APPLIED PHYSICS LETTERS
VOLUME 79, NUMBER 26
24 DECEMBER 2001
Magnetic anisotropy in prismatic nickel nanowires
L. Sun and P. C. Searsona)
Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, Maryland 21218
C. L. Chien
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218
共Received 18 June 2001; accepted for publication 13 October 2001兲
Nickel nanowire arrays with a diamond-shaped cross section and the same orientation have been
fabricated in nanoporous single mica crystal membranes by electrodeposition. All wires are 5 ␮m
long with an effective diameter of 120 nm. The sample can be considered as a collection of laterally
and vertically aligned identical micromagnetic prisms. We report on the magnetic anisotropy due to
the quasi-one-dimensional wire shape and diamond cross section. © 2001 American Institute of
Physics. 关DOI: 10.1063/1.1428113兴
Electrodeposition of metals into porous templates has
been used as a method to fabricate a wide range of quasione-dimensional nanostructures.1–5 The intrinsic properties
of nanowire arrays are directly related to properties of the
nanoporous template such as the pore shape, the relative pore
orientation in the assembly, the pore size distribution, and the
surface roughness of the pores.
Ferromagnetic nanowires exhibit strong shape anisotropy due to the high aspect ratio where the nanowire axis is
the easy axis for magnetization.6 –10 The difference in the
saturation field with the applied magnetic field perpendicular
or parallel to the wire axis corresponds to 2 ␲ M s , where M s
is the saturation magnetization, as expected for an infinitely
long cylinder. Furthermore, large enhancements in coercivity
and squareness have been reported with decreasing wire
diameter.8 –10
Nanowires formed in polycarbonate or alumina membranes are circular in cross section and hence there is no
shape anisotropy perpendicular to the wire axis. However,
nuclear track etching in crystalline inorganic materials can be
used to produce nanoporous templates with asymmetric cross
sections. Etched particle tracks in 关001兴 single crystal muscovite mica are diamond shaped in cross section with angles
of 60° and 120°.11,12 Due to the crystal structure of the mica,
the diamond-shaped pores are aligned with respect to each
other allowing the investigation of anisotropic magnetic
properties perpendicular to the wire axis.
Figure 1 shows a plan view scanning electron micrograph image of etched particle tracks in a single crystal mica
membrane. The particles are collimated so that the damage
tracks are within 2° to the membrane normal. The length of
the diagonals of the diamond-shaped pores are 115 and 200
nm, respectively. For convenience we define an effective diameter corresponding to the diameter of a circle with the
same area. From an effective diameter of 120 nm and a pore
density of 2⫻108 cm⫺2, we obtain a porosity of 2.26% and
an average pore–pore distance of 700 nm.
Nickel nanowire arrays were prepared by electrochemical deposition of nickel from a solution of 20 g L⫺1
NiCl2•6H2O, 515 g L⫺1 Ni共H2NSO3兲2•4H2O, and 20 g L⫺1
a兲
Electronic mail: searson@jhu.edu
H3BO3 at ⫺1.0 V 共Ag/AgCl兲. From buoyancy measurements
we determined the density of Ni thin films deposited from
sulfamate solution at ⫺1.0 V to be 98% that of pure Ni. The
saturation magnetization of the electrodeposited thin films
was 98.6% that of pure Ni, indicating a low impurity concentration. Electrical contacts were made by sputter deposition of 300 nm gold onto one side of the nanoporous mica
templates. For 5 ␮m long nanowires the effective aspect ratio
共defined by the ratio of the wire length and effective diameter兲 is 41.7. Since the pores in the mica are aligned, the
nanowire array can be considered a collection of identical
laterally and vertically aligned micromagnetic prisms.
Magnetic measurements were performed on a vibrating
sample magnetometer 共VSM兲 from 80 K to room temperature. The saturation magnetization was obtained from linear
extrapolation of the high field magnetization data 共6500–
10 000 Oe兲 to zero field. The saturation field was defined as
the field where the magnetization reached M s . The data
were corrected for the background signal obtained from a
blank mica film from the same sample 共unirradiated area兲.
Due to the relatively large wire spacing, magnetic interactions between wires can be neglected.13 Furthermore, the
crystalline anisotropy of Ni can also be neglected as a result
of the polycrystalline structure of the as-grown wires and the
relatively small crystalline anisotropy. Consequently, aniso-
FIG. 1. Scanning electron microscope image of 120 nm pores in single
crystal mica.
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© 2001 American Institute of Physics
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Appl. Phys. Lett., Vol. 79, No. 26, 24 December 2001
Sun, Searson, and Chien
FIG. 2. Magnetization hysteresis loops for 120 nm Ni nanowires with the
applied field 共a兲 parallel to the wire axis, 共b兲 perpendicular to the wire axis
along the short diagonal of the diamond, and 共c兲 along the long diagonal of
the diamond.
tropic magnetic properties are dominated by the wire shape.
Figure 2 shows the magnetization hysteresis loops for
the nanowire array when the applied field is parallel to wire
axis c and perpendicular to the wire axis along the diamond
diagonals a and b. Due to the large wire aspect ratio, the
magnetic easy axis is parallel to the nanowire. The measured
squareness 共SQ, defined by the ratio of remanent magnetization and saturation magnetization M r /M s 兲 along the wire
axis is 0.89. Perpendicular to the wire are the magnetic hard
axes, however, there is clear in-plane magnetic anisotropy
due to the diamond-shaped cross section. Rotating the field
from along the short diagonal a to along the long diagonal b
results in a decrease in the saturation field from 4650 to 3380
Oe, as shown in Fig. 3. At the same time, the coercivity
decreases from 220 to 80 Oe and the squareness decreases
from 0.066 to 0.056. Measurement of hysteresis loops as a
function of temperature revealed that the coercivity increased
linearly with decreasing temperature although the squareness
was essentially independent of temperature.
This in-plane magnetization anisotropy can be qualitatively discussed based on the ellipsoid approximation. For an
ellipsoid with three different axes a, b, and c, the demagnetization factors along three axes are defined as N a , N b , and
N c , respectively. Using the notation shown in the inset of
Fig. 2, the magnetization energy can be written as
E F ⫽2 ␲ M s2 共 N c cos2 ␪ ⫹N a sin2 ␪ cos2 ␾
⫹N b sin2 ␪ sin2 ␾ 兲 ,
共1兲
where ␪ is the angle between the applied field and c, and ␾ is
the angle between the in-plane projection of the applied field
and a.
When the magnetization aligns in the ab plane ( ␪
⫽90°), Eq. 共1兲 reduces to
FIG. 3. The angular dependence of 共a兲 the saturation field and 共b兲 the coercivity with the applied magnetic field parallel to the wire axis. The solid line
in the plot of the saturation field corresponds to a fit according to Eq. 共3兲.
E F ⫽2 ␲ M s2 共 N a cos2 ␾ ⫹N b sin2 ␾ 兲
⫽K a cos2 ␾ ⫹K b sin2 ␾ ,
共2兲
where K a and K b are the uniaxial anisotropy constants along
the a and b directions. From this expression we can write the
saturation field as
H s ⫽4 ␲ M s 共 N a cos2 ␾ ⫹N b sin2 ␾ 兲
⫽
2K a
2K b 2
cos2 ␾ ⫹
sin ␾ .
Ms
Ms
共3兲
Figure 3 shows excellent agreement between the measured angular dependence of the saturation field and Eq. 共3兲.
From the fit, we obtain K a ⫽1.13⫻106 erg cm⫺3 and K b
⫽8.2⫻105 erg cm⫺3. The corresponding demagnetizing factors are N a ⫽0.764 and N b ⫽0.556. These values can be
compared to the calculated demagnetizing factors for a triaxial ellipsoid with c/a⫽43.8 and c/b⫽25.3 of N a ⫽0.633
and N b ⫽0.365.14 These values are in reasonable agreement
given the difference in cross section between a diamond and
an ellipse. Thus the in-plane shape anisotropy caused by the
diamond-shaped cross section can be described by a simple
model based on two mutually perpendicular anisotropic axes.
Hysteresis loops were measured with the external field
rotated in the ac plane or the bc plane from parallel to the
wire axis ( ␪ ⫽0°) to along the a or b axis of the diamond
( ␪ ⫽90°). The squareness of the hysteresis loops decreased
with increasing ␪. Since the magnetization at zero external
field is aligned along the easy axis and the magnetization is
measured along the field direction, we expect the SQ to be
dependent on ␪ according to
SQ⫽SQ0兩 cos ␪ 兩 ,
共4兲
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Appl. Phys. Lett., Vol. 79, No. 26, 24 December 2001
Sun, Searson, and Chien
FIG. 4. Dependence of 共a兲 squareness and 共b兲 coercivity on the angle of the
applied magnetic field with respect to 共䊊兲 the wire axis and the short diagonal of the diamond 共ac plane兲 and 共䉭兲 the wire axis and the long diagonal
of the diamond 共bc plane兲. The dashed line corresponds to H c ⫽H c ( ␪
⫽0°)/cos ␪.
where SQ0 is the squareness when the applied field is along
the wire axis. Figure 4共a兲 shows that the measured data follow Eq. 共4兲.
Figure 4共b兲 shows the angular dependence of the coercivity. Magnetic reversal in a nanowire can occur by curling
or coherent rotation. The mechanism is dependent on the
diameter and length of the nanowires as well as the angle of
the applied field with respect to the wire axis. For an infinitely long nickel cylinder with a diameter larger than about
400 nm and the external field aligned parallel to the wire axis
( ␪ ⫽0°), curling is expected to be the dominant reversal
mode.15 For the case of curling, the magnetic field corresponding to the onset of magnetization reversal for an elongated ellipsoid is approximately equal to the coercivity16 –18
so that Fig. 4共b兲 can be used to determine the angular dependence of the nucleation field for the nanowires. According to
the curling model, the angular dependence of the normalized
nucleation field for an ellipsoid in the limit of an infinitely
large aspect ratio is given by18
Hn
1
⫽
.
H n 共 ␪ ⫽0 兲 兩 cos ␪ 兩
共5兲
Figure 4共b兲 shows that the coercivity increases with increasing angle as expected for the curling mechanism. Other
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groups19–21 have used magnetoresistance and micro-SQUID
共superconducting quantum interference device兲 measurements to determine the nucleation field in cylindrical nickel
nanowires 75– 80 nm in diameter and have shown a similar
increase in nucleation field with increasing angle consistent
with the curling model.
At higher angles when the external field rotates away
from the wire axis there is a critical angle, dependent on
diameter and aspect ratio, above which magnetization reversal occurs by coherent rotation.18 For coherent rotation, the
coercivity decreases with increasing ␪.18 From Fig. 4共b兲 it is
seen that the transition to coherent rotation occurs at about
78° when the field is aligned in the ac plane. When the field
is aligned in the bc plane the transition is shifted to about 85°
due to the increase in the length of the diagonal 共decrease in
aspect ratio兲.
In summary, Ni nanowire arrays with a diamond-shaped
cross section and the same orientation have been fabricated
to study the magnetic shape anisotropy perpendicular and
parallel to the wire axis. The magnetic anisotropy due to the
diamond-shaped cross section can be well described by two
mutually perpendicular uniaxial anisotropic axes along the
diagonals based on a simple ellipsoid approximation. As the
applied field rotates from the wire axis ( ␪ ⫽0°) to perpendicular to the wire axis ( ␪ ⫽90°), the squareness of the hysteresis loop follows a 兩 cos ␪兩 dependence caused by the
uniaxial anisotropy along the wire axis. The magnetization
reversal is dominated by curling for values of ␪ up to about
80°.
The authors acknowledge helpful discussions with Gary
Prinz. This work was supported by the JHU MRSEC 共NSF
Grant No. DMR00-80031兲.
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