculated coercivity is
higher in the presence of anisotropy, except at the
smallest diameter. The coercivity of the two
samples measured at 10 K is in good agreement
with the coercivity calculated from the model in
the presence of anisotropy. At room temperature
the measured coercivity agrees more closely with
the calculated coercivity in the absence of aniso-
tropy. Thus, it appears that the increase in
switching field with decreasing temperature, mea-
sured for these two samples, is primarily due to the
change in the magnetic properties of Ni with
decreasing temperature. Similar calculations and
5. Conclusions
A variety of ‘nanowire’ arrays has been fabri-
cated lithographically, consisting of cylindrical
particles with aspect ratios of up to 3 and
diameters below 180 nm. Magnetic force micro-
scopy shows that the smaller diameter particles
have high out-of-plane remanence while larger-
diameter particles have low remanence. This is
consistent with the predictions of a micromagnetic
model, which indicates a change from a ‘flower’ to
a ‘vortex’ remanent state with increasing diameter.
The flower–vortex transition occurs at a diameter
of 3:5lex for cylinders without any magnetocrystal-
line ansiotropy. However, it is important to note
that the remanence only decreases slowly as the
vortex develops, and high aspect ratio vortex-state
particles can still have significant remanence and
appear as dipoles in magnetic force images. These
results are consistent with several previous reports
of the behavior of elongated magnetic particles
[3,18–23], for instance, in one study 50–70 nm
diameter Ni cylinders showed dipolar magnetic
force images while 110 nm diameter cylinders did
not [20,21].

C.A. Ross et al. / Journal of Magnetism and Magnetic Materials 249 (2002) 200–207
207
Magnetostatic interactions between particles
dominate the behavior of closely spaced arrays.
The importance of interactions can be assessed
from the ratio of the average switching field of the
array to the maximum interaction field acting on
any particle. If this ratio is smaller than 1, a
saturated array is unstable and it can sponta-
neously demagnetize, leading to a remanence less
than 1. Experimentally, small flower-state particles
were found to have higher coercivity than larger
particles with vortices or multi-domain states. For
two samples of small-diameter single-crystal Ni
particles, a good agreement was obtained between
calculated and measured switching fields, indicat-
ing for these samples that the increasing magne-
tocrystalline anisotropy contributes to increased
coercivity at low temperatures.
These results can be used in the design of
particles for applications such as patterned media,
where each particle stores one bit according to its
magnetization direction. High-remanence states
are required for the readback process, and
sufficiently high coercivity is needed to avoid
spontaneous demagnetization of the array due to
interactions between particles.
[3] J. Wong, A. Scherer, M. Todorovic, S. Schultz, J. Appl.
Phys. 85 (1999) 5489.
[
4] C.A. Ross, M. Hwang, M. Shima, J.Y. Cheng, M.
Farhoud, T.A. Savas, H.I. Smith, W. Schwarzacher,
F.M. Ross, M. Redjdal, F.B. Humphrey, Phys. Rev. B
6
5 (2001) 144417.
[5] M. Shima, M. Hwang, M. Farhoud, T.A. Savas, A.
Tkaczyk, H.I. Smith, C.A. Ross, W. Schwarzacher, Proc.
Electrochem. Soc. PV2000-29 (2000) 111.
[
6] C.A. Ross, M. Farhoud, M. Hwang, H.I. Smith, M.
Redjdal, F.B. Humphrey, J. Appl. Phys. 89 (2001) 1310.
7] C.A. Ross, H.I. Smith, T.A. Savas, M. Schattenburg, M.
Farhoud, M. Hwang, M. Walsh, M.C. Abraham, R.J.
Ram, J. Vac. Sci. Technol. B 17 (1999) 3168.
[
[
[
8] M. Redjdal, F.B. Humphrey, J. Appl. Phys. 79 (1996)
6
464.
9] M.E. Schabes, H.N. Bertram, J. Appl. Phys. 64 (1988)
347.
[10] W. Rave, K. Fabian, A. Hubert, J. Magn. Magn. Mater.
90 (1998) 332.
11] C. Seberino, H.N. Bertram, IEEE Trans. Magn. 33 (1997)
055.
1
1
[
3
[
[
12] C. Seberino, H.N. Bertram, J. Appl. Phys. 85 (1999) 5543.
13] M. Hwang, M. Farhoud, Y. Hao, M. Walsh, T.A. Savas,
H.I. Smith, C.A. Ross, IEEE Trans. Magn. 36 (2000) 3173.
14] G. Zheng, M. Pardavi-Horvath, G. Vertesy, J. Appl. Phys.
[
[
[
[
[
[
8
1 (1997) 5591.
15] D. Grundler, G. Meier, K.B. Broocks, C. Heyn, D.
Heitmann, J. Appl. Phys. 86 (1999) 6175.
16] M.C. Abraham, H. Schmidt, T.A. Savas, H.I. Smith, C.A.
Ross, R.J. Ram, J. Appl. Phys. 89 (2001) 5667.
17] K.Y. Guslienko, S.B. Choe, S.C. Shin, Appl. Phys. Lett. 76
(
2000) 3609.
Acknowledgements
18] S. Wirth, M. Field, D.D. Awschalom, S. von Molnar,
Phys. Rev. B 57 (1998) R14028.
The authors are grateful to F.M. Ross of IBM
for electron microscopy, J. Cheng and A. Tkaczyk
for sample preparation, and support from the
National Science Foundation.
19] K. Nielsch, R.B. Wehrspohn, S.F. Fischer, H. Kronmuller,
J. Barthel, J. Kirschner, U. Gosele, Proc. Mater. Res. Soc.
705 (2001) Y9.3.
20] B. Cui, W. Wu, L. Kong, X. Sun, S.Y. Chou, J. Appl.
Phys. 85 (1999) 5534.
[
[
[
21] S.Y. Chou, Proc. IEEE 85 (1997) 652.
22] M. Zenger, W. Breuer, M. Zolfl, R. Pulwey, J. Raabe, D.
Weiss, IEEE Trans. Magn. 37 (2001) 2094.
23] R. O’Barr, S.Y. Yamamoto, S. Schultz, W. Xu, A. Scherer,
J. Appl. Phys. 81 (1997) 4730.
References
[
[
[
1] C.A. Ross, Ann. Rev. Mater. Res. 31 (2001) 203.
2] P.R. Krauss, P. Fischer, S.Y. Chou, J. Vac. Sci. Technol. B
12 (1994) 3639.