Finite-size effects in nickel nanowire arrays

Article abstract of DOI:10.1103/PhysRevB.61.R6463

Nickel nanowire arrays with diameters in the range 30-500 nm have been fabricated by electrochemical deposition into nanoporous, single-crystal mica templates, which allow measurements of the magnetic properties of nickel nanowire arrays at high temperatures. The Curie temperature is found to be reduced by as much as 51 K for the 30 nm diameter nanowires. The Curie temperature shift with wire diameter follows the finite-size scaling relation with λ=0.94 and ξ₀=22 A. 2000 The American Physical Society.

Full text of DOI:10.1103/PhysRevB.61.R6463

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PHYSICAL REVIEW B
VOLUME 61, NUMBER 10
1 MARCH 2000-II
Finite-size effects in nickel nanowire arrays
L. Sun and P. C. Searson
Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore, Maryland 21218
C. L. Chien
Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218
͑Received 11 June 1999͒
Nickel nanowire arrays with diameters in the range 30–500 nm have been fabricated by electrochemical
deposition into nanoporous, single-crystal mica templates, which allow measurements of the magnetic prop-
erties of nickel nanowire arrays at high temperatures. The Curie temperature is found to be reduced by as much
as 51 K for the 30 nm diameter nanowires. The Curie temperature shift with wire diameter follows the
finite-size scaling relation with ␭ϭ0.94 and ␰ ϭ22 Å.
0
The influence of reduced physical dimensions on mag-
netic entities is of both fundamental and technological inter-
est. In bulk magnetic systems, the correlation length ␰ in-
creases with temperature and diverges at the bulk transition
the Curie temperature for bulk Ni ͑ϳ630 K͒. The porous
templates were fabricated by nuclear track etching. Particle
tracks were formed in 5 ␮m thick mica wafers by exposure
to Ϸ6 meV ␣ particles from a 100 ␮CiCf-252 source in a
Ϫ3
temperature T (ϱ). When one or more dimensions in the
chamber at a pressure of about 10 Torr. The alignment of
C
system are small, the growth of ␰ will eventually be limited
by the smallest dimension d and the system displays a re-
the particle tracks was within 5° through collimation of the
␣-particle beam. The particle tracks were etched by immers-
ing the tracked wafers in 20 wt. % HF at room temperature.
duced transition temperature T (d) due to finite-size effects.
C
Technologically, as the feature sizes of magnetic structures
continue to decrease, the influence of dimensionality on their
magnetic properties has also become an important issue. To
date, reports of finite-size effect in magnetic systems have
been largely limited to ultrathin films and quasi-two-
dimensional systems. Measurements on quasi-one-
dimensional systems have been hampered by the difficulty in
fabricating structures that are sufficiently small and stable
over the required temperature range.
From electrical conductance measurements we determined
Ϫ1 26
the etch rate of the particle tracks to be about 1200 Å s
.
The lateral etch rate of the bulk mica was determined to be
Ϫ1 26
0.35 Å s
.
From the ratio of the normal and lateral etch
rates we determine that the taper on the pore walls due to
etching is 0.02°. Pore diameters in the range 30–500 nm
were obtained by varying the etching time. In order to mini-
mize the number of overlapping pores, the volume fraction
of nickel in the films was set at about 0.02 for all samples by
7
Ϫ2
In quasi-two-dimensional systems, thickness dependent
phase transition temperatures have been measured in ultra-
adjusting the track density from 1ϫ10 cm for the 500 nm
9
Ϫ2
pores to 2ϫ10 cm for the 30 nm diameter pores. The
relevant parameters are shown in Table I. For a volume frac-
tion of 0.02, the fraction of tracks resulting in overlapping
pores is less than 4%.26
thin ferromagnetic films of Ni,1 Fe, Co, and Gd ͑Refs.
1
–6
7,8
9
0–12͒ and CuMn spin glass films.13,14 Recently, finite-size
effects have also been reported in antiferromagnetic CoO
Refs. 15 and 16͒ and Cr ͑Ref. 17͒ thin films. In quasizero
͑
Figure 1 shows a scanning electron microscope image of
etched particle tracks in mica. The pores are perpendicular to
the film plane and the pore walls are smooth and free from
etching residues. The pores are diamond shaped with the
pore walls defined by the ͕110͖ planes corresponding to the
oxygen terminated planes in the mica lattice.25 For conve-
nience the pore diameter is defined as the diameter of the
dimensional systems, such as granular thin films, phase tran-
sitions are not observed due to the onset of superparamag-
netism when the particle size is very small.18
Electrochemical deposition of metals into porous polymer
films has been used to fabricate quasi-one-dimensional
1
9–22
nanowire arrays
and the ferromagnetic properties of Ni
and Co have been studied both at low temperatures and at
2
2–25
room temperature.
However, measurements of magnetic
TABLE I. Effective diameter ͑d͒, number density of tracks ͑n͒,
and volume ͑area͒ fraction ͑f ͒ of pores.
phase transitions are not possible in these structures since the
Curie temperatures for elements such as Ni, Co, and Fe are
much higher than the temperature range of polymer tem-
plates. In this paper we describe the fabrication of quasi-one-
dimensional nickel nanowire arrays in porous mica films and
show that this approach can be used to determine the tem-
perature dependence of the magnetic properties at elevated
temperatures.
n ͑cmϪ2
d ͑nm͒
͒
f
7
500
200
150
100
50
1ϫ10
0.0196
0.0157
0.0177
0.0236
0.0196
0.0141
7
5ϫ10
8
1ϫ10
8
3ϫ10
9
Nickel nanowire arrays were fabricated by electrochemi-
cal deposition into porous single-crystal muscovite mica
templates. Mica is chemically stable up to 770 K, well above
1ϫ10
9
30
2ϫ10
0
163-1829/2000/61͑10͒/6463͑4͒/$15.00
PRB 61
R6463
©2000 The American Physical Society

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L. SUN, P. C. SEARSON, AND C. L. CHIEN
PRB 61
FIG. 1. Scanning electron microscope image of 2 ␮m pores in
single-crystal mica.
circle having the same cross-sectional area as the diamond-
shaped pores.
Nickel nanowire arrays were fabricated by electrochemi-
cal deposition into the mica templates. The electrode contact
was provided by a sputter deposited gold layer. Nickel was
Ϫ1
FIG. 3. ͑a͒ Normalized magnetization and ͑b͒ normalized de-
rivatives of the M-T curves vs temperature for nickel nanowire ar-
rays with diameters ͑from left to right͒ of 30, 50, 100, 150, 200, and
deposited from a solution of 20 g l
NiCl •6H O,
2
2
Ϫ1
Ϫ1
5
15 g l Ni͑H NSO ͒ •4H O, 20 g l H BO buffered to
2
3 2
2
3
3
2
5
pH 3.4 at a potential of Ϫ1.0 V ͑Ag/AgCl͒. Scanning elec-
tron microscopy and atomic force microscopy were used to
verify that ϳ100% of the pores were filled during the depo-
sition process and that the nickel nanowires grew at a similar
rate. An advantage of this geometry is that the nickel nanow-
ires are embedded in the mica films, reducing oxidation and
structural damage at elevated temperatures.27
500 nm. The solid curves correspond to bulk nickel. All measure-
ments were obtained at Hϭ2000 Oe.
squareness ͑the ratio of the remanence and saturation mag-
netization͒ is strongly dependent on the physical properties
of the porous template, particularly the alignment of the
25
pores. Recently, we have shown that values of the square-
After dissolving the mica matrix in concentrated HF͑ϳ48
wt. %͒, free standing Ni nanowires were obtained on the gold
electrode. Figure 2 shows an SEM image of free standing
ness as high as 0.96 can be obtained with mica templates due
to the improved collimation of the pores, the uniform pore
cross section, and the low density of overlapping pores.
Figure 3͑a͒ shows M-T curves for nickel nanowire arrays
as a function of the wire diameter from 30 to 500 nm. The
temperature was calibrated prior to each measurement using
a bulk nickel sample. Figure 3͑b͒ shows the derivative of the
M-T curves from which we determined the Curie tempera-
ture; identical results were obtained from examination of the
hysteresis loops. These results clearly show that the Curie
temperature progressively decreases with decreasing wire di-
ameter. The Curie temperatures obtained by this method
were independent of the applied magnetic field over the mea-
sured range 2 000 to 12 000 Oe. Figure 4͑a͒ shows the de-
pendence of the measured Curie temperature on the wire
diameter.
150 nm nanowires. In the cross section the wires have a
diamond shape due to conformal filling of the diamond
shaped pores in the mica.
The magnetization measurements were conducted on a
vibrating sample magnetometer. Due to the strong shape an-
isotropy of the nickel nanowires, the applied external mag-
netic field was parallel to the wire axis. The room-
temperature magnetic coercivity of the nickel nanowire
arrays increases with decreasing wire diameter, reaching val-
ues of 800–900 Oe for 30 nm diameter wires.22–25 The
The reduction of the Curie temperature for nanowires
with decreasing diameter is due to finite-size effects. The
correlation length ␰(T) of a magnetic system increases with
temperature and at temperatures close to the bulk transition
temperature T (ϱ), the correlation length ␰(T) has an
C
asymptotic behavior described by
Ϫ␯
T
␰
͑T͒ϭ␰0
ͯ
1Ϫ
ͯ
,
͑1͒
T ͑ϱ͒
C
where ␰ is the correlation length extrapolated to Tϭ0, and ␯
0
2
8
is the critical exponent for correlation. For a magnetic sys-
tem with a small dimension of size d ͑e.g., the diameter of
the nanowires͒, the growth of ␰(T) with increasing tempera-
FIG. 2. Scanning electron microscope image of 150 nm diam-
eter Ni nanowires after etching of the mica template.

RAPID COMMUNICATIONS
PRB 61
FINITE-SIZE EFFECTS IN NICKEL NANOWIRE ARRAYS
R6465
3
D Heisenberg model (␭ϭ1.4) and the 3D Ising model (␭
2
7,28
ϭ1.58),
however both models assume nearest neighbor
interactions whereas nickel is a ferromagnet that exhibits
longer range interactions. Spin-wave studies of Ni indicate
that the magnetic interactions extend beyond the fourth
neighbors.30 For the same reason the critical exponent ␤ for
the magnetization of Ni is 0.4, much larger than 0.36 for a
3
D Heisenberg system with nearest-neighbor interactions.31
It may be noted that Eq. ͑1͒, from which Eq. ͑3͒ is de-
rived, is valid for T close to T (ϱ), i.e., in the critical region
C
where T (d) is close to T (ϱ) for systems with relatively
C
C
large d. Thus for the relatively large diameters of the nickel
nanowires, as required by the scaling law, the extrapolated
correlation length ␰ carries a larger uncertainty. However,
0
the extrapolated correlation length ␰ ϭ22 Å is close to the
0
6
value of 20 Å reported for polycrystalline nickel thin films,
although it is somewhat larger than the values of 4–10 Å
obtained for epitaxial single-crystal nickel films.4
,5
Finally, we comment on the possible effects on T due to
strain. Large strains are known to exist in thin films, how-
C
FIG. 4. ͑a͒ Curie temperature T (d) of nickel nanowire arrays
vs wire diameter d. ͑b͒ The log-log plot showing the reduced tem-
C
ever, the effects on T from mismatch in lattice and thermal
C
perature ͓T (ϱ)ϪT (d)͔/T (ϱ) normalized to the Curie tempera-
C
C
C
expansion are rarely incorporated. This is because of the dif-
ficulty in quantifying strain and the lack of simple relation
ture for bulk Ni ͓T (ϱ)ϭ631 K͔ vs wire diameter. The solid line
C
in ͑b͒ corresponds to ␭ϭ0.94 and ␰ ϭ22 Å.
0
between strain and the resultant T . In thin films, the prob-
C
lem is further compounded by the variation of strain with
film thickness. As a result, practically all finite-size scaling
studies in thin films, including all the results mentioned
above, neglect any effects due to strain. In the nanowire ge-
ometry, as long as the volume fraction of nickel is constant
and sufficiently small that all of the strain occurs in the nano-
wires, the lateral strain is expected to be independent of wire
diameter. Thus, an upper limit for such an effect is 4 K,
ture will be constrained by the wire diameter d, resulting in a
reduced Curie temperature defined by
␰0 ␭
T ͑d͒ϭT ͑ϱ͒
ͫ
1Ϫͩ ͪ
ͬ
͑2͒
͑3͒
C
C
d
or
␭
T ͑ϱ͒ϪT ͑d͒
␰0
C
C
corresponding to the shift in T for the largest wire diameter
C
ϭ
ͩ ͪ
,
T ͑ϱ͒
C
d
of 500 nm. However, as can be seen from Figure 4͑b͒, since
all the data, including that of dϭ500 nm, follow the finite-
size scaling relation, the actual contribution due to strain is
likely to be negligible.
In summary, we have measured the reduction of Curie
temperature of Ni nanowires as a function of the nanowire
diameter from 30 nm to 500 nm. The mica templates in
which nickel nanowires are imbedded enable such measure-
ments for nanowires. The TC reduction follows a finite-size
scaling relationship.
where T (d) is the Curie temperature for nanowires with
diameter d, and ␭ϭ1/␯ is the shift exponent.
C
Due to the relatively large diameters, the nanowires are
2
6
expected to behave as a constrained 3D system ͓Eq. ͑3͔͒,
without the complexity of 3D to 1D crossover.29 Figure 4͑b͒
shows a log-log plot of the reduced temperature ͓T (ϱ)
C
ϪT (d)͔/T (ϱ) versus wire diameter d, illustrating that the
C
C
measured values for T (d) follow the finite-size scaling re-
C
lation of ͓Eq. ͑3͔͒. From this figure we obtain ␭ϭ0.94 and an
extrapolated value of ␰ ϭ22 Å. The observed exponent of
This work was supported by NSF Grant No. DMR-96-
32526.
0
␭
ϭ0.94 is lower than the theoretical values predicted by the
1
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