Magnetoimpedance dependence on width in Co66.5Fe3.5Si12.0B18.0amorphous alloy ribbonsL. González-Legarreta, V. M. Prida, B. Hernando, M. Ipatov, V. Zhukova et al. Citation: J. Appl. Phys. 113, 053905 (2013); doi: 10.1063/1.4790480 View online: http://dx.doi.org/10.1063/1.4790480 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v113/i5 Published by the American Institute of Physics. Related ArticlesTheory of magnetoelectric effect in multilayer nanocomposites on a substrate: Static bending-mode response AIP Advances 3, 022103 (2013) Giant magnetocaloric and barocaloric effects in R5Si2Ge2 (R=Tb, Gd) J. Appl. Phys. 113, 033910 (2013) Effect of mechanical strain on magnetic properties of flexible exchange biased FeGa/IrMn heterostructures Appl. Phys. Lett. 102, 022412 (2013) Direct measurements of field-induced strain at magnetoelectric interfaces by grazing incidence x-ray diffraction Appl. Phys. Lett. 102, 011601 (2013) Alternating domains with uniaxial and biaxial magnetic anisotropy in epitaxial Fe films on BaTiO3 Appl. Phys. Lett. 101, 262405 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

Magnetoimpedance dependence on width in Co66.5Fe3.5Si12.0B18.0 amorphousalloy ribbons

L. Gonz�alez-Legarreta,1 V. M. Prida,1 B. Hernando,1 M. Ipatov,2 V. Zhukova,2

A. P. Zhukov,2,3 and J. Gonz�alez2,a)

1Departamento de F�ısica, Facultad de Ciencias, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo,Spain2Departamento F�ısica de Materiales, Facultad de Qu�ımica, UPV, 1072, 20080 San Sebasti�an, Spain3IKERBASQUE Foundation, Bilbao, Spain

(Received 29 November 2012; accepted 22 January 2013; published online 5 February 2013)

The magnetoimpedance (MI) response of near-zero magnetostriction Co-based amorphous ribbons

with different width ranging from 0.35 mm to 0.90 mm was investigated in the frequency range of

10 MHz–3.5 GHz. It was found that the wider ribbon displays the softer magnetic behavior and

larger magnetoimpedance. MI response is characterized by two symmetrical peaks corresponding at

the two opposite directions of applied magnetic field. The value of magnetic field at the peaks of MI

should be assigned to the anisotropy field. Frequency dependencies of anisotropy field for the range

500–1000 MHz could be understood in the framework of skin penetration effect in the ribbons

except to that of lowest width (0.35 mm) where the ferromagnetic resonance phenomenon could be

predominant at this frequency range. Ferromagnetic resonance was detected in all samples, and for

magnetic fields above 4 kA/m the square of resonance frequency quadratically fits vs. the applied

field. Given the saturation magnetization, both the anisotropy field and the Land�e factor have been

determined. VC 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790480]

I. INTRODUCTION

From the discovery of the giant magnetoimpedance

(GMI) effect in 1994 by Panina and Mohri1 and Beach and

Berkowitz2 in non-magnetostrictive soft magnetic amor-

phous wires (diameter around 120 lm), there has been an

intensively research activity owing to the promising and,

even, real technological applications based in the GMI phe-

nomenon.3,4 Such scientific research has dealt with several

aspects concerning the intrinsic magnetotransport properties

(i.e., frequency range, intensity of the effect, magnetic field

to observe possible maximum, noise, etc.) as well as those

related with microstructural (mainly amorphous or nanocrys-

talline) or geometrical character (as has been mentioned, ini-

tially wire, but GMI has been reported in glass-coated

microwire,5,6 ribbon,7 micro-patterned ribbon,8 multilayers9)

and, therefore, GMI is actually opening a new branch of

research combining the micromagnetics of soft magnets with

the classical electrodynamics. Obviously, the different geom-

etry leads to some differences in the GMI response like the

range of frequency or the magnetic field dependence of the

impedance curve with one or two peaks, or it could be rele-

vant the shape of the peak, etc.

In addition, the demand on the new magnetic sensors

requires, among other factors, the reduction of dimension of

the device that affects, of course, to the sensing element. In

this sense, it must be mentioned that the last strong tendency

in miniaturization of the magnetic sensing elements has

resulted in the development of the thinner wires produced by

the Taylor–Ulitovsky method5 (1–30 lm in diameter).

Accordingly, we have recently focused the attention in the

research of GMI effect in a very thin amorphous ribbon

which could result attractive for future applications in

micro-sensors either due to low dimensions or by the relative

low-cost fabrication of these amorphous ribbons.10 Since

GMI effect is associated with the sensitivity of the circular/

transverse component of the magnetic susceptibility to the

external magnetic field, it is reasonable to investigate the

effect of the ribbon width on the magnetoimpedance (MI)

effect, since this parameter affects drastically to the trans-

verse magnetoelastic anisotropy arising from the internal

stresses developed during the fabrication process. In this

work, we present magnetoimpedance results obtained in a

nearly zero magnetostrictive Co-rich amorphous alloy ribbon

fabricated with different width values by rapid quenching

(single-roller technique) and, consequently, with different

transverse susceptibility.

II. EXPERIMENTAL DETAILS

Amorphous ribbons of nominal composition Co66.5Fe3.5

Si12.0B18.0 (saturation magnetostriction of the order of

kS��0.1� 10�6) were fabricated by the melt-spinning

technique using a Fe wheel. The ribbons were cast in a 10�3

mbar vacuum and with different (0.35, 0.60, 0.70, and

0.90 mm) width, around 20 lm thick. Hysteresis loops were

measured in 4 cm long samples. The impedance, Z, of as-cast

1 cm long samples with different widths (values have been

mentioned above) was measured with a network analyzer at

moderate frequencies 10–100 MHz and at high frequencies

1.0–3.5 GHz, as described elsewhere.6 Z of ribbon samples

was determined with a N5230A vector network analyzer

through reflection coefficient measurement. The analyser

output power was �10 dBm that corresponds to 1.4 mA driv-

ing current.

a)Author to whom correspondence should be addressed. Electronic mail:

julianmaria.gonzalez@ehu.es.

0021-8979/2013/113(5)/053905/6/$30.00 VC 2013 American Institute of Physics113, 053905-1

JOURNAL OF APPLIED PHYSICS 113, 053905 (2013)

An external magnetic field up to 15 kA/m can be applied

along the longitudinal direction of the ribbon. Hysteresis

loops have been measured at 112 Hz using the technique

described elsewhere.4,5 Either hysteresis loops and/or MI

response, Z(H,f), of nearly zero magnetostrictive Co66.5Fe3.5

Si12.0B18.0 amorphous ribbons obtained with different widths

by quenching exhibit a distinctive behaviour.

III. EXPERIMENTAL RESULTS AND THEIRDISCUSSION

The resulting hysteresis loops of ribbons were measured

along the ribbon axis at a low frequency (112 Hz) being dis-

played in Fig. 1(a). The saturation magnetization, Ms, is

found to be in the range 470–510 kA/m for all ribbons,

meanwhile for the 0.90 width sample the lowest coercivity

of 5.5 A/m is detected, which is a half lower than the respec-

tive value for the other ribbons as can be observed in Fig.

1(b). Also the remanence is lower for the wider ribbon. From

the knee area just before to the approach magnetic saturation,

as is indicated in Fig. 1(b) by the arrow, a value of the effec-

tive anisotropy field of 17.1 A/m was estimated which is an

average over the whole sample being the dominant contribu-

tion the corresponding to the bulk ribbon. Coercive and ani-

sotropy fields within the 0.5% accuracy for all ribbons were

determined. Amorphous materials have a small effective ani-

sotropy and a soft magnetic behaviour is observed due to the

scaling down of the local anisotropy, as is described by the

random anisotropy model (RAM).11,12 This can be recog-

nized in all studied samples although when the width dimin-

ishes the magnetization reversal takes place in a wider range

of magnetic field values, involving more rotations, and

showing an increase in both the coercivity and the anisotropy

effective field. These features could be related to a less ani-

sotropy easy axis dispersion for the less wide samples, being

the magnetization more strongly constrained by the orienta-

tion of the local anisotropy and as a consequence the satura-

tion of magnetization is harder to achieve. Therefore, the

ribbon produced with the larger value of width presents the

softer magnetic behaviour.

3D variation of the electrical impedance, Z(H,f), with Hthe applied magnetic field, f, the frequency (10–1000 MHz)

of the ac electrical current flowing along the ribbon with dif-

ferent width, 0.35, 0.60, 0.70, and 0.90 mm, respectively, is

shown in Figs. 2(a)–2(d). It can be seen that the two-peak

behaviour (symmetrically with respect to H) emerges more

clearly as increasing the frequency. The value of H corre-

sponding to the peaks (Z maximum value) is linked to the

FIG. 1. Normalized hysteresis loops at 112 Hz meas-

ured parallel to the ribbon axis (a), and positive part of

the hysteresis loops (b), of four Co66.5Fe3.5Si12.0B18.0

ribbons with different widths. Arrows indicate the ani-

sotropy field for each sample.

053905-2 Gonz�alez-Legarreta et al. J. Appl. Phys. 113, 053905 (2013)

average value of the anisotropy field, HK, at high frequency

values, and to the anisotropy distribution in the sample. As it

is expected, the evolution of Z(H) with the frequency for the

ribbon of widths 0.60 mm (Fig. 2(b)), 0.70 mm (Fig. 2(c)),

and 0.90 mm (Fig. 2(d)) shows that the maximum Z increases

with the frequency, remaining the two-peak behaviour. In

the case of 0.90 mm width ribbon, MI peaks shift to higher

magnetic fields. The origin of this shift is related to the

change in skin depth with the frequency-dependent magnetic

permeability. As increasing the driving frequency of the ac

electric current along the ribbon, a decrease of the surface

layer thickness is produced and permeability should drasti-

cally change. The application of a longitudinal magnetic

field large enough for saturating the sample modifies the

transverse permeability, by the reorientation of the static

magnetization and by the intrinsic field change of permeabil-

ity, simultaneously. As a consequence, the effective skin

depth increases, providing an impedance decreasing. Fur-

thermore, the MI response results to be more relevant as

increasing the width of the ribbon.

Accordingly, we present in Fig. 3 the anisotropy field,

HK (which is the value of the magnetic field to obtain the MI

peak), for the ribbons with different width in the frequency

range 500–1000 MHz. As the drive current frequency

increases, the sample starts to be shielded and the current

passes through the outer shell of the sample. In addition,

these values of anisotropy field obtained from Fig. 2 are very

different to those obtained from the analysis of the hysteresis

loops (Fig. 1(b)), because they are related to the anisotropy

existent in the layer where the current flows that depends on

the stress distribution in the surface layer. This reflects the

mentioned skin effect associated with the pass of the ac elec-

trical current along the ribbon, as increasing the frequency of

the ac electrical current a decrease of the surface layer thick-

ness should be expected and the magnetic permeability

should drastically change with the thickness of the surface

layer. Then, it is reasonable to assume that in this frequency

range the decrease of the surface layer thickness owing to

the effective skin depth drastically affects to MI response.

Therefore, these experimental data have been fitted to an

expression such as

HK ¼ aþ bf c; (1)

where f is the frequency expressed in MHz and HK, in A/m;

a, b, and c are parameters of fitting. To note that a parameter

corresponds to HK value for f¼ 0, which could be correlated

to HK, which is estimated from the hysteresis loop (Fig. 1).

In Table I, the equations obtained from such fitting are given

as well as the anisotropy field. Therefore, the values of HK

deduced from the hysteresis loop (112 Hz), which can be

understood as HK value for the bulk, are in good agreement

FIG. 2. Impedance of samples with dif-

ferent values of the width: 0.35 mm (a),

0.60 mm (b), 0.70 mm (c), and 0.90 mm

(d), as a function of the magnetic field

applied in the ribbon direction, for dif-

ferent frequency values in the range 10–

1000 MHz.

FIG. 3. Frequency dependence (range: 500–1000 MHz) of the anisotropy

field for all ribbons with different width values. Symbols denote experimen-

tal data and lines denote theoretical fittings.

053905-3 Gonz�alez-Legarreta et al. J. Appl. Phys. 113, 053905 (2013)

with those deduced from Eq. (1) in all ribbons except to rib-

bon with smallest width value (0.35 mm) with a clear differ-

ent tendency of HK with f. This behaviour rather different

could be related to the influence of the shape anisotropy for

this ribbon. When the ribbon width is decreasing, the edge

roughness could worsen the MI effect. Certainly, the cross

section of this smallest width ribbon is still quite large as

comparing to that of microribbons,8 and glass-coated micro-

wires where a linear dependence of HK with the square of

the frequency was reported in the range of 0.5–15 GHz (Ref.

13) indicating that the reduction of cross section changes the

mentioned tendency to appear the ferromagnetic resonance

phenomenon. In fact, the frequency dependence of HK for

the ribbon of 0.35 mm width in the range of 1.0–3.0 GHz

showed in Fig. 4 leads to a different behaviour comparing

with the low frequency range of Fig. 3. Now, from the fitting

can be also obtained a value at f¼ 0 similar to that deduced

from the hysteresis loop. Concerning the results of c expo-

nent, it must be indicated that the increases with the width

samples could be understood in terms of complex mecha-

nisms of the magnetization process, which at this high fre-

quency range are connected mainly to spin rotations.14

On the other hand, at higher frequencies (1–3.5 GHz),

the MI effect is displayed in Fig. 5 for all studied ribbons. It

shows a significant increase of all the ribbons impedance but

the Z(f,H) behaviour is rather different for each sample. In

general, in the low field region, that is, for applied fields

below HK, the impedance change should be attributed to the

magnetization reorientation.15 At higher magnetic fields,

when the ribbon is close to magnetic saturation, the magnet-

ization reorientation no longer has much influence, being the

MI response essentially governed by the field variation of

the magnetic permeability, with ferromagnetic resonance

signature at high field. The large transverse permeability at

resonance strongly decreases the effective skin depth and the

impedance, Z, increases. As can be observed, there are Zpeaks at the resonance frequency for each value of the

applied static field, H. They become broader and diverge

from the centre of each curve as the frequency increases

remarking the ferromagnetic resonance contribution to the

impedance. As shown in Fig. 6(a), the resonance frequencies

f satisfy rather well the Kittel resonance condition for a uni-

axial thin film magnetized along the plane, which can also be

applied to the ribbons, and can be written as16,17

f 2 ¼ ðc2lo2=4p2Þ½ðH þ HKÞðH þ HK þMsÞ�; (2)

where c is the gyromagnetic ratio of an electron. With re-

spective saturation magnetization, Ms, determined from the

hysteresis loops measurements, the experimental results for

the high field data can be quadratic fitted with an anisotropy

field HK¼ 38.7 6 0.2 A/m and a Land�e splitting factor

g¼ 2.08 6 0.02 for the 0.35 mm width ribbon (Ms¼ 510 kA/

m). For the 0.60 mm sample (Ms¼ 470 kA/m), HK¼ 28.8

6 0.3 A/m and g¼ 2.01 6 0.01. In the case of the 0.70 mm

width ribbon (Ms¼ 490 kA/m), HK¼ 13.6 6 0.2 A/m and

g¼ 2.14 6 0.03, being HK¼ 12.2 6 0.2 A/m and g¼ 2.08

6 0.02 for the wider ribbon (Ms¼ 480 kA/m). Consequently,

obtained magnetic anisotropy field values are in good agree-

ment with HK values for the bulk alloys estimated from the

hysteresis loops, as can be seen in Fig. 1(b). In the low field

range, and considering that the saturating magnetic field of

these nearly zero magnetostrictive amorphous ribbons is

much lower than their saturation magnetization, (H þ HK)� Ms, Eq. (2) simplifies to

f 2 ¼ ðc2lo2=4p2Þ½ðH þ HKÞMs�: (3)

However, the linear fit holds only for static field values

stronger than HK in each sample as is presented in Fig. 6(b).

Moreover, for the narrower ribbon the slope is negative. Lin-

ear fits do not match the behaviour of the square resonance

frequency in the low field region. Deviations at applied fields

low 3 kA/m can be observed for all the samples that could be

ascribed to the specific anisotropy easy axis dispersion in

both strength and direction present in each ribbon. Other

source of this behaviour may be the inhomogeneity of Ms

through the cross section of the sample. MI-related phenom-

ena take place only in a thin outer layer of the ribbon, where

permeability inhomogeneity and surfaces defects may occur,

whereas hysteresis loop measurements provided average val-

ues of Ms and HK over the whole sample.

TABLE I. Fitting equations for the anisotropy field as a function of the frequency in the range 500–1000 MHz of several ribbons with different width.

Ribbon width (mm) Fitting equation Hk (112 Hz) (fitting) (A/m) Hk (112 Hz) (hysteresis loop) (A/m)

0.35 Hk¼ (39.2 6 0.6)þ (3.3 6 0.3)� 106�f (�1.18 6 0.16) … 38.2

0.60 Hk¼ (35.6 6 0.3)þ (98 6 8)�f (0.482 6 0.013) 36.8 36.0

0.70 Hk¼ (25.9 6 0.4)þ (5 6 3)�f (0.90 6 0.10) 25.9 26.0

0.90 Hk¼ (16.8 6 0.2)þ (10 6 3)�f (0.92 6 0.05) 16.8 17.1

FIG. 4. Frequency dependence (range: 1000–3000 MHz) of the anisotropy

field for the ribbon with 0.35 mm width. Symbols denote experimental data

and the line denotes the theoretical fitting.

053905-4 Gonz�alez-Legarreta et al. J. Appl. Phys. 113, 053905 (2013)

The results concerning the frequency dependence of the

anisotropy field in the range 500–1000 MHz in the ribbons

with different width indicate that the exponent c should be

further explored in order to control their magentoimpedance

response in a wide frequency range.

IV. CONCLUSIONS

Magnetoimpedance response of Co66.5Fe3.5Si12.0B18.0

amorphous alloy ribbons results to be very sensitive to the

width ribbon as a consequence of the average process of the

random distribution of magnetic moments through the width

dimension affecting drastically to the soft magnetic charac-

ter. Two-peak behaviour of the GMI effect is observed in all

studied ribbons, appearing the sharper peaks for a width

equal to 0.70 mm although the effect is enhanced as increas-

ing the value of the ribbon width in all frequency range (10–

3500 MHz). This behaviour is explained in terms of the skin

depth penetration and the dispersion of easy axes through the

ribbon thickness. The possibility about tuning the GMI two

peaks with both the applied magnetic field and the drive fre-

quency with different widths has been analyzed. Research

activities involving induced anisotropies with stress anneal-

ing treatment and/or by depositing an antiferromagnetic

layer on the ribbon surface are in progress.

ACKNOWLEDGMENTS

This work has been supported by Spanish MICINN under

projects MAT2009-13108-C02-01 and MAT2010-18914 and

by EU ERA-NET programme under project “SoMaMicSens”

(MANUNET-2010-Basque-3). Authors from UPV/EHU

acknowledge the financial support from the Department of

Industry of the Basque Government (Programme SAIO-

TEK2011, Projects: S-PE11UN013 and S- PE11UN087). FPI

grant is acknowledged by L.G.-L. Technical and human sup-

port provided by SGIker (UPV/EHU, MICINN, GV/EJ,

ERDF and ESF) is gratefully acknowledged.

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FIG. 5. Impedance of samples with dif-

ferent values of the width: 0.35 mm (a),

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applied in the ribbon direction, for fre-

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FIG. 6. Square of resonance frequency

as a function of the resonance field for

ribbons with different width. A quadratic

fit of the high field data was done (a),

and a linear fit was used for the low field

data (b). Symbols denote experimental

data and lines denote theoretical fits.

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