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Magnetic field effects in artificial dielectrics with arrays of magneticwires at microwaves

L. V. Panina,1,2,a) M. Ipatov,1 V. Zhukova,1 A. Zhukov,1 and J. Gonzalez11Dpto. de Fisica de Materiales, Fac. Quimicas, Universidad del Pais Vasco, P.O. Box 1072, 20080,San Sebastian 20009, Spain2School of Computing and Mathematics, University of Plymouth, Drake Circus, PL4 AA, Plymouth,United Kingdom

(Received 10 August 2010; accepted 9 December 2010; published online 2 March 2011)

A magnetic field tunable electromagnetic response in periodic lattices of conducting magnetic wires

is demonstrated. The wire medium having a negative permittivity in the lower frequency band is

customarily investigated as an important component of so-called double negative metamaterials.

Here we are interested in a strong dispersion of the permittivity in these structures and a possibility

to alter it by changing the losses in magnetic wires with an external magnetic field. The theoretical

approach is based on calculating the relaxation parameter depending on the wire surface

impedance, and hence, on the wire magnetic properties. Thus, in arrays of Co-based amorphous

wires the application of a moderate magnetic field (of about 12 kA/m) which causes the

magnetization reorientation is capable of few fold permittivity change in the frequency range of

12 GHz. Such efficient tuning for certain structural and magnetic parameters was confirmed

experimentally by measuring the transmission and reflection spectra from lattices ofCo66Fe3.5B16Si11Cr3.5 glass-coated amorphous wires with a different wire cross-section and a

different lattice period. The chosen wires are also confirmed to show a large magnetoimpedance

effect at GHz frequencies, which constitutes the underlying mechanism of magnetic field dependent

permittivity in wire media.VC 2011 American Institute of Physics. [doi:10.1063/1.3548937]

I. INTRODUCTION

Thin conducting wire structures are commonly used as

metamaterials with negative permittivity. Owing to this

property, they are one of the basic components of the double-

negative medium characterized by a range of unusual proper-

ties. This generated a considerable interest in wire media and

vast literature is devoted to the subject. Negative electricalresponse also suggests that the wire medium is characterized by

a low frequency stop band from zero frequency to the cutoff

frequency which is often referred to as plasma frequency. For

the wire radius in micron scale, and lattice constant in mm

scale, the plasma frequency is in the GHz range. In this fre-

quency band, a strong dispersion of the effective permittivity

may be used to engineer a specific electric response. Thus, orig-

inally the wire arrays were considered as artificial dielectrics

for beam shaping applications.1,2 It was also notated their re-

semblance with plasmonic systems. Recently, new effects of

magnetic tunability and stress sensing in magnetic wire compo-

sites were put forward, which utilize the combination of permit-

tivity dispersion and magnetoimpedance in individual wires.36Applying external stimuli such as a moderate magnetic field or

stress to the whole wire-composite sample, it was possible to

alter greatly the values of the effective permittivity and reflec-

tion/transmission parameters. In particularly, these effects were

rigorously investigated in short-cut wire composites having res-

onant dispersion of the effective permittivity.4,5 This paper pro-

vides detailed investigation of the effective permittivity of

continuous magnetic wire arrays demonstrating that the losses

are determined by the surface impedance depending on the

wire magnetic properties. In this way, a change in the wire

magnetic structure influences the relaxation parameter of the

effective permittivity and makes it possible to tune the electric

response of the whole system at GHz frequencies.

When using wire-arrays as a component of a double

negative medium, the relaxation parameter is considered to

be small and is typically neglected. Here we are interested in

realizing the conditions when the losses may become rela-

tively large. We will demonstrate that when the skin effect is

essential the loss parameter is enhanced by the wire dynamic

permeability. However, when the skin effect is too strong so

that the wire radius is much larger than the penetration depth,

the relaxation is indeed small and has little effect. Therefore,

a condition of moderate skin effect is needed to realize an

effective tuning. The experimental data for wires of different

radius support the theoretical results.

II. EFFECTIVE PERMITTIVITY OF MAGNETIC WIREARRAYS

Here we consider the dispersion properties of magnetic

wire arrays placing emphasis on the role of relaxation due to

losses in wires. When the wavelength k of the incident radia-

tion is much longer than the intrinsic length-scales of the

structure k ) b ) a, where b is the lattice period and a isthe wire radius, it is very helpful to consider the wire me-

dium as a homogeneous material with averaged constitutive

material parameters. A number of quasistatic models of the

effective permittivity eef are available.79 These models

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

[email protected].

0021-8979/2011/109(5)/053901/8/$30.00 VC 2011 American Institute of Physics109, 053901-1

JOURNAL OF APPLIED PHYSICS 109, 053901 (2011)

Downloaded 02 Mar 2011 to 149.171.67.164. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions
http://dx.doi.org/10.1063/1.3548937http://dx.doi.org/10.1063/1.3548937http://dx.doi.org/10.1063/1.3548937http://dx.doi.org/10.1063/1.3548937http://dx.doi.org/10.1063/1.3548937http://dx.doi.org/10.1063/1.3548937

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demonstrate that the electromagnetic response from the wire

medium imitates ideal (collisionless) electron plasma. For

1D wire lattice shown in Fig. 1, the effective permittivity has

a tensor form with the component along the wires given by

eef edx2p

x2: (1)

The parameterxp plays the role of an equivalent plasma

frequency, ed is the permittivity of the dielectric medium of

the host isotropic matrix, and x is the angular frequency. If

the wires are assumed to be very thin, so that their electrical

polarization in the orthogonal direction can be neglected, the

effective permittivity for the electric field polarization orthog-

onal to the wires is ed. Different approaches to calculate eefgive varying results for the plasma frequency, however, in

the logarithmic approximation ( ln(b/a))1 ) this discrepancyis not greater than 10%. Customarily, xp is written as

x2p 2pc2

b2 ln b=a; (2)

where c is the velocity of light (cgs units are used). Taking

the geometric parameters a 10 lm and b 1 cm, theplasma frequency is fp xp/2p 4.8 GHz. A number ofexperimental and numerical studies confirmed validity of

Eqs. (1) and (2) predicting a negative permittivity below the

cutoff frequency in the GHz region.10,11

In this way, the wires are considered as ideally conduc-

tive and the losses in the system are ignored. This approxi-

mation would be valid for frequencies where the skin effect

in wires is strong. In some cases (see, for example, Ref. 12)

the resistive losses were accounted for by considering a uni-

form distribution of currents inside the wires, which corre-

sponds to the opposite limit of a weak skin effect. In this

approach, the permittivity is given by

eef edx2p

x21 ic ; (3)

c d=a2

= lnb=a: (4)

Here the relaxation parameter c is proportional to the skin

depth d c= ffiffiffiffiffiffiffiffiffiffiffiffi2pxrp ; r is the wire conductivity. It followsfrom (4) that the losses in a lower frequency range when

d/a) 1 may be large. In general, for potential applicationsof metal mesostructures it is crucial to have small losses,

which is possible only when the skin effect is strong. There-

fore, the relaxation parameter for the wire medium has to be

considered accounting for the skin effect in wires.A rigorous approach to the problem is based on the solu-

tion of the Maxwell equations in the elementary cell and

consequent homogenization procedure to find the averaged

electric field and displacement.13 The field distribution inside

the wires accounts for the skin effect. In this approach at

high frequencies (d/a( 1 ), for nonmagnetic wire arrays therelaxation parameterc can be written in the form:

c 1 id=2a= lnb=a: (5)This demonstrates that indeed choosing a suitable geome-

try to realize the condition of a strong skin effect at the frequen-

cies of interest, the losses could be made small. It also showsthat in a high frequency approximation the plasma frequency

gets a contribution occurring due to final conductivity of wires.

We will further demonstrate that in the case of magnetic

wires the loss factor strongly depends on the magnetic struc-

ture. It could be expected that for magnetic wire arrays the

skin depth parameter in (5) should be simply replaced with

that valid for a magnetic conductor. This would result in fur-

ther decrease in c since the magnetic skin depth is inversely

proportional to the wire circular permeability. Physically this

does not sound correctly since an additional mechanism of

relaxation should result in c increase. Accurate consideration

shows that indeed the relaxation parameter increases with

increasing the wire permeability.The field distribution inside the wire and outside it is

bounded by imposing the impedance boundary conditions at

the wire surface:

eza 1zzh/a: (6)

Here ez(a) and h a) are the longitudinal electric and cir-

cular magnetic fields at the wire surface, and fzz is the longi-

tudinal component of the surface impedance. In the vicinity

of wires the field distribution has a cylindrical symmetry, but

typically a square cell is considered to be able to set periodi-

cal boundary conditions. Such cell contains a wire in its cen-

ter. In a logarithmic approximation (ln(b/a)) 1), the electricfield in the cell and outside the wire has the following form

ezr! a; r< b=2 eza 1 ixac1zz

lnr

a

and involves the surface impedance of the wires. The effective

permittivity is found by averaging over a unit cell the electrical

field and displacement he(r)ez(r) i eefh ez(r)i from the follow-ing condition:

pechezr a i 1 pedhezr> ai eefhezri:

Here hi denotes spatial averaging, p pa2/b2 is thevolume concentration of wires and ec i4pr/x is the

FIG. 1. (Color online) Sketch of 1D wire medium.

053901-2 Panina et al. J. Appl. Phys. 109, 053901 (2011)


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permittivity of metal. The average field inside the wire is

expressed through the total induced current I cah/(a)=2,and consequently using (6),

hezr ai Ipa2r

ezac21zzpar

:

This yields the following equation for the effective

permittivity:

eef p

2ic

ax1zz 1 ped

1 ixa

c1zzhln r

ai

pc

2par1zz 1 p

1 ixa

c1zzhln r

ai :

For p( 1, ln(pb/a) $ ln(b/a) p = 1, this can be furtherreduced to the form of (3) where the relaxation parameter

takes the form:

c ic1zzxalnb=a : (7)

The detailed analysis of the surface impedance in mag-

netic wires with a uniaxial anisotropy valid for any fre-

quency has been developed in Ref. 14. The calculation of the

impedance tensor is based on the solution of the Maxwell

equations inside the wire together with the linearized equa-

tion of motion for the magnetization vector. Small coherent

precessions of the magnetization around its static position

M0 are typically considered and the domain wall motions are

neglected since at high frequencies they are strongly

damped. In the approximation of a strong skin effect, the

wire longitudinal impedance is given by

1zz 1 ixd

2c ffiffiffilp cos2 h sin2 h: (8)

Here l is the circular permeability with respect to the

magnetization M0 and h is the angle between M0 and the

wire axis. Substituting (8) into (7) shows that the relaxation

parameterc increases as a square root of the permeability. It

is also seen that c depends on the static magnetisation angle.

Forl 1 Eq. (8) reduces to that given by (5) for nonmag-netic wires. Therefore, we have demonstrated that the disper-

sion properties of the effective permittivity in magnetic wire

arrays depend on the wire static magnetization and dynamic

permeability. The underlying physical mechanism involves

the magnetoimpedance (MI) effectthe dependence of high

frequency impedance on magnetic properties. In certain mag-

netic wires MI can be very sensitive to the application of exter-

nal magnetic field or mechanical stress. Using these wires, it

will be possible to realize magnetically tuneable wire structures.

III. FIELD DEPENDENT PERMITTIVITY IN ARRAYSOF CO-BASED AMORPHOUS WIRES

Further analysis will be related to arrays with soft mag-

netic amorphous wires showing large and sensitive MI up to

frequencies of few GHz.1517 In these systems, the magnetic

anisotropy is primarily of magnetostrictive origin. For Co-

rich wires with a diameter of 10-70 lm, the combination of

negative magnetostriction and tensile stress creates a unique

circular anisotropy; then the impedance changes greatly (50

100%) in the presence of an axial magnetic field, Hex. The

characteristic field of impedance change is in the order of the

anisotropy field HK which is needed to rotate the magnetiza-

tion toward the axis. For certain compositions, HK can be

made small in the range of 110 Oe, which ensures a high

sensitivity of MI effect. In the presence of the field, the wire

impedance is also sensitive to the external stress.18 There-

fore, at certain conditions the permittivity spectra of arrays

of Co-rich microwires can be actively tuned by application

of a small magnetic field and a mechanical load.

At microwave frequencies, the highest sensitivity is

related with changing the magnetization direction whereas

the permeability parameter is rather insensitive to moderate

magnetic fields since at such frequencies the condition of the

ferromagnetic resonance requires a much stronger magneticfield. This conclusion is supported by the permeability spec-

tra shown in Fig. 2 with the external field as a parameter

(normalized with the anisotropy field). The calculation is

done using the magnetic parameters typical of amorphous

Co-based wires. It is seen that for frequencies higher than

2 GHz the value of permeability changes little in the pres-

ence of the field Hex%HK. Therefore, for a sensitive imped-

ance change a reorientation in the magnetization direction is

FIG. 2. (Color online) Spectra of the circular permeability of a wire having

a circumferential anisotropy with the axial field as a parameter. The parame-

ters used for calculations are: M0 500 G, HK 5 Oe, the anisotropy devia-tion from circular direction is 5 degrees.

FIG. 3. (Color online) Real part of the wire impedance as a function of the

axial magnetic field with a frequency f x/2p as a parameter. The wire mag-netic parameters are the same as for Fig. 2, but the anisotropy axis deviation is

15 degrees (which is needed to fit the experimental data), a

10 lm,

r 1016

s1

. The impedance is normalized to its value at f 1 GHz, Hex 0.



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essential. This is known as nonresonant low field microwave

absorption19 and is realized in magnetic wires with a circular

anisotropy where the magnetization is rotated from circular

to axial direction by applying an axial field equal to the

anisotropy field. If the magnitude of the permeability is

essentially greater than unity, the microwave impedance of

the wire will be highly sensitive to relatively small fields

HexHKas shown in Fig. 3 .

The permittivity spectra given in Fig. 4 are calculated

using Eqs. (3), (7), (8), and the impedance data of Fig. 3. It is

seen that the effect of the field is strong in lower frequency

band (lower than the plasma frequency). For a frequency of

1 GHz, the real part of the permittivity changes from 78(no field) to 23 when Hex 2HK and it changes little withfurther increase in the field. In the presence of the field there

is also a large change in the imaginary part of the permittiv-

ity since the relaxation parameter increases. With increasing

frequency toward the plasma frequency the relaxation

parameter decreases, then, the effect of magnetic field on the

permittivity dispersion becomes small.

The field effect on the permittivity spectra will depend

on the wire radius and geometrical parameters of the lattice

as demonstrated in Fig. 5. The plasma frequency is higher

for a smaller lattice period, b. Then, decreasing b it is possi-

ble to extend the frequency range where the magnetic field

causes substantial changes in permittivity toward higher fre-

quencies (within, of course, the frequency range where the

wire permeability still differs noticeably from unity). In this

case the wire radius should be relatively decreased since the

relaxation parameter will not depend on the wire magnetic

properties if the skin effect is too strong (or too weak). Thus,

for b

1 cm, a strong field effect is seen below 1 GHz

with the optimal wire radius of about 20 microns, whereas

for b 0.5 cm a significant field dependence exists ata frequency of 2 GHz but this requires a smaller wire radius

(510 micron).

IV. EXPERIMENTAL

A. Magnetic and impedance properties of individualwires

Wire arrays were fabricated using as-cast glass coated

amorphous wires with a composition of Co66 Fe3.5B16Si11Cr3.5having a small negative magnetostriction of the order of

107. Typically, the wires with negative magnetostrictionhave a circumferential anisotropy in the outer shell and an

axial anisotropy in the core. The surface anisotropy of a cir-

cumferential type is important to realize a large MI at GHz fre-

quencies as discussed above. The magnetic hysteresis loops

shown in Fig. 6 demonstrate that all the wires have a similar

magnetic structure with distributed anisotropy axes and good

soft magnetic properties. The wire circumferential anisotropy

could be improved and extended into the central region by a

specific stress annealing.20 This would be important for sensor

applications operating at MHz frequencies. However, at GHz

frequencies the MI effect depends on the magnetization in a

thin surface layer where the anisotropy is predominantly cir-

cumferential for negative magnetostrictive wires with glass

coating as the latter creates quite strong tensile stress. This was

confirmed by measuring the impedance of individual wires. At

lower frequencies, there is a large difference in MI plots of the

three samples which becomes insignificant at frequencies

above 700 MHz.

The impedance Z 2fzzl/ca of a short wire sample withlength l of 36 mm was obtained from S11-parameter

FIG. 4. (Color online) Effective permit-

tivity spectra eef(f) of magnetic wire

arrays with the axial field as a parameter.

(a) and (b) are for real and imaginary parts,

respectively. b 0.5 cm, a 10 lm.

FIG. 5. (Color online) Demonstration of

the magnetic field effect on the permit-

tivity spectra for different geometrical

parameters. b 1 cm in (a) and b 0.5cm in (b). Solid and dashed curves repre-

sent spectra for Hex 0 and Hex 2HK,respectively. The plots are labeled

according to the insert tables.



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(forward reflection) measured by means of Agilent N5230A

network analyzer. The wire was placed in the holder as a

central conductor of the short-circuited coaxial line. Thecalibration procedure is standard and consists of two stages.

First, a 1-Port short-open-load-thru calibration sets the refer-

ence plane at the cable end. After completing the measure-

ments, the serial and parallel parasitic impedances associated

with the sample holder were removed from the measure-

ments. These parasitic parameters were found from open and

short circuited measurements of the empty sample holder.

The impedance plots for the wire with a 10 lm versus Hexare shown in Fig. 7 for a number of frequencies from 10

MHz up to 4 GHz. It is seen that at 10 MHz the relative

impedance change in the low-field range is about 30%. This

relatively small value is associated with the distribution of

the anisotropy in the entire wire. With increasing a fre-quency, the impedance change ratio also increases becoming

more than 150% at 1 GHz for fields smaller than 1 kA/m. At

such high frequencies, it is also possible to distinguish the

impedance change due to the static magnetization change

which occurs at relatively small fields and due to the ac

permeability change which would require much higher fields

with increasing frequency. This is in agreement with the

theoretical plots given in Fig. 3. However, the theory does

not explain quite sharp impedance peaks for higher fields at

GHz frequencies. This could be related with calibration diffi-

culties since around the peak value the imaginary part of the

impedance changes sign. There are some conflicting results in

literature on the MI behavior at GHz frequencies and this will

require further investigations.1517,21,22 But it is interesting to

notice here that the field effect on the permittivity behavior

obtained from the free space measurements is most essentialat the field range typical of the magnetization processes.

B. Scattering spectra and effective permittivityof magnetic wire arrays

The wires described above were used to prepare a one-

layer lattice with in-plane size of 50 cm 50 cm suitable forfree-space measurements. The wires were glued in a sheet of

paper parallel to each other at a distance of 0.5 and 1 cm. To

apply a magnetic field, the sample was placed in a plane coil

having 70 turns with a relatively large step of 1 cm, which is

capable of producing a uniform magnetic field in the central

plane. A 35 A Agilent 6674A DC power supply is used tofeed the coil creating the magnetic field as high as 3000 A/m

with resolution below 1 A/m. The coil turns are perpendicu-

lar to the wires and generate the magnetic field along them.

The electric field of the microwave radiation has to be along

the wires therefore the coil will not interact with this field.

The free-space experimental setup consists of an Agilent

N5230A 20 GHz network analyzer with time domain option,

a pair of broadband (0.8517.44 GHz, aperture 342 256mm2) horn antennas and a compact anechoic chamber with

dimensions 80 80 80cm3 covered inside with a micro-wave absorber. The coil with the sample is placed in the mid-

dle of the chamber at a distance of 40 cm from each horn

antennas, appearing in the radiating near-field region in the

whole range of the investigated frequencies 0.917 GHz.

The Gated Reflect Line free space calibration23,24 was car-

ried out before the measurements. This relatively new tech-

nique based on Fourier transformation between frequency

and time domains allows the errors from parasitic reflections

to be greatly reduced. During the calibration procedure with

and without the metal plate placed in the middle of the cham-

ber, the metal plate position (and therefore the position of

the sample) and the required time gate span were defined in

the time domain. Gating of 400 ps was applied to the meas-

ured data. In addition, Agilent 85071E Material Measure-

ment Software was used for calculating the effectivepermittivity of the samples. In this calculation, the effective

thickness ofthe sample was considered to be equal to the lat-

tice period b.11

Figure 8 shows the effect of the external field on the

scattering spectra (reflection and transmission) of the sam-

ples with spacing between the wires b 0.5 cm. The fieldeffect is stronger for arrays with thinner wires (a 10 lm)for which the reflection coefficient decreases from 0.84 at

zero field to 0.72 for Hex 2 kA/m. This behavior isexpected as the skin effect is much stronger for thicker wires

with a 36 lm. The overall reflection increases in this caseand the effect of the magnetic properties of wires is less

noticeable. It is also seen that the highest field sensitivity

FIG. 6. (Color online) Hysteresis loops of as-cast glass-coated amorphous

wires of composition Co66 Fe3.5B16Si11Cr3.5 with different metal core radius

a, and glass thickness d: (1) a 36 lm, d 4 lm; (2) a 10 lm,d 2.4lm; (3) a 20 lm, d 5lm.

FIG. 7. (Color online) Real part of the impedance of Co66 Fe3.5B16Si11Cr3.5wire as a function of the magnetic field for different frequencies. The wire

parameters: a 10 lm, d 2.4 lm, l 3 mm.



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occurs at lower field range (less than 1 kA/m) where there is

change in the magnetization direction.

The scattering spectra were used to deduce the effective

permittivity with the help of Agilent 85071E Material

Measurement Software. The permittivity behavior for wire

arrays with the scattering spectra shown in Fig. 8 are given in

Fig. 9 Their dispersion is typical of a plasmonic type with

negative values of the real part in a low frequency band and

agrees well with theory. Without the field the real part of thepermittivity has the highest in magnitude values. When the

magnetic field is applied and the impedance is increased,

these values are decreased. Thus, for wires with a 10 lmand frequency 1 GHz, real part e0ef changes from 56 to 21when the field of 1 kA/m is applied. This is accompanied by

a substantial increase in the imaginary part. With increasing

frequency toward the plasma frequency, the losses are greatly

reduced and the field effect on the permittivity spectra

becomes weak. In the case of a thicker wire with a 36lmthe value ofe0efat f 1 GHz changes from 82 to 54 whenthe field is increased from zero to 1.5 kA/m Therefore, thefield effect is smaller than in the case of thinner wires due to

a stronger skin effect. The theory quantitatively gives very

FIG. 8. (Color online) Reflection (a,c)

and transmission (b,d) spectra of Co66Fe3.5B16Si11Cr3.5 wire arrays with the

spacing between the wires b 0.5 cm.(a), (b): a 10 lm; (c), (d): a 36 lm.

FIG. 9. (Color online) Effective permit-

tivity spectra of Co66 Fe3.5B16Si11Cr3.5wire arrays deduced from the scattering

spectra in Fig. 8 with the external mag-

netic field as a parameter. b 0.5 cm;(a), (b): a 10 lm, (c), (d): a 36 lm.



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similar results for the permittivity as can be seen by compar-

ing plots in Figs. 5(a), 9(a) and 9(c).

We also investigated electromagnetic response from

composites with larger spacing and lower plasma frequency.

In this case, the best field effect at GHz frequencies is

obtained for wires with a 20 lm. At 1GHz the real part ofthe permittivity changes from 11 to 4 when the field of0.5 kA/m is applied. For comparison, the spectra of wire

array with b

1 cm and a

36 lm is also given. In the latter

case, e0ef changes in the presence of the field from 16 to14 at 1GHz. These results also agree well with the theoreti-cal data shown in Fig. 5(a).

V. CONCLUSIONS

This paper provides a detailed investigation into the

electromagnetic response from magnetic wire media, i.e.,

periodic lattices of continuous ferromagnetic wires. The wire

medium is characterized by a negative permittivity in the

lower frequency band and has received much attention as a

component of double negative (also known as left-handed)

metamaterials. Here we are interested in another aspect of

the wire media, namely, a strong dispersion of the effectivepermittivity. For the wire radius in micron scale, and lattice

constant in mm scale, the plasma frequency which deter-

mines the frequency dispersion is in the GHz range. In this

frequency band, the permittivity dispersion may be used to

engineer a specific tuneable electric response. Using ferro-

magnetic wires makes it possible to alter the permittivity by

changing the losses in the system with an external magnetic

field or a mechanical stress which produces a change in the

wire magnetic configuration. The underlying physical mech-

anism involves a large magnetoimpedance (MI) effect.

We demonstrated both theoretically and experimentally

the efficient tuning of the permittivity and reflection/transmis-

sion spectra in glass-coated CoFeBSiCr wire lattices in the

presence of a moderate magnetic field (12 kA/m). The wires

are in amorphous state and have excellent soft magnetic prop-

erties with a circumferential magnetic anisotropy in the sur-

face layer. This is important to realize large MI at GHz

frequencies, in the order of 100%. The extent of the field tun-

ing depends not only on MI but also on the geometrical pa-

rameters of the wires and lattices. Thus, for the lattice period

of 0.5 cm and the wire radius of 10 lm, the real part of the

permittivity changes from

56 (no field) to

21 (1 kA/m) at

1 GHz as was deduced from the experimental scattering spec-tra obtained by a free-space measurement method. The theo-

retical results agree well with the experiment. The analysis is

based on calculating the relaxation parameter within the

effective medium theory, which depends on the wire MI.

The magnetic wire media could find various applications

due to the tuneable properties discussed in this paper. They

could be used as reconfigurable frequency selective surfaces

and constitute novel methods of nondestructive test for

structural health monitoring.

ACKNOWLEDGMENTSThis work was supported by EU ERA-NET program

under project DEVMAGWIRTEC, Grant No. MANUNET-

2007-Basque-3; by the Basque Government under Saiotek08

METAMAT Project. One of the authors, L. V. Panina,

also wishes to thank Ikerbasque Foundation for visiting

professorship.

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FIG. 10. (Color online) Effective per-

mittivity spectra of Co66Fe3.5B16Si11Cr3.5wire arrays with b 1 cm deduced frommeasured S-parameters for different mag-

netic fields. (a), (b): a 20 lm; (c), (d):a 36 lm.


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