Magnetization reversal dynamics in Co nanowires with competing magnetic anisotropies

Article abstract of DOI:10.1016/j.ssc.2011.09.006

We present the magnetization reversal dynamics of Co nanowires with competing magnetic anisotropies. The aspect ratio (R) of the nanowires is varied between 2.5 and 60, and we observe a cross-over of the directions of the magnetic easy and hard axes at R=6.8. Micromagnetic simulations qualitatively reproduce the observed cross-over and give detailed insight into the reversal mechanisms associated with the cross-over. The reversal mechanism for a field applied along the long axis of the nanowire exhibits a quasi-coherent rotation mode and a corkscrew-like mode, respectively, above and below the cross-over, with the formation of a Bloch domain near the cross-over region. For a field applied along the short axis, the reversal occurs by nucleation and propagation of reversed domains from the two ends of the nanowires for very high values of the aspect ratio down to the cross-over region, but it transforms into quasi-coherent rotation mode for smaller aspect ratios (below the cross-over region)

Full text of DOI:10.1016/j.ssc.2011.09.006

Solid State Communications 151 (2011) 1994–1998
Contents lists available at SciVerse ScienceDirect
Solid State Communications
journal homepage: www.elsevier.com/locate/ssc
Magnetization reversal dynamics in Co nanowires with competing magnetic
anisotropies
∗
Semanti Pal, Susmita Saha, Debanjan Polley, Anjan Barman
Department of Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata, 700098, India
a r t i c l e i n f o
a b s t r a c t
Article history:
We present the magnetization reversal dynamics of Co nanowires with competing magnetic anisotropies.
The aspect ratio (R) of the nanowires is varied between 2.5 and 60, and we observe a cross-over of
the directions of the magnetic easy and hard axes at R = 6.8. Micromagnetic simulations qualitatively
reproduce the observed cross-over and give detailed insight into the reversal mechanisms associated with
the cross-over. The reversal mechanism for a field applied along the long axis of the nanowire exhibits
a quasi-coherent rotation mode and a corkscrew-like mode, respectively, above and below the cross-
over, with the formation of a Bloch domain near the cross-over region. For a field applied along the short
axis, the reversal occurs by nucleation and propagation of reversed domains from the two ends of the
nanowires for very high values of the aspect ratio down to the cross-over region, but it transforms into
quasi-coherent rotation mode for smaller aspect ratios (below the cross-over region).
Received 21 July 2011
Accepted 7 September 2011
by D.D. Sarma
Available online 16 September 2011
Keywords:
A. Magnetic nanowires
B. Electrodeposition
B. Micromagnetic simulations
D. Magnetisation reversal
©
2011 Elsevier Ltd. All rights reserved.
1
. Introduction
crystallinity. Previous reports on electrodeposited Co nanowires
have shown that the high melting point and high binding energy
of Co with hexagonal close-packed (hcp) crystalline structure
favors aggregation of atoms into small three-dimensional (3D)
clusters, which form Co nanowires with their c-axis orientated
either parallel [13] or perpendicular [13,14] to the long axis
of the nanowire depending on the pH of the electrolyte used
during electrodeposition. On the other hand, the shape anisotropy
naturally occurs along the long axis of the wire, and competing
magnetic anisotropy has become an important topic due the
possibility of tuning of the magnetic anisotropy energy barrier
in these nanowires simply by tuning their aspect ratio. The
competing magnetic anisotropies and the consequent cross-over
of the magnetic easy and hard axes that depends the aspect ratio
have been studied in ferromagnetic nanowires and nanotubes with
large magnetocrystalline anisotropy [15–18]. The cross-over has
been observed both by varying the diameter and length of the
nanowires and from the measurements of magnetization as a
function of the amplitude and orientation of the applied magnetic
field. However, the detailed magnetization reversal mechanisms
associated with the cross-over of the magnetic easy and hard axes
have not been studied in detail. Here, we present a systematic
study of the magnetization reversal mechanisms in Co nanowires,
where the competing magnetic anisotropies are observed. In order
to minimize the further complications arising from magnetostatic
interactions between the nanowires, we have grown them in
track-etched polycarbonate membranes (PCTE) with very low pore
density. We have performed 3D micromagnetic simulations to
obtain an extensive understanding of the magnetization reversal
processes in the nanowires.
Ordered arrays of magnetic nanowires have tremendous
potential in technological applications including in magnetic
storage [1], field sensors [2], logic devices [3], and magnonic
crystals [4]. Measurements and understanding of magnetization
reversal [5–7], domain wall movements [8,9] and spin wave
dynamics [10,11] in magnetic nanowires and nanopillars have
emerged as important problems from the viewpoints of both
fundamental science and for the above applications. The ever-
increasing demand for storage density leads towards the reduction
of bit size, but an upper limit to the storage density occurs
due to superparamagnetism. Densely packed ordered arrays of
magnetic nanowires with large aspect ratios (R) may overcome
this problem due to the large volumes of the individual nanowires
and large shape anisotropy along the wires axis, associated with
larger areal density. On the other hand, in nanowires formed
of magnetic materials with high magnetocrystalline anisotropy,
a competition between the two anisotropies may arise if the
anisotropy directions are different.
Electrodeposition through nanoporous templates [12] is a very
efficient and cost-effective method to produce large aspect ratio
nanowires at large scales with different diameters, lengths, and
∗
Corresponding author. Tel.: +91 33 23355706 8, 23353057/61, 23350312/1313;
fax: +91 33 23353477/23351364.
E-mail address: abarman@bose.res.in (A. Barman).
0
038-1098/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2011.09.006

S. Pal et al. / Solid State Communications 151 (2011) 1994–1998
1995
Fig. 1. Scanning electron micrographs of Co nanowires with different aspect ratios: (a) 60, (b) 49.5, (c) 18.1, and (d) 6.8. (e) The EDX data and (f) the XRD data obtained from
the electrodeposited Co nanowires.
2
. Experimental methods
software object oriented micromagnetic framework (OOMMF),
from the NIST website [20]. We have simulated the magnetization
(M) as a function of the applied magnetic field (H) for cobalt
nanowires with aspect ratio varying between 2.5 and 60.
Calculations were performed by dividing the samples into 3D
The Co nanowires were prepared by a standard three-electrode
electrodeposition process through commercially available PCTE
templates (Whatman) with a fixed nominal diameter of about
3
1
00 nm. The deposition was carried out by the application of a
arrays of cuboidal cells with dimensions 2 × 2 × 5 nm . The linear
pulsed potential with voltage levels at 0.1 and −1.0 V and with
uniform pulse width = 10 s. The electrolyte used is a 100 ml so-
lution of 30 mM CoSO4.7H2O and 120 mM H3BO3 in distilled wa-
ter [19]. The templates were left into a solution of sodium lauryl
sulphate prior to deposition to allow wetting and opening up of
the pores and to have smooth and uniform deposition. The back-
side of the PCTE membrane was coated with a 100 nm thick Au
layer, which served as the cathode. The lengths of the nanowires
were varied by varying the electrodeposition time between 2000
and 80 s. For structural and compositional analyses the templates
were dissolved in dichloromethane and washed several times with
ethanol and distilled water to clean the Co nanowires. The crys-
tal structure of the nanowires was studied by using X-ray diffrac-
tion (XRD; PANalytical X’Pert PRO). The surface morphology and
the dimensions of the nanowires were studied with field emission
scanning electron microscopy (FESEM; Helios NanoLab, FEI). The
compositional analysis was made by using energy dispersive X-ray
spectroscopy (EDX; Helios NanoLab, FEI). Finally, the static mag-
netic properties of the nanowires embedded inside the templates
and lying vertically on the substrate plane were studied by vibrat-
ing sample magnetometry (VSM; Lakeshore model 7407) at room
temperature. The magnetic field (up to 16 kOe) is applied either
parallel or perpendicular to the long axis of the nanowires during
the measurements.
dimensions of the cells are comparable to the exchange length
√
2
of Co, which is defined as (A/2πM ), where A is the exchange
s
constant and Ms is the saturation magnetization, respectively.
The simulations assume the following material parameters for
Co: 4πMS
=
17.59 kOe, exchange stiffness constant A
=
−
7
30 × 10 erg/cm, magnetocrystalline anisotropy K = 4.5 ×
6
10 erg/cc along the [100] direction, and gyromagnetic ratio
γ = 17.6 MHz/Oe. Shape anisotropy is already included in the
calculation of the demagnetizing field of the system. The applied
magnetic field was varied between +15 to −15 kOe in steps of
50 Oe. In some cases, when required, a field step of 5 Oe was also
used to observe finer details. The stopping criterion is given on the
change in magnetization with time. A damping coefficient α = 0.9
was used to ensure that the system finds equilibrium within the
allowed simulation time between two consecutive steps of the
applied magnetic field.
4. Results and discussions
The scanning electron micrographs of Co nanowires with
different aspect ratios are shown in Fig. 1(a)–(d), after dissolving
the templates. The diameters of the nanowires are found to be
about 95 nm ± 5 nm. By varying the deposition time between
2000 and 80 s, the lengths of the nanowires that are obtained are
between 5.75 µm and 240 nm, which correspond to a variation
of aspect ratio between about 60 and 2.5. The EDX spectrum
3. Simulation methods
(
Fig. 1(e)) confirms the chemical purity of the nanowires whereas
We performed micromagnetic simulations to numerically solve
the XRD data (Fig. 1(f)) confirms the hcp crystal structure, but the
crystallinity is not very high, which may result in a reduction of
the Landau–Lifshitz–Gilbert equation by using the public domain

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996
S. Pal et al. / Solid State Communications 151 (2011) 1994–1998
a
b
Fig. 2. (a) Experimental and (b) simulated M–H curves of Co nanowires with different aspect ratio (R). The black symbols (lines) correspond to the M–H curves with H
applied parallel to the long axis of the nanowire and the red symbols (lines) correspond to the M–H curves with H applied perpendicular to the long axis of the nanowire.
Fig. 3. Vector maps of magnetization reversal in a Co nanowire with R = 20. The magnetic field is applied along (a) the long axis and (b) the short axis of the nanowire.
The coordinate system and the colour map indicating the direction of the magnetization are shown next to the images. (For interpretation of the references to colour in this
figure legend, the reader is referred to the web version of this article.)
magnetocrystalline anisotropy compared to the value for single-
crystal Co. The magnetization (M) as a function of applied magnetic
field (H) for three different samples, measured by VSM at T =
to nanowires axis) has higher coercive field and remanence and
lower saturation field than those obtained from the short axis loop
(magnetic field applied perpendicular to nanowires axis). As the
aspect ratio is decreased, the differences between the loops are
reduced. For 3 < R < 10, the two loops are close to each other.
3
00 K, are shown in Fig. 2(a). For nanowires with R > 10, we clearly
observe that the long-axis loop (magnetic field applied parallel

S. Pal et al. / Solid State Communications 151 (2011) 1994–1998
1997
For nanowires with large aspect ratio (R > 10), the shape
anisotropy, parallel to the axis of the nanowires, dominates, which
causes higher coercive field and remanence and lower saturation
field for the long-axis loop. For intermediate values of R (10 <
R < 3), the contributions from the shape and magnetocrystalline
anisotropies are comparable and it is difficult to distinguish the dif-
ferences between the loops along the long and short axes. For R <
3
, the magnetocrystalline anisotropy starts to clearly dominate,
and the short axis loop shows higher coercivity and remanence and
lower saturation field. According to the macrospin model [21], the
cross-over should ideally occur sharply at R ∼ 7.0 (for saturation
magnetization Ms = 1400 emu/cc, magnetocrystalline anisotropy
6
K = 5×10 erg/cc along the [100] direction). However, the smear-
ing of the cross-over point, as observed in our experiment, is pos-
sibly due to a distribution of magnetocrystalline anisotropy over
the nanowires and due to the complicated magnetization reversal
processes that is not considered in the macrospin model.
To understand the details of the magnetization reversal mecha-
nisms associated with the cross-over, we performed a series of mi-
cromagnetic simulations. Some typical simulated M–H loops are
shown in Fig. 2(b). Since the measured samples were deposited
inside PCTE templates, the nanowires embedded inside the pores
are separated by large distance, and we may neglect the dipolar
interaction between the nanowires. Hence, the simulations were
performed in single nanowires without losing any non-trivial in-
formation. The M–H loops obtained for R = 60 and R = 20 are
almost identical, and hence for visual clarity of the magnetization
reversal modes (as presented later) we have shown the results for
R = 20 only. The simulated data qualitatively agree with the ex-
perimental data, but detailed quantitative agreement is not ex-
pected, as the simulations were performed at T = 0 K and the
experiment was at T = 300 K.
Fig. 4. Vector maps of magnetization reversal in a Co nanowire with R
=
7.
The magnetic field is applied along (a) the long axis and (b) the short axis of the
nanowire. The coordinate system and the colour map indicating the direction of
the magnetization are as shown in Fig. 3.
In general, for small nanoparticles with dimensions ≤100 nm,
In Fig. 2(a), we show that for R = 6.8 the two loops are almost
identical, defining the cross-over point between the easy axis and
the hard axis. With further reduction in aspect ratio (R < 3), the
short axis loop starts to show higher coercivity and remanence and
lower saturation field than the values in the long-axis loop.
the magnetization reversal is primarily dominated by coherent
(
quasi-coherent) rotation, although the enhancement of dimen-
sions along one or more axes may lead to various other reversal
modes [22], including curling, fanning, buckling, and generation of
local magnetic domains such as vortex and Bloch domains. This
a
b
Fig. 5. Vector maps of magnetization reversal in a Co nanowire with R = 2.5. The magnetic field is applied along (a) the long axis and (b) the short axis of the nanowire.
The coordinate system and the colour map indicating the direction of the magnetization are as shown in Fig. 3.

1
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S. Pal et al. / Solid State Communications 151 (2011) 1994–1998
depends upon the competition between various magnetic ener-
gies, which, in turn, depends strongly upon the parameters of the
system and external fields. Here, we study how the competing
magnetic anisotropy energies influence the reversal modes in Co
nanowires. For large aspect ratio (R = 20, shown in Fig. 3) and H
applied parallel to the long axis, the reversal starts at the two ends
below the cross-over region, the reversal mode in the short axis
loop transformed from nucleation and propagation of reversed do-
mains to quasi-coherent rotation. These observations are impor-
tant both from the viewpoints of fundamental science and for ap-
plications of magnetic nanowires in various devices.
(
Fig. 3(a)), but before the end regions reverse, the magnetization in
Acknowledgments
the central region of the nanowire reverses drastically and nearly
coherently at about H = −1.05 kOe. The two ends reverse grad-
ually and completely reverse at a larger magnetic field. When the
field is applied along the short axis, the reversal occurs by nucle-
ation of reversed domains at H = −0.65 kOe at the two ends of the
nanowires and slow propagation of the reversed domains towards
the centre of the nanowires (Fig. 3(b)).
We gratefully acknowledge financial assistance from the
Department of Science and Technology, Government of India under
the India–EU collaborative project ‘‘DYNAMAG’’ (grant number
INT/EC/CMS (24/233552)) and the Nano Mission (grant number
SR/NM/NS-09/2007).
At R = 7, when the field is applied parallel to the long axis,
the reversal occurs via formation of a Bloch domain along the
length of the nanowire (Fig. 4(a)). With decreased field, the width
of the domain shrinks towards the centre of the nanowire. At H =
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