What is the total field acting on one wire?

When all the moments are aligned perpendicular to the wires the total field acting on one wire is the sum of the dipole fields and the self-demagnetizing field of the wireBx522.1 m0 4p • p d3 1Bdem.

What is the difference between the hcpi and the hcp'?

When the field is applied parallel to the wires a dip in the spectra appears at the position of hcpi and when the field is applied perpendicular to the wires there is less intensity at the position of hcp', from which directly follows that the texture of the hcp

(Open Access) Structure and magnetization of arrays of electrodeposited Co wires in anodic alumina (1999) | Gustav J. Strijkers

Q: What is the effect of the reversal of the Keff?

As already mentioned before, the analysis of Keff is based on a uniform magnetization reversal without domain wall motion, curling or buckling of the magnetization in the wires, which lead to a smaller effective anisotropy than for purely magnetostatic interactions.

Q: What is the reason why some of the wires seem distorted?

To obtain a cross section image the filter was broken which is probably the reason why some of the wires seem somewhat distorted and blurred in the picture.

Structure and magnetization of arrays of electrodeposited Co

wires in anodic alumina

Citation for published version (APA):

Strijkers, G. J., Dalderop, J. H. J., Broeksteeg, M. A. A., Swagten, H. J. M., & Jonge, de, W. J. M. (1999).

Structure and magnetization of arrays of electrodeposited Co wires in anodic alumina.

Journal of Applied

Physics

(9), 5141-5145. https://doi.org/10.1063/1.371490

DOI:

10.1063/1.371490

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Published: 01/01/1999

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Structure and magnetization of arrays of electrodeposited Co wires

in anodic alumina

G. J. Strijkers,

J. H. J. Dalderop, M. A. A. Broeksteeg, H. J. M. Swagten,

and W. J. M. de Jonge

Department of Physics and Research School COBRA, Eindhoven University of Technology, P. O. Box 513,

5600 MB Eindhoven, The Netherlands

共Received 21 December 1998; accepted for publication 21 July 1999兲

We have produced arrays of Co nanowires in anodic porous alumina ﬁlters by means of

electrodeposition. The structure and magnetization behavior of the wires was investigated with

nuclear magnetic resonance 共NMR兲 and magnetization measurements. NMR shows that the wires

consist of a mixture of fcc and hcp texture with the 共0001兲 texture of the hcp fraction oriented

preferentially perpendicular to the wires. The magnetization direction is determined by a

competition of demagnetizing ﬁelds and dipole–dipole ﬁelds and can be tuned parallel or

Physics. 关S0021-8979共99兲00421-1兴

I. INTRODUCTION

The fabrication and properties of arrays of tunable mag-

netic nanostructures are of interest not only from a funda-

mental, but also from a technological point of view, as re-

cording technologies in the future will require higher bit

densities to fulﬁll the unrelenting demand for more storage

capacities. There are several approaches to fabricate large

arrays of magnetic structures, for example, by lithographic

techniques such as electron beam lithography and ion beam

lithography. The disadvantage of these techniques is that

they are expensive and it is time consuming to write nano-

structures on large scales, although recently

optical interfer-

ence techniques are being developed to circumvent this prob-

lem. Another way to fabricate large scale periodic

nanostructures is by electrodeposition of magnetic materials

in the pores of nuclear track etched polycarbonate

membranes

2–6

or in the pores of self-ordered nanochannel

material formed by anodization of Al in an acid solution,

7–10

a low cost and fast technique to produce large arrays of iden-

tical magnetic entities, with a very large aspect ratio 共length

divided by diameter兲, which is not possible with standard

lithographic techniques. Wires in anodic alumina have the

advantage above wires in polycarbonate membranes in that

they are completely parallel and exactly perpendicular to the

membrane surface and, moreover, the wires are assumed to

have a constant diameter

throughout their entire length.

Speciﬁcally, here we present a study of the structure and

magnetization behavior of Co wires electrodeposited in

commercially

available nanoporous alumina, with nominal

pore diameters of 100 and 20 nm. Nuclear magnetic reso-

nance 共NMR兲 is used to determine the microstructure of the

wires and it will be shown that the crystallographic structure

of the Co wires consists of a mixture of fcc and hcp stacking.

The crystallographic quality of the Co is comparable to sput-

tered or molecular beam epitaxy 共MBE兲 grown Co layers.

The magnetization behavior, studied with direct magnetiza-

tion measurements and through the anisotropy of the reso-

nance ﬁelds, is determined by a competition of self-

demagnetization of the wires and dipolar interactions

between the wires. It will be shown that dipolar interactions

can lead to a preferential direction of the magnetization per-

pendicular to the wires, which can be tuned by changing the

length of the wires.

II. EXPERIMENT

As a starting material, commercially available

nanopo-

rous alumina ﬁlters were used with a thickness of 60

␮

m and

nominal pore diameters of 100 and 20 nm. Scanning electron

microscopy 共SEM兲 images of the surface of the ﬁlters sug-

gest that the diameter of the pores is up to a factor of 2 larger

than the nominal diameter. However, we will refer in the rest

of this article to the nominal pore diameter as the precise

diameter of the pores is not crucial for our analysis. The

nominal pore density is 1⫻ 10

in both cases, which is

conﬁrmed by SEM images, yielding an average spacing be-

tween individual pores of approximately 320 nm. One side

of the ﬁlters was covered with a few

␮

m-thick-dc-sputtered

gold layer to obtain a conducting base layer at the bottom of

the pores. The Co wires were then grown by electrodeposi-

tion of Co

2⫹

ions from an electrolyte with the following

composition: 400 g CoSO

• 7H

O, 40 g H

, and 1

l H

O. Deposition is performed in an ertalyte cell with the

nanopores facing upwards at a deposition potential of U

⫽⫺1.05 V with respect to a saturated calomel reference

electrode 共SCE兲. The total thickness of the alumina ﬁlter is

␮

m. Deposition is stopped when the desired wirelength is

reached, which was determined from the total integrated

charge passing between the working electrode and the

counter electrode. The length of the wires was separately

a兲

Author to whom correspondence should be addressed. Electronic mail:

Strijkers@phys.tue.nl

JOURNAL OF APPLIED PHYSICS VOLUME 86, NUMBER 9 1 NOVEMBER 1999

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checked after deposition with cross section SEM images and

with a normal light microscope and is found to be uniform

within 5%. The area of deposition is approximately 1 cm

which can easily be enlarged to fabricate larger arrays of

wires. NMR measurements were performed with a phase co-

herent spin-echo spectrometer at T⫽ 4.2 K in the frequency

range between 195 and 235 MHz and ﬁelds up to 4.5 T.

Magnetization measurements were done with a Quantum De-

sign superconducting quantum interference device 共SQUID兲.

In Fig. 1 a cross section SEM image is shown for Co

wires grown in 20 nm anodic alumina. The bright broad line

at the bottom of the ﬁgure is the Au base layer with a thick-

ness of about 3

␮

m. As can be seen, the individual wires are

very straight indeed and parallel with a length of about 40

␮

m, which corresponds to an aspect ratio of about 2000. To

obtain a cross section image the ﬁlter was broken which is

probably the reason why some of the wires seem somewhat

distorted and blurred in the picture. SEM images of the sur-

face show that the array of pores is rather disordered and not

hexagonally ordered as they were produced recently.

III. RESULTS AND DISCUSSION

Figure 2 shows zero-ﬁeld and ﬁeld-swept NMR spectra

of our 100 and 20 nm Co wires. All spectra are recorded at

4.2 K and corrected for enhancement of the spin-echo signal

because of oscillations of the electronic moment.

We have

used NMR because it is a powerful technique

14–16

to probe

the microstructure of Co. Furthermore, through the anisot-

ropy of the resonance ﬁelds we can obtain valuable informa-

tion on the magnetic behavior. Figure 2共a兲 and 2共d兲 show the

zero applied ﬁeld NMR spectra of the 100 and the 20 nm

wires. In both spectra a clear peak can be distinguished at

about 217 MHz which corresponds to fcc Co and contributes

to about 40% of the total spectrum. To the right of this fcc

peak a mixture of hcp Co and stacking faults 共twinning, de-

formation, etc.兲 are visible. Co in hcp structure gives rise to

a resonance frequency along the c axis 共hcp

储

) at 20 MHz and

perpendicular to the c axis (hcp

⬜

) at 228 MHz. On the left

hand side of the fcc peak the intensity does not drop to zero

completely which might be caused by Co atoms at the inter-

faces with Al

or by grain boundaries.

The zero-ﬁeld

spectra resemble NMR spectra of sputtered

and even MBE

grown

Co layers, which indicates that the crystallographic

quality of our Co wires can be compared to layers made with

other fabrication techniques.

The resonance condition for NMR in this conﬁguration

f⫽

␥

␲

共

⫺ B

appl

⫹ B

surr

⫹ B

dem

兲

共1兲

with B

surr

the ﬁeld produced by the surrounding Co lines and

dem

the self-demagnetizing ﬁeld of the wires. In an in-plane

magnetized uniform ﬁlm the last two ﬁelds are not present.

For long wires, however, B

dem

perpendicular to the wire axis

共⬇0.9 T兲, with M

the saturation magnetization of

Co,

and wire–wire interactions can lead to a sizable B

surr

From Eq. 共1兲 it is clear that we can measure B

surr

by record-

ing a NMR spectrum as a function of an externally applied

ﬁeld and hence we can gain more insight into the magnitude

FIG. 1. Cross section SEM picture of Co wires in 20 nm anodic alumina

ﬁber. The bright broad line at the bottom of the ﬁgure is the gold base layer.

FIG. 2.

Co nuclear magnetic resonance spectra of 100 and 20 nm wires.

共a兲 and 共d兲 Spin-echo intensity as function of frequency in zero ﬁeld. 共b兲 and

共e兲 Spin-echo intensity as function of an applied ﬁeld perpendicular to the

wires. 共c兲 and 共f兲 Spin-echo intensity as function of an applied ﬁeld parallel

to the wires. The arrows indicate the shift of the spectra with respect to the

zero-ﬁeld spectra. The line positions of fcc Co and hcp Co are indicated

with the dashed lines. Spectra 共b兲 and 共c兲 are recorded at a frequency of 200

MHz; 共e兲 and 共f兲 at 195 MHz.

5142 J. Appl. Phys., Vol. 86, No. 9, 1 November 1999 Strijkers

et al.

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of the wire–wire interactions. In Figs. 2共b兲,2共c兲,2共e兲, and

2共f兲 the NMR spectra at constant frequency of the 100 and

20 nm wires are shown as function of the ﬁeld applied either

perpendicular or parallel to the wires. The horizontal axes of

the spectra are plotted in such a way that they scale with the

frequency axes of the zero-ﬁeld spectra via Eq. 共1兲, assuming

surr

⫹ B

dem

⫽ 0. This means that the line shifts indicated with

arrows in Fig. 2 are equal to B

surr

⫹ B

dem

. First we consider

the spectrum of 100 nm Co wires with the applied ﬁeld per-

pendicular to the wires 关Fig. 2共b兲兴. With respect to the zero-

ﬁeld spectrum of Fig. 2共a兲 the overall spectrum is shifted

with about 0.3 T, which gives B

surr

⫽⫺0.6 T using B

dem

⫽ 0.9 T. Figure 2共c兲 shows the NMR spectrum with the ap-

plied ﬁeld along the wire axes. The shift with respect to the

zero-ﬁeld spectrum is about 1.30 T, even higher than with

the ﬁeld perpendicular to the wires, and because B

dem

⫽ 0

along the wire axis this results in B

surr

⫽ 1.30 T. Apparently,

for the 100 nm Co wires the surrounding ﬁeld introduces an

easy axis perpendicular to the wires, although a magnetiza-

tion along the wires axes was expected from the magnitude

of the self-demagnetizing ﬁeld of the long wires. On the

other hand, the 20 nm wires behave more isotropic with a

small preference for the magnetization parallel to the wires.

The overall shift of the spectrum is about 0.75 T when the

applied ﬁeld is perpendicular to the wires and only 0.43 T

when the applied ﬁeld is parallel to the wires, leading to

surr

⫽⫺0.15 T and B

surr

⫽ 0.43 T, respectively.

Before focusing further on this magnetization behavior

for the different wire diameters, ﬁrst the shape of the NMR

spectra will be discussed in more detail. The NMR spectra

with the ﬁeld perpendicular to the wire in Figs. 2共b兲 and 2共e兲

consist of a fcc Co peak, hcp

储

and hcp

⬜

, and stacking faults,

which are also located at the right hand side of the fcc

peak.

When the ﬁeld is applied parallel to the wires a dip in

the spectra appears at the position of hcp

储

and when the ﬁeld

is applied perpendicular to the wires there is less intensity at

the position of hcp

⬜

, from which directly follows that the

texture of the hcp Co fraction is mainly with the c axis per-

pendicular to the wires. As a result, an extra anisotropy con-

tribution of the magnetic anisotropy along the c axis has to

be taken into account. This also was observed in electrode-

posited Co wires in polycarbonate membranes by Ounadjela

et al.

and by Piraux et al.

Now we will discuss in more detail the magnetization

behavior of the wires. Figure 3 shows the magnetization

measurements for the 100 and 20 nm Co wires. The satura-

tion ﬁelds are qualitatively in agreement with the shift of the

NMR spectra indicated with arrows in Fig. 2. The 100 nm

Co wires are more easily saturated perpendicular to the wires

than parallel to the wire axes, while the 20 nm wires behave

more isotropic as saturation is reached at approximately the

same value for the ﬁeld parallel and perpendicular to the

wires. From this we conclude that the magnetization behav-

ior is mainly a result of a competition of demagnetization of

the individual wires and dipole–dipole interaction between

the wires.

The small differences in magnitude between the satura-

tion ﬁelds observed in the magnetization measurements and

the shifts of the NMR spectra are caused by the magneto-

crystalline anisotropy of the hcp Co fraction, which does

affect the shape of the magnetization curve in a way that it

slightly favors a magnetization direction perpendicular to the

wires, but does not add to the shift of the NMR spectra.

Therefore, saturation for the 20 nm wires 关see Fig. 3共d兲兴 with

ﬁeld parallel to the wires is reached at higher ﬁelds than for

the ﬁeld perpendicular to the wires, while the NMR spectra

关see Figs. 2共e兲 and 2共f兲兴 suggest a slight tendency for an easy

axis of magnetization parallel to the wires. Because the crys-

talline anisotropy of hcp Co decreases at higher

temperature

the saturation ﬁelds parallel to the wires de-

crease at higher temperatures.

From a simple consideration we can understand that a

competition of dipole–dipole interactions and demagnetiza-

tion can lead to a preferential direction of magnetization per-

pendicular to the wires. The array of wires may be approxi-

mated as a two dimensional inﬁnite array of magnetic

dipoles located on a square grid. The total ﬁeld acting on one

wire is the total dipole sum produced by all the other wires

and reads

20,21

⫽ 4.2

␮

␲

•

共2兲

when all the moments are aligned along the wires. Here, p is

the moment of one wire and d the distance between the

wires. When all the moments are aligned perpendicular to

the wires the total ﬁeld acting on one wire is the sum of the

dipole ﬁelds and the self-demagnetizing ﬁeld of the wire

⫽⫺2.1

␮

␲

•

⫹ B

dem

. 共3兲

The sign of B

and B

is chosen with reference to Eq. 共1兲,

that is opposite to the applied ﬁeld. Depending on the mag-

nitude of the moment p, which in our experiments can be

chosen by changing the wire length or diameter, either B

is smallest leading to an easy direction of magnetization

parallel or perpendicular to the wires, respectively.

We realize that this model based on a uniform magneti-

zation reversal is in principle too simple and does not de-

scribe detailed magnetization reversal processes in the wires.

FIG. 3. Magnetization hysteresis curves of 100 nm wires 共a兲 and 共b兲 and 20

nm wires 共c兲 and 共d兲 at 300 and 10 K, with the applied ﬁeld perpendicular

共open circles兲 and parallel 共solid squares兲 to the wires.

5143J. Appl. Phys., Vol. 86, No. 9, 1 November 1999 Strijkers

et al.

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Including these would require extensive micromagnetical

calculations, which are far beyond the scope of this article.

Nevertheless, as will be shown in the following, we can

qualitatively describe the basic magnetization behavior with

our simple magnetostatic model.

In accordance with the previous predictions, we have

experimentally observed such a transition, as shown in Fig.

4. When the wire length is decreased from 40 to 0.5

␮

crossover takes place from a perpendicular easy direction of

magnetization towards an easy direction parallel to the wires.

This can be quantiﬁed by the effective anisotropy constant

eff

, derived from the magnetic anistropy density, that is the

area between the magnetization curves with ﬁeld orientation

parallel and perpendicular to the wire axes, which is pre-

sented in Fig. 5. The magnetostatic energy E per unit volume

is given by E⫽⫺K

eff

⫻ cos

␪

, with

␪

the angle between the

wire axes and the magnetization direction. A change from

easy axis of magnetization perpendicular (K

eff

⬍ 0) to paral-

lel (K

eff

⬎ 0) occurs at a wire length of about 1

␮

Assuming a diameter of 100 nm and an average distance

between the wires of 320 nm we have calculated the effec-

tive anisotropy constant as function of the wire length from

Eqs. 共2兲 and 共3兲, which also is shown in Fig. 5 共dashed line兲.

The calculated change from perpendicular to parallel magne-

tization 共 K

eff

⫽ 0兲 at about 4

␮

m is in reasonable agreement

with the measured change at 1

␮

m. Moreover, as mentioned

before, we have some indications from SEM images that the

actual diameter of the wires is up to a factor of 2 larger than

the nominal diameter, which would explain this difference of

a factor of 4. However, the calculated magnitude is much

larger than the measured K

eff

, especially for the longest

wires, when clearly the assumption of two dimensional array

of magnetic dipoles no longer holds. As already mentioned

before, the analysis of K

eff

is based on a uniform magnetiza-

tion reversal without domain wall motion, curling or buck-

ling of the magnetization in the wires, which lead to a

smaller effective anisotropy than for purely magnetostatic

interactions. Furthermore, for the sample with the shortest

wires we may have to consider the possibility that, due to

inhomogeneities in the electrodeposition process, part of the

pores is not ﬁlled. This also would lead to a decrease of the

dipole interactions and could account for the sharp increase

in K

eff

. Although we cannot rule out these inhomogeneities

completely, the NMR linewidths for these short wires are not

signiﬁcantly different from those observed in Fig. 2, as

would be the case for inhomogeneities growth with a large

spread in dipole ﬁelds.

IV. CONCLUSIONS

In summary, we have produced large arrays of identical

Co nanowires by electrodeposition in commercially available

anodic alumina. We have demonstrated that the magnetiza-

tion behavior is determined by a competition of demagnetiz-

ing ﬁelds and dipole–dipole interactions and to a lesser ex-

tent by magnetocrystalline anisotropy. The easy direction of

magnetization can be tuned either perpendicular or parallel

to the wires by changing the length of the wires.

ACKNOWLEDGMENTS

The authors would like to thank H. J. M. Heijligers, B.

H. van Roy, and L. M. F. Kaufmann for SEM measurements,

H. van Luytelaar for assistance with preparing the wires, and

G. W. M. Baselmans and J. J. P. A. W. Noijen for technical

assistance. The work of G. J. Strijkers is supported by the

Foundation for Fundamental Research on Matter 共FOM兲.

FIG. 4. Magnetization hysteresis curves of 100 nm wires as a function of the

wire length at 10 K, with the applied ﬁeld perpendicular 共open circles兲 and

parallel 共solid squares兲 to the wire axes.

FIG. 5. Effective anisotropy constant K

eff

as function of wire length; mea-

sured 共open squares兲 and calculated 共dashed line兲 from Eqs. 共2兲 and 共3兲.

5144 J. Appl. Phys., Vol. 86, No. 9, 1 November 1999 Strijkers

et al.

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Structure and magnetization of arrays of electrodeposited Co wires in anodic alumina

Figures

Citations

Ultrahigh-Density Nanowire Arrays Grown in Self-Assembled Diblock Copolymer Templates

Characterization and Analysis of Porosity and Pore Structures

Hexagonally ordered 100 nm period nickel nanowire arrays

Fabrication of nanomaterials using porous alumina templates

Low-temperature study of the magnetization reversal and magnetic anisotropy of Fe, Ni, and Co nanowires

References

Classical Electrodynamics

Self-organized formation of hexagonal pore arrays in anodic alumina

Highly ordered nanochannel-array architecture in anodic alumina

Topics in Current Physics

Giant magnetoresistance in magnetic multilayered nanowires

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Frequently Asked Questions (10)

Q1. What contributions have the authors mentioned in the paper "Structure and magnetization of arrays of electrodeposited co wires in anodic alumina" ?

Q2. What is the effect of the reversal of the Keff?

Q3. What does the hcp Co fraction affect?

Q4. What is the advantage of anodic alumina wires?

Q5. What is the structure of the Co nanowires?

Q6. What is the difference between the saturation fields of the 100 and 20 nm Co wires?

Q7. What is the reason why some of the wires seem distorted?

Q8. What is the simplest way to fabricate large scale periodic nanostructures?

Q9. What is the total field acting on one wire?

Q10. What is the difference between the hcpi and the hcp'?