gmi

1. Ž .Sensors and Actuators 81 2000 86–90
www.elsevier.nlrlocatersna
Effect of AC driving current on magneto-impedance effect
P. Aragoneses a
, A.P. Zhukov b,),1
, J. Gonzalez b
, J.M. Blanco a
, L. Dominguez a
a
Departamento de Fisica Aplicada I, EUITI, UniÕersidad del Pais Vasco, San Sebastian, aÕda Felipe IV 1B, 20011, San Sebastian, Spain´
b
Departamento de Fisica de Materiales, Facultad de Quımica, UniÕersidad del Pais Vasco, San Sebastian, 1072, 20080, San Sebastian, Spain´ ´
Abstract
Ž . Ž . Ž . Ž . Ž .Magneto-impedance MI ratio DZrZ sZ H yZ H rZ H has been measured in different materials: amorphousmax max
Ž .Fe Co B Si wires and Co Mn Si B microwires and nanocrystalline Fe Si B Nb Cu ribbons, with axial0.94 0.06 72.5 15 12.5 68.5 6.5 10 15 73.5 13.5 9 3 1
magnetic field H, intensity I, and frequency f, of the AC driving current as the parameters. The common feature of these samples is that
Ž . Ž .they show a peculiar MI effect with a maximum of DZrZ at a certain axial magnetic field value, H . Dependencies of DZrZ andm
H on the AC driving current amplitude I have been observed: H decreases with I. The MI ratio can be optimised by means ofm m
Ž .choosing an adequate value of I. Particularly, in the case of microwires, DZrZ has a maximum at Is2.8 mA. The observed effect is
explained taking into account the tensor character of magnetic permeability and the circular magnetisation processes. q 2000 Elsevier
Science S.A. All rights reserved.
Keywords: Giant magnetoimpedance; Skin effect; Magnetic permeability
1. Introduction
The recently discovered giant magneto-impedance ef-
fect, GMI, became a topic of intensive research in the field
w xof applied magnetism during the last few years 1–3 . The
main technical and scientific interest is related to the high
sensitivity of the impedance in the range of low applied
magnetic fields. Relative changes of impedance around
300% for dc fields of the order of tenths of Oe, with a
maximum sensitivity up to 100%rOe for fields less than 1
Oe were found. This research has been done mainly in
amorphous wires with vanishing magnetostriction, al-
though some reports are also dealing with amorphous
w x w xribbons 4,5 , thin films 6 and quite recently in mi-
w xcrowires 7,8 .
The GMI effect has been interpreted in terms of classi-
cal electrodynamics by considering the change in the
penetration depth of the AC current flowing in a magnetic
conductor caused by the DC magnetic applied field. The
Žfrequency, f, of the AC current which is necessary to
)
Corresponding author. Tel.: q34-9-434-55022; Fax: q34-9-43471098
1
On leave of the ‘AmoTec’, 277038; Kishihev, Moldova.
.evaluate the impedance must be high enough, typically
above 100 kHz. The impedance, Z, for a magnetic conduc-
w xtor is given by 1,2
ZsR kr J kr r2 J kr 1Ž . Ž . Ž . Ž .dc o 1
Ž .with ks 1qj rd, where J and J are the Besselo 1
functions. d is the penetration depth given by
y1r2
ds psm f 2Ž .Ž .f
where s is the electrical conductivity, f the frequency of
the AC current along the sample, and m the circularf
permeability assumed to be scalar. The DC applied field
changes the penetration depth through the modification of
m which finally results in a change of the impedancef
w x2,7 .
The main experimental and theoretical activity was
devoted to study the effect of axial magnetic field and
frequency of the AC driving current on the GMI effect. On
the other hand, in some cases, the GMI effect depends on
the amplitude of AC driving current, I. Therefore, choos-
ing an adequate I, the GMI effect can be significantly
w xenhanced 8 . Accordingly, the aim of this paper is to
present and analyse the experimental data concerning the
AC driving current dependence of the GMI effect in
different amorphous magnetic materials.
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved.
Ž .PII: S0924-4247 99 00092-8

2. ( )P. Aragoneses et al.rSensors and Actuators 81 2000 86–90 87
2. Experimental technique
The impedance was evaluated by means of the four
point technique when an AC current with frequency rang-
ing from 0.5 to 1.1 MHz flows along the samples. Its
amplitude, I, was varied between 1 and 4 mA for mi-
crowires, and 1–25 mA for wires and ribbons. This ampli-
tude, I, has been measured by means of an AC current
sensing device CT-1. Electrical contacts were carefully
prepared with Ag paint. The glass coating was mechani-
cally removed in the case of glass coated microwires. The
magneto-impedance ratio, DZrZ, has been defined as:
DZrZs Z H yZ H rZ H 3Ž Ž . Ž . Ž . Ž .max max
where the maximum DC axial applied field takes the value
H s20 Oe.max
3. Experimental results and discussion
Ž .The dependencies of DZrZ H for amorphous mi-
crowires Co Mn Si B measured in as-prepared state68.5 6.5 10 15
Ž .and after different heat treatments between 200 and 3508C
Ž .are presented in Fig. 1. A drastic change of the DZrZ H
dependence with annealing temperature as parameter can
Ž .be seen. Generally, a peculiar shape of the DZrZ H
dependence first increasing and then decreasing of DZrZ,
i.e., with a maximum at certain magnetic field H , ism
typical for as-prepared Co Mn Si B microwire with68.5 6.5 10 15
vanishing magnetostriction constant. Subsequent annealing
Ž .results in a change of shape of the DZrZ H dependence.
A monotonous decay of DZrZ with H is finally observed
after heat treatments at temperatures T above 2008C.ann
Ž .Similar non-monotonous dependencies of DZrZ H were
observed also in the other magnetic materials, like amor-
Ž .phous Fe Co B Si wire and nanocrystalline0.94 0.06 72.5 15 12.5
Fe Si B Nb Cu ribbon after annealing for nanocrys-73.5 13.5 9 3 1
Ž .tallization see Fig. 2a–c . A common characteristic fea-
ture of these materials is that they show dependencies of
ÄwŽ Ž . Ž .x Ž .4DZrZ s Z H yZ H rZ H and Hmax max max max m
on the amplitude of the AC driving current, I. The most
important changes in the value of DZrZ and H weremax m
observed in microwires and wires. For instance, DZrZmax
of microwires is twice at Is2.7 mA than the value of
DZrZ at Is1.8 mA. On the contrary, DZrZ de-max max
creases with I in amorphous wires. As it can be noted
from Fig. 2, values of H decrease with I. Besides, inm
fact, another important property, as the frequency depen-
dence of DZrZ , changes also with I. Fig. 3 presentsmax
frequency dependencies of DZrZ measured in amor-max
Ž .phous Fe Co B Si wire at different I. It can0.94 0.06 72.5 15 12.5
be noted that for any value of I there is a maximum
between 500 and 700 kHz, but the position of this maxi-
mum is not the same for different I values. These experi-
mental results clearly show the importance of AC driving
current for GMI measurements.
Let us now discuss the observed dependencies. The first
important point is that the present state-of-the-art concern-
w xing GMI effect 1,2 is based mainly on classical skin
w xtheory, developed by Landau and Lifshitz 9 in the case of
a magnetic conductor with scalar magnetic permeability. A
detectable AC current dependence of DZrZ was observed
only in samples with a peculiar axial field dependence of
Ž .Z H with a maximum at certain H , which was ascribedm
Ž .Fig. 1. Axial field dependencies of DZrZ % in as-prepared and annealed at different temperatures amorphous CoMnSiB microwires, measured at 500
kHz. Lines are a guide of the eye.

3. ( )P. Aragoneses et al.rSensors and Actuators 81 2000 86–9088
w xbefore to the high transverse magnetic anisotropy 3,4 .
Therefore, the observed effect could be explained taking
into account a tensor character of the magnetic permeabil-
w xity, mentioned before in 10 . Actually, the radial compo-
nent of the magnetic permeability tensor should be also
considered in the case of a wire, owing to their peculiar
Ž . Ž .domain structure. As it follows from Eqs. 1 and 2 ,
changes of total impedance, Z, with the axial magnetic
field are originated from the axial magnetic field depen-
dence of circumferential magnetic permeability, m .f
Ž . Ž .Fig. 2. AC driving current amplitude dependencies of GMI spectra for amorphous CoMnSiB microwire a , amorphous Fe Co B Si wires0.94 0.06 72.5 15 12.5
Ž . Ž . Ž . Ž . Ž .b and nanocrystalline Fe Si B Nb Cu ribbons c . Lines are a guide to the eye. DZrZ I dependenies are shown in the insets of a and b .73.5 13.5 9 3 1 max

4. ( )P. Aragoneses et al.rSensors and Actuators 81 2000 86–90 89
Ž .Fig. 2 continued .
The permeability tensor can be written as:
m m mx x x y x z
m m mms 4Ž .y x y y y z
m m mz x z y z z
where the circumferential components of the magnetic
permeability depending on axial magnetic field H , i.e.,x
m , m , m , m , are important in the case of conven-x z z y z x y z
Ž .tional DZrZ H dependence. Consequently, the AC driv-z
ing current gives rise to the circumferential magnetic field,
H :f
H r sIrr2p R2
5Ž . Ž .f
where R is the radius of the sample. In the particular case
of a microwire with the radius of 2–3 mm, the circular
field, H , on the surface is between 0.5 and 1 Oe, i.e., thef
tensor components m , m , m , m of the magneticy y y x x y x x
permeability can be affected by the circular magnetic field
H . Additionally, different components of the magneticf
permeability tensor are important in the cases of axial
magnetic field and AC driving current dependencies of the
GMI effect. In the case of wire-shaped samples, a cylindri-
cal co-ordinate presentation is more appropriate. Fig. 4
presents a simplified 3D picture, illustrating the impor-
tance of both axial and circular magnetic field.
The magnetic field amplitude, I, seems likely to be
associated with the rotational circular magnetisation pro-
cess. The circular magnetisation process can be described
through a circular permeability, m , which depends on thef
amplitude of that field reaching a maximum at around the
circular coercive field value.
Fig. 3. Frequency dependence of DZrZ measured at different AC current amplitudes. Lines are a guide to the eye.max

5. ( )P. Aragoneses et al.rSensors and Actuators 81 2000 86–9090
Fig. 4. The 3D schematic picture illustrating dependence of GMI effect
on axial and circular magnetic fields.
ŽThe impedance, Z, changes with the circular field am-
.plitude of current I through its dependence on the circular
Ž Ž ..1r2
permeability as m H . In the low frequency case, Zf f
w xcan be approached as 2 :
24
ZsR 1q rrd 0.14q d r2r yjfL 6Ž . Ž . Ž .Ž .dc dw i
where L slm r2, is the internal part of self-inductancei f
when second order terms are neglected, l is the sample
length and d is the skin effect penetration length fromdw
Ž .domain wall movements. From the analysis of Eq. 6 one
can expect the main contribution to arise from the second
term in the case of the thinner samples. It explains particu-
Ž .larly a more significant DZrZ I dependence in mi-
crowires, since their radius is around one order of magni-
tude lower than in wires.
On the other hand, a change of the coercivity with
amplitude of the exciting AC magnetic field, H , has beeno
w xfound 11 . In agreement with this fact, a change of Hm
with amplitude of the current I at a given frequency is just
a consequence of the magnetic field amplitude dependence
of the circular coercivity.
The following conclusions can be outlined from the
present work:
–AC driving current dependencies of the GMI effect
has been observed in different amorphous materials, like
amorphous wires, ribbons and microwires in a particular
case, when their axial field dependence of the GMI effect,
Ž .DZrZ H shows a maximum at a certain value of the
axial field.
–The observed effect of AC driving current was ex-
plained taking into account the tensor character of the
magnetic permeability and was ascribed to the components
of that tensor responsible for transverse magnetic anisotro-
py.
Acknowledgements
A. Zhukov gratefully acknowledges the Gobierno Vasco
for a fellowship. The work has been supported by the
Departamento de Industria del GV under project
OD98UN27 and by the GV under project PI-1997-33.
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