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Progress in Materials Science 58 (2013) 183–259

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Progress in Materials Science

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Ferromagnetic microwires enabled multifunctionalcomposite materials

Faxiang Qin a,⇑, Hua-Xin Peng a,b,⇑a Advanced Composites Centre for Innovation and Science (ACCIS), University of Bristol, Queen’s Building, University Walk,Bristol BS8 1TR, UKb Bristol Centre for NanoScience and Quantum Information (NSQI), University of Bristol, Tyndall Avenue, Bristol BS8 1FD, UK

a r t i c l e i n f o

Article history:Received 28 August 2011Received in revised form 25 April 2012Accepted 12 June 2012Available online 29 June 2012

0079-6425/$ - see front matter � 2012 Elsevier Lthttp://dx.doi.org/10.1016/j.pmatsci.2012.06.001

⇑ Corresponding authors. Address: Advanced CoQueen’s Building, University Walk, Bristol BS8 1TR

E-mail addresses: [email protected] (F.X. Q

a b s t r a c t

The last two decades have witnessed increasing internationalinterest in ferromagnetic microwires research. Recent attentionhas turned to the development of innovative materials and com-posites derived from these microwires, such as microwire polymercomposites. Through incorporating an extremely small concentra-tion of microwires (10�2 vol.%), the resultant composite exhibits amultitude of functionalities which are desirable for a range of tech-nological applications. This article aims to provide a comprehen-sive review of current microwire composites research, fromprocessing to structural and property evaluations with a focus onthe multi-functionalities presented in these microwire composites.Starting with an introduction to multifunctional composites andthe theories pertinent to the multiple functionalities of microwirecomposites, a detailed description of fabrication methods of micro-wire composites is given with a comparison of different processingtechniques. Two fundamental effects, namely, giant magnetoim-pedance (GMI) and giant stress-impedance (GSI) of microwirecomposites, are discussed in relation to monolithic microwires.Microwave tunable properties in the presence of a dc magneticfield, stress or temperature field are presented and analysed indepth. The ferromagnetic wire composites have also been shownto possess metamaterial characteristics and microwave absorptioncapability. A detailed discussion of the influence of compositearchitecture, such as local properties of microwires and topologyof wire arrangements, on the performance of resultant composites,provides useful insights for an effective design of smart composites

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mposites Centre for Innovation and Science (ACCIS), University of Bristol,, UK (H-X. Peng).in), [email protected] (H-X. Peng).

http://dx.doi.org/10.1016/j.pmatsci.2012.06.001

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184 F.X. Qin, H-X. Peng / Progress in Materials Science 58 (2013) 183–259

for specific engineering applications, such as structural healthmonitoring, stress sensing, invisible cloaking, microwave absorp-tion and biomedical applications.

� 2012 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1842. Fundamentals of multifunctional composite materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

2.1. What is a ‘‘multifunctional composite’’? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1862.2. Fundamentals of multiple functionalities of microwire composites . . . . . . . . . . . . . . . . . . . . . 186

2.2.1. Giant magnetoimpedance and stress-impedance effects . . . . . . . . . . . . . . . . . . . . . . . . 1872.2.2. Microwave interactions with materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892.2.3. Field and stress tunable properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1922.2.4. Metamaterial properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1952.2.5. Electromagnetic interference shielding and microwave absorption . . . . . . . . . . . . . . . 199

3. Techniques for processing microwires and their composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
3.1. Amorphous metallic wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2023.2. Microwire composites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
3.2.1. Microwires-epoxy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2033.2.2. Microwires-elastomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2033.2.3. Microwire E-glass prepregs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

4. Basic magnetic and mechanical properties of microwire composites. . . . . . . . . . . . . . . . . . . . . . . . . . . 206
4.1. Magnetic properties of composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2064.2. GMI effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2074.3. GSI effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2094.4. Mechanical properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
5. Microwave tunable properties of microwire composites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
5.1. Field tunable properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
5.1.1. Field effect on the impedance of single wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2145.1.2. Continuous-wire composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2155.1.3. Short-wire composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

5.2. Stress tunable properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.2.1. Stress sensing based on microwires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2255.2.2. Stress tunable properties of composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
5.3. Temperature tunable properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6. Metamaterial and microwave absorption characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
6.1. Effectuation of microwire composite metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2366.2. Microwave absorption capacity of microwire composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

6.2.1. Dielectric loss dominated absorbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2396.2.2. Magnetic loss dominated absorbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

7. Potential applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
7.1. Microwave applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2427.2. Structural reinforcement and health monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2447.3. Other applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
8. Summary and directions for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
8.1. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2478.2. Outlook for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
1. Introduction

Materials we are dealing with today can be classified into structural materials and functional mate-rials in terms of their functionalities. Conventionally, composite materials are designed to be used as

F.X. Qin, H-X. Peng / Progress in Materials Science 58 (2013) 183–259 185

lightweight structural materials alternative to their metallic counterparts for structural functions only.In another aspect, functional materials have found a range of domestic and engineering applicationswith significant impacts. Naturally, an integration of these two categories of functionalities is muchaspired for yielding the so-called multifunctional composites as against to the unifunctional ones,in that a wealth of applications can be explored ranging from aircraft wings to drugs dispensing [1].A multifunctional composite must essentially meet the criteria of good mechanical performanceand another one or more value-added physical or chemical functionalities, such as good electricalor thermal conductivity and peculiar electromagnetic behaviours.

To materialise the multifunctional concept, adding functional fillers is considered as one of, if notthe only, the most effective routes. To name but a few examples, one of the most intensive researchsubjects is nanocomposites incorporating carbon nanotubes or nanoclays inside the polymer matrixto obtain favourable thermal and electrical conductivity for some specific applications such as de-icing, electromagnetic interference shielding and sensing applications [2,3]. Sufficient carbon blackis capable of turning an insulating polymer into a conductive one when it is added into the polymerin a proper manner [4]. The bioactive fillers can make a dull matrix biologically sensible in vivo andgreatly extend the scope of tissue engineering applications [5].

In the past two decades, the ferromagnetic microwires have been intensively studied due totheir particular magnetic properties which are of strong application interest [6–10]. Consisting ofa metallic core and glass coat, these microwires are primarily of CoFeSiB in composition (oftendoped with transition metal elements e.g., Mo, Cr, Nb), thereby giving very good ferromagneticproperties. They are structurally amorphous thanks to the existence of metalloid elements andthe fast-cooling process, but magnetically anisotropic in part due to their specific domain structurevarying with their composition and in part due to their geometry, such as microscale diameter andlarge aspect ratio. The most important properties of these wires are the so-called giant magnetoim-pedance (GMI) and stress-impedance (SI) effects, by virtue of which they can be used as functionalfillers to enable their resultant composites to have particular properties such as field/stress tunableproperties, microwave absorption functionality whilst retaining the mechanical performance of thecomposite.

Among the extensive literature on the multifunctional composite topic, there have been someexcellent monographs published: the book edited by Xanthos [11] gives a panorama of functional fill-ers and their composites and the latest review paper by Gibson [1] surveyed different classes of mul-tifunctional composites for hot topics such as self-healing composites and energy harvestingcomposites. Interested readers are referred to these works and the references therein. In these publi-cations, however, there is no mention of the microwires composites. Although Makhnovskiy and Pan-ina [12] contributed an outstanding book chapter on ferromagnetic microwires-based composites, it isfocused on the theoretical treatment of microwave tunable properties. In this context, it would be ofsignificant scientific interest to have a dedicated monograph on the microwire composites to summa-rise the on-going research on their fabrication, characterisation and perspective applications from anengineering perspective. The aim of this work is exactly to fill this gap by presenting a systematic re-view of microwire composites from their fabrication to the characterisation of the structural and elec-tromagnetic functionalities of the composites. With this understanding of the structure–propertyrelationship, they can be best exploited to meet a range of specific applications.

The rest of the review is organised as follows: Section 2 introduces the fundamentals of multifunc-tional composite from fundamental concept to expected properties. The fundamentals and theories ofGMI/GSI, microwave tunable properties, metamaterial behaviour and microwave absorption capacityare elucidated. Section 3 details the fabrication techniques of microwires and their composites. TheGMI/GSI effects and mechanical properties of microwire composites are elaborated in Section 4. Sec-tion 5 is devoted to the study of microwave tunable properties including magnetic field tunable prop-erties, stress tunable properties and temperature tunable properties. The high frequency behaviours ofmicrowires for magnetic and stress sensing are also expounded there. Section 6 is targeted on the sin-gular microwave absorption capacity of the microwire composite. Corresponding to the properties ofmicrowires and their composites, potential applications are outlined in Section 7. The main conclu-sions of the whole review are summarised in Section 8 together with an outlook.


2. Fundamentals of multifunctional composite materials

2.1. What is a ‘‘multifunctional composite’’?

A multifunctional composite conventionally refers to a composite material that, beyond the pri-mary structural function, possesses other functionalities as well achieved by constituent componentsin an optimised structure [13,14].1 Therefore, two points are underscored in this definition: (i) the com-posite must have multiple functions; and (ii) they are enabled by the constitutive materials. Such a logicmay lead one to a picture of a complicated composite structure consisting of any specific materialsaccording to the recipe of intended functionalities without regard to the compatibility of these materials.However, the architecture design of the composite will be a huge issue to tackle and it would also bedifficult for one to predict the properties of the resultant composite from those of the constitutive mate-rials insofar as the physical and chemical interactions between them are concerned. The brilliant idea ofmultifunctionalities is then tarnished by the high manufacture and maintenance cost. It appears to makethis kind of composite remain at the conceptual level or far from ideal, as demonstrated by a wide spec-trum of so-called multifunctional composites in the literature, inasmuch as they merely show a plusfunctionality at the expense, more often than not, of the mechanical performance. Strictly speaking, theyare closer to multi-functional structures or systems rather than materials. To address these issues, thefollowing should be realised: (i) an omnipotent functional filler is essential in that it will ensure theachievement of multifunctionalities and a relatively simple composite architecture. It does not necessar-ily mean all the functionalities must be exceptional. But the versatility so obtained warrants no increaseof cost, weight and complexity [15]; and (ii) a homogeneous material is a great priority for structuralintegrity and implementation, which can be approached in two ways: chemical intimacy between thefillers and matrix and extremely low loading of fillers that permits physical perturbations only. It istherefore reasonable to consider these standards as implicit behind the term of multifunctionalities,based on which the concept of truly multifunctional composites is initiated. To approach this concept,a couple of aspects are of major concern: (i) the functional fillers as described above; and (ii) the topo-logical arrangements of these fillers. From the vantage point of a bottom-up method, a perfect crystal (atabsolutely zero degree and no impurities) is invoked with all atoms static at their own sites presentingsuperb properties. If such a nanostructure is upgraded to a higher hierarchy at the mesoscale, analo-gously, one will end up with a composite material with periodical arrangements of static fillers. Thus,it is logical to infer that the composite property can be precisely predicted, when it is subjected to anenergy wave, via the interactions between the filling elements and the wave, and nearest neighbour-fillerinteractions provided that the single filler is well understood. In short, in realising the multifunctional-ities, the filler answers the question of yes or no and the filler topology answers the question of how goodit can be.

2.2. Fundamentals of multiple functionalities of microwire composites

In general, the multiple functionalities of composites are enabled by the functional fillers. The rel-evant theory associated with these functionalities should, therefore, be based on the physics pertinentto these fillers. In other words, although the local properties of fillers cannot decide the average com-posite behaviour, it may set a limitation for what could be achieved by their composites. Another cru-cial factor is the topological arrangement of these fillers as discussed above. Other factors include thematrix properties, interfacial properties, geometry of composites and so forth. Clearly, the research ofmultifunctional composites involves multidisciplinary science as against a unique physical phenome-non that can be explained within one theoretical framework. In this sense, rather than try to lay outuniversal principles for multifunctional composites, our discussion has been restricted to the micro-wire composites and narrowed down the relevant theories to specific targets. Since the functionalities

1 Gibson [1] divided multifunctional composites into three types: (i) multiple structural functions, (ii) non-structural functionsplus structural functions, (iii) both. This is a classification of multifunctionalities in a broad sense. In view of the recentdevelopment and the trend of multifunctional composites, our discussion has been limited to the type (ii), which we deem to be ajudicious and strict definition.


of microwire composites stem from the unique properties of microwires and their arrangements, thefollowing discussion will start with the GMI and GSI fundamentals of microwires, which lays the basisfor the particular microwave properties of their composites. Subsequently, the fundamentals of micro-wave interactions with materials and characterisation methods will also be introduced as essentialbackground knowledge. Following this, microwave properties of the composites including field tunableproperties, metamaterial property and microwave absorption properties are addressed separately. Itneeds to be highlighted that these three classes of properties are actually interdependent, as all of themare characterised by the effective permittivity and/or permeability, i.e. the average dielectric/magneticresponse of the material to electromagnetic irradiation.

2.2.1. Giant magnetoimpedance and stress-impedance effectsIn this section, a brief introduction to GMI will be given, providing essential knowledge for the fol-

lowing discussion on the microwave tunable properties. GMI is defined as the large variation of mag-netic impedance that happens in a soft magnetic conductor carrying a driving alternating current (ac)when it is subjected to a static external magnetic field [16]. The GMI effect is illustrated in Fig. 1, whichshows the magnetic field dependence of impedance and GMI for an Fe-based ribbon at 500 kHz. In thisexample, the maximum of GMI arrives at 33% (Fig. 1b).

Quantitatively, the GMI can be expressed as

Fig. 1.Fe71Al2

DZ=Z% ¼ 100%� ZðHÞ � ZðHmaxÞZðHmaxÞ

; ð2:1Þ

where Z(H) and Z(Hmax) are the impedance magnitudes of the microwire in the measured externalmagnetic field and maximum magnetic field to saturate the wire, respectively. The key points for thisdefinition are discussed as follows:

1. Giant magnetoimpedance, as it manifests itself, has to present a large change in the total imped-ance of more than 100% in quantity [17]. Vázquez [18] reported on a pronounced GMI of more than600%. In this case, it is quite promising for the application of magnetic sensors.

2. The GMI materials, whether wires, ribbons or films, are soft magnetic materials. The reasons forthis are twofold: first, only magnetic materials are sensitive to the application of an external mag-netic field; secondly, they are narrowed down to soft magnetic materials appropriate for applica-tions as magnetic sensors and actuators requiring essentially their low coercivity, small hysteresisloss and high initial permeability that ensure an easy magnetisation process. Note that the magni-tudes of these properties described above lead to a narrow hysteresis loop.

3. The alternating current plays an important part in the GMI effect. According to Iac ¼ I�jwt0 , its ampli-

tude and frequency are significant parameters to influence the GMI as a result of affecting the signand magnitude of alternative current. Numerous reports on the influence on GMI of these two

1.5

1.6

1.7

1.8

1.9

2.0 f = 0.5 MHz

Z ( Ω

)

H (Oe)-40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40

0

7

14

21

28

35

ΔZ/Z

(%)

H (Oe)

f = 0.5 MHz(a) (b)

(a) The impedance (Z) and (b) GMI ratio [i.e., DZ/Z(%)] change as a function of external field (H) for aSi14B8.5Cu1Nb3.5 nanocrystalline ribbon. Reprinted with permission from [7], copyright 2008 Elsevier.


agents have been published as regards its mechanism right down to the alteration of samples’domain structures, which are determined by the magnetic anisotropy associated with the alterna-tive current. It is highlighted that the orientation of the current should be perpendicular to theanisotropy direction for the purpose of producing the best GMI effect. In microwires, for instance,the current and the external magnetic field should be in the same direction along the axis so thatthe circular field it creates can interact with the magnetic structure of the wire and the externalmagnetic field, yielding a GMI effect based on the dynamics of magnetisation consequently.

4. The last but not least key point concerns the external magnetic field. Its function is realised by itsinfluence on the magnetisation process of the materials, therefore its orientation should be chosento make the best of this function with respect to the magnetic structures of the materials. It hasbeen proved that longitudinal giant magnetoimpedance (LGMI) gave rise to the largest magnetoim-pedance ratio (MIR) and field sensitivity compared with the transverse GMI (TGMI) and perpendic-ular GMI (PGMI), for example, in the case of ribbon [19]. In the LGMI and TGMI measurements,the dc magnetic field is applied in the ribbon plane, parallel and perpendicular, respectively, tothe probe current. In the PGMI geometry, the dc field is perpendicular to the sample plane andthe probe current. Also, the magnitude of the external magnetic field should be of the order of afew Oersteds (Oe)2 because the essence of GMI is that it occurs at relative low frequencies, and itis sensitive to a variation of external field of only few Oe, i.e., high field sensitivity, which is desirablefor applications of magnetic sensors and transformers.

Now let us dig a bit deeper into the GMI effect in physics terms. The GMI effect has an origin basedon the theory of classical electrodynamics, unlike giant magnetoresistance (GMR) that cannot be ex-plained without appealing to the quantum mechanics [20,21]. A theoretical explanation through thededuction originated from the Maxwell equations and Landau-Lifshitz equation is given here.

Basically, magnetoimpedance can be approached by solving Maxwell equations

2 1Oeelectromadvised

curlH ¼ J; ð2:2aÞ

curl J ¼ �lqð _Hþ _MÞ; ð2:2bÞ

and

divðHþMÞ ¼ 0; ð2:2cÞ

which can be reduced to

r2H� l0

q_H ¼ l0

q_M� grad divM; ð2:3Þ

where l0 and l is the vacuum permeability and material permeability, respectively; q stands for elec-trical resistivity. and the Landau–Lifshitz equation simultaneously

M ¼ cM �Heff �a

MsM� _M� 1

sðM0 � _MÞ; ð2:4Þ

where c denotes gyromagnetic ratio, Ms the saturation magnetisation, M0 the static magnetisation, Heff

the effective magnetic field and a the damping parameter. The impedance can be calculated. But dueto the difficulty in solving both equations simultaneously, Eq. (2.4) is often dismissed as far as a linearrelationship between the inductance and magnetic field is concerned. In this way, by solving Eq. (2.3),impedance for the wire can be resolved as follows [16,22]:

Z ¼ RdcktJ0ðkaÞ=2J1ðkaÞ: ð2:5Þ

In Eq. (2.5), Rdc is the electrical resistance, k = (1 + j)/dm, a is the radius of the wire, and J0 and J1 are theBessel functions of order 0 and 1, respectively.

= 80 A/m, we try to restrict the use of units to SI system, yet the prevalence of mks units in majority of publications onagnetic materials hinders us to do so. As such, both units will be regarded in the present paper. Unfamiliar readers areto refer to textbooks on electromagnetism for unit conversion.


The penetration depth is a function of the effective permeability, resistivity and frequency as de-scribed in the following equation for wire-shaped ferromagnetic materials [7]:

Fig. 2.field. R

dm ¼cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

4p2frleff

q : ð2:6Þ

From Eqs. (2.5) and (2.6), a convincing explanation can be reached that a variation of permeabilitycaused by the static external field gives rise to changes in the skin depth and finally in impedance.Obviously, in order to obtain a large MI ratio (MIR), a small resistivity and large permeability are nec-essary. On the other hand, reduction of resistivity and/or increase of permeability do not necessarilyresult in an improvement of GMI in that the dominating factor that determines the MIR is circumstan-tial. That is why strikingly different results and simulation models are often given regarding the rela-tionship between the same two parameters and a reason as well for further research on the GMI effectwith respect to exploring new materials and theories [23].

Research on the mechanism of GMI is also done from another perspective, whereby the real partand imaginary part of complex impedance are investigated separately according to the mathematicalexpression of complex impedance Z = R + Xi. It has been found that the extent of influence on the resis-tance (real part) [24] and the reactance (imaginary part) [25] varies with the frequency, but the influ-ences on both do exist and amount to the influence on the total impedance. It is worth highlightingthat Yelon et al. [26–29] have successfully established the connection between GMI and FMR at highmicrowave frequency and argued that they are rigorously equivalent, which proves to be instrumentalfor design of microwire arrays in order to manipulate the so-called GMI resonance [30] or FMR in themicrowave frequency range of specific application interest [30]. For more detailed discussion on theGMI theory, one can refer to previous reviews and the references therein [7,31].

2.2.2. Microwave interactions with materialsBefore proceeding directly to the electromagnetic properties of composites, one has to understand

the basics of microwave interactions with different kinds of materials. This section provides the pre-paring knowledge for one to understand the non-linear field effect and specific dispersion propertiesas well as the reflection and transmission features of the microwire composites.

The responses of materials to the incident microwave, in general, are characterised by two funda-mental parameters, namely, (relative) complex permittivity e = e0 � je00 and relative complex magnetic

Planar coil (current bus)or

TransmittingHorn Antenna

ReceivingHorn Antenna

Anechoic chamberwith the walls covered by a microwave absorber

Composite sample

External load

E

H

k

E

H

k

Fasteners

Free space measuring system. Two types of external action were applied to the sample: tensile stress and dc magneticeprinted with permission from [366].

Fig. 3. The scheme of measuring track showing the option of switching between chamber and cell. Reprinted with permissionfrom [366].


permeability l = l0 � jl00; Permittivity is to measure how much resistance is encountered when anelectric field is formed in a vacuum. It represents the ability of a material to polarise or ’permit’ inthe electric field. Likewise, the permeability is to measure the ability of a material to magnetise or’permeate’ in the magnetic field. ‘Relative’ refers to the normalisation by the vacuum permittivity(8.85 � 10�12 F/m) or permeability 4p � 10�7 H/m. e00 and l00 represent the dielectric and magneticlosses, respectively. They are close to zero at zero frequency or infinite frequency. The root reasonfor the emergence of dielectric/magnetic loss is the lag of response of materials to the external field.As

e00 ¼ e00p þrdc

e0x; ð2:7Þ

where e00p denotes polarisation or relaxation loss, rdc is dc conductivity. The dielectric loss is mainlycontributed by Ohmic (conduction) loss and/or polarisation (relaxation loss). It follows that, for con-ductors, higher conductivity tends to result in a larger energy dissipation. On the other hand, largerconductivity indicates a stronger skin effect according to Eq. (2.6) and the matter would be morereflective. Magnetic loss mainly results from the ferromagnetic resonance at high frequency, amongother mechanisms such as hysteresis loss, eddy current loss and the magnetic after-effect for low fre-quency. They can to some extent indicate the microwave absorption capacity of a material, however,to get accurate information, they should be considered together with the loss tangent (or loss factor),which are defined as tandE = e00/e0 (dielectric loss tangent) and tandM = l00/l0 (magnetic loss tangent).When the electromagnetic wave is incident on a material, the microwave energy is dissipated as heatthrough the interactions of electromagnetic force fields with the material’s molecular and electronicstructure, i.e., through damping forces on the polarised atoms and molecules and through finite con-ductivity. Based on the complex Poynting vector theorem, the absorbed power of the EM flowing into avolume V through a closed surface S is given as [32]:

Pdiss ¼ Re12

ISðE�H�Þ � �dS

� �¼ x

4

ZZZe0e00jEj2 þ l0l

00jHj2dv : ð2:8Þ

The characterisation of electromagnetic parameters at gigahertz frequency can be measured throughdifferent means. Here we introduce two methods that are dedicated to study the external field effectson the microwave properties.

strip of wood

Coil turns: red — ahead, blue - behind

+

_

“Slanting transition”between layers

Composite sampleWire inclusions

strip of wood

d/2

d

L

Fig. 4. The construction of a planar coil for laboratory investigations. The composite sample is placed in between two coillayers. The coil becomes ‘‘invisible’’ for a plane-polarised wave with the electrical vector directed transversely to the coil turns,as shown in Fig. 2. To provide the uniform magnetic field inside the coil, the distance between the coil layers must be equal tothe interturn distance d, and these layers must be shifted transversely across one another over steps of d/2. Reprinted withpermission from [366].


2.2.2.1. Free space measurement system. Investigation of the microwave tunable properties of compos-ites was carried out in the free space using the standard calibration technique named Through-Reflec-tion-Line (TRL) as a well-received testing method for dielectric materials and any non-coaxialmeasurements of S-parameters [33–37]. The schematic graph of the measuring system employedfor our experiments is shown in Fig. 2 [38]. To neutralise the influences of the noises on the scattering,the walls of the compact anechoic chamber are made of plywood and covered on the inside by amicrowave absorber and a Network Analyser with the time domain option is employed [34,39,40].Antennas are connected to the ports of a HP8720ES Spectrum Network Analyser through RG402cables with the Subminiature Version A (SMA) connectors (see Fig. 3) [41]. The detailed features ofantennas are as follows: (1) length: 887 mm; (2) aperture: 351 � 265 mm; (3) frequency range:0.85–17.44 GHz; (4) standing-wave ratio (SWR) < 1.7; (5) effective area > 150 mm2 in the range of0.85–15 GHz.

(a) Top view: A: measurement cell; B: tabletop tensilestretching unit; C: network analyser.

(b) The measurement cell. A: jaw, B: measurement celland C: sample to be measured.

Fig. 5. Photographs of instrumentation for microwave measurements. Reprinted with permission from [277], copyright 2005IOP.


The distance between antennas is controllable with the mobile front walls of the chamber wherethe antennas are fastened to meet the requirement of preliminary TRL calibration. The frame’s func-tion is to guarantee the uniform heating or magnetic field along the sample surface when the micro-wave response depends on the external stimuli including field, stress and temperature. A current busor a planar coil was used for the same reason and also makes the composites easily tunable by a weakmagnetic field. It is highlighted that the parallel current wires must be oriented perpendicularly to thevector of the electrical field in the plane-polarised accidental electromagnetic wave in order to allowfor nothing but the interaction between the composites and electromagnetic wave. Note that the de-sign of the switch makes the most of the analyser, between the non-contact microwave test in the an-echoic chamber and the contact test on magnetic wires in the measuring cell (Fig. 3) [38,41].

If a very high magnetic field is required, the planar coil is preferred to the current bus because allturns in a coil are connected in series, so passing the total current. The construction of the frame out ofplanar coil is shown in Fig. 4. The sample is placed between the two coil layers.

The complex permittivity can be computed from the S-parameters collected from the measure-ment. S-parameters S11 and S21 can be expressed via reflection coefficient C and transmission coeffi-cient T as [33]:

S11 ¼Cð1� T2Þ1� C2T2 ; ð2:9aÞ

and

S21 ¼Tð1� C2Þ1� C2T2 : ð2:9bÞ

Cand T can then be calculated by:

C ¼ ðZsn � 1ÞðZsn þ 1Þ ; ð2:10aÞ

and

Zsn ¼ ð1=ffiffiffiffiffie�pÞT ¼ e�cd; c ¼ ð2p=k0Þðe�Þ1=2

; ð2:10bÞ

where k0 is the wavelength in the free space and d is the thickness of the sample. The complex per-mittivity is given by:

e� ¼ cc0

1� C1þ C

� �: ð2:11Þ

2.2.2.2. Microwave frequency-domain spectroscopy. A modified microwave frequency-domain spec-trometer is shown in Fig. 5. Fig. 5a shows the instrument specifically designed for study the effectsof stresses on the samples. A strain as large as 100% is obtainable if within the flexibility of the sample.The extension was measured with a hand gauge. The samples were mounted strictly along the direc-tion of stress applied. A solenoid can be easily set up to allow a measurement in the presence of mag-netic field along the wave propagation direction.

Fig. 5b illustrates the perspective view of the measurement cell. With S-parameters measured bythe network analyser, the permittivity and permeability can be extracted by a utility program. Notethat this instrument is capable of simultaneous measurement of electric permittivity and magneticpermeability in the presence of magnetic field and/or stress at a very wide spectra coverage up togigahertz.

2.2.3. Field and stress tunable propertiesThe microwave tunable properties of a microwire composite, by nature, are the response of effec-

tive permittivity to the electromagnetic wave through the surface impedance. Therefore, to explainthis phenomenon, one needs to understand the basics of wave interactions with the materials andthe effective medium approaches to characterise heterogeneous composites.


2.2.3.1. Effective permittivity. The effective permittivity should be treated differently in two types ofcomposites. In composites containing short wires, the Lorentz model proves to be effective, whereasthe Drude model is applicable to composites containing long wires. The Lorentz model is first consid-ered to be applicable to all insulator materials. Along the inclusion length the current with a lineardensity j(x)e�ixt is induced by the local electrical field elocexp(�ixt). Using the continuity equationand integration by parts with boundary conditions the electric dipole moment D can be calculated:

D ¼ ix

Z l=2

l=2jðxÞdx) a ¼ D

Veloc; ð2:12Þ

where l is the length of the wire and V is the inclusion volume. And within the frame of this approachthe dielectric polarisability a of the inclusion can also be calculated [42]:

aðxÞ ¼X

n

An

x2res;n �x2

� �� iCnx

; ð2:13Þ

where xres,n is the angular resonance frequency, An are amplitude constants and Cn are the dumpingparameters. A1 whereof contributes most to the polarisability corresponding to the lowest frequency.Cn is considerably influenced by the resistive magnetic losses [43] and it presents a strong dependenceon the external magnetic field or stress in the vicinity of an antenna resonance in certain conditions.An experimental proof of this equation has been provided in Refs. [44,45].

The bulk polarisation of the composites can be expressed as:

P ¼ helocipva ¼ e0veff ; ð2:14Þ

where eloc is the averaged local field, pv is the volume concentration of the inclusions, e0 is the externalelectric field and veff is the effective bulk susceptibility. When pv� pc, it follows that eloc � e0 [46].Thus the effective permittivity can be obtained by:

eeff � eþ 4ppvhai; ð2:15Þ

where e is the permittivity of matrix, ha i is the averaged polarisability of an individual inclusion. Fur-ther calculations involve the GMI effect and surface impedance of wires, which are presented in thefollowing section.

For continuous-wire composites, charge distribution along the wire axis is absent and hence nocurrent or dipole response exists. It can then be treated as a medium with diluted plasma accordingto Pendry et al. [47]. Thus, the dispersion of effective permittivity for this kind of composite is char-acterised by the plasma frequency expressed as:

x2p ¼

2pc2

b2lnðb=aÞ; ð2:16Þ

where b is the wire period. In this context, the deduction of effective permittivity can be approachedby solving the Maxwell equations in a homogenisation procedure as the wire parameters have noinfluence on the permittivity. For a nonmagnetic wire composite, the effective permittivity can be gi-ven by [48]:

eeff ¼ e� pv2ecF1ðkcaÞ

ðakcÞ2F1ðkcaÞlnðL=aÞ � 1;

F1 ¼ J1ðxÞ=xJ0ðxÞ; pv ¼ pa2=L2;

ec ¼ 4pir=x; kc ¼ 4pixr=c2;

ð2:17Þ

where pv is the wire volume concentration, ec is the dielectric permittivity of the conductor, r is thewire conductivity, kc is the wave number, and J0,1 are Bessel functions. At microwave frequency, thereis a very strong skin effect, i.e., akc � a/d 1. Thus Eq. (2.17) can be reduced to Eq. (2.16), justifying theapplication of the model for continuous-wire composites. As with short-wire composites, impedanceshould be calculated first.


2.2.3.2. Impedance tensor. The surface impedance is a parameter to characterise the voltage responsein the wire system, as described in the GMI phenomenon. To calculate the impedance tensor in thewire, the electromagnetic conditions about the wire should be fully understood. Fig. 6 shows the cur-rent ex along the wire axis direction inducing the circular field h/, of which the tangential componenthx,0 plus the external field induce the electric field e/. In this case, the response to the electromagneticfield from the wire via the impedance tensor with the boundary conditions can be written as [49]:

Fig. 6.Science

Et ¼ 1̂ðHt � nÞ; ð2:18Þ
where n is the unit normal vector directed inside the wire, Et and Ht are the tangential vectors of thetotal electric and magnetic fields at the wire surface, including both scattered and external fields.Adopting the typical simplified approach for antenna problems, Eq. (2.18) can be written in polar coor-dinates (x,/) [12]:
Ex ¼ 1xxH/ � 1x/Hx;

E/ ¼ 1/xH/ � 1//Hx: ð2:19Þ

2.2.3.3. Stress and field dependence of impedance and permittivity. For short-wire composites, it followsEq. (2.15) that the averaged polarisability needs to be worked out. When the interactions between thewires are reasonably neglected, it can be derived as [50]:

hai ¼ 1

2p lnðl=aÞðkaÞ22kl

tanðkl=2Þ � 1� �

;

k ¼ xffiffiffiep

c1þ ic1xx

xalnðl=aÞ

� �1=2

:

ð2:20Þ

It should be noted that the equations are established in the frame of the composites in question with amoderate skin effect, under which the radiation loss is overshadowed by the magnetic and resistivelosses.

It can be seen from Eqs. (2.15) and (2.20) that the permittivity depends on the surface impedance inthis case. Due to the GMI effect as previously analysed, the dependence of permittivity through imped-ance on the external field is well established according to Eqs. (2.5), (2.6), and (2.23).

In the case of long-wire composites, Eq. (2.17) was extended to approach to the case of magneticwires. By substituting the impedance formula, Eq. (2.17) is transformed to [51]:

eeff ¼ e� pvw2

p

w2 1þ i c1xxxa lnðb=aÞ

� � : ð2:21Þ

Thus, the effective permittivity for continuous-wire composites is dependent on the wire surfaceimpedance via the plasma frequency.

Schematic diagram of the magnetic configuration in a wire. Reprinted with permission from [12], copyright 2005 Nova.


Due to the amorphous structure of the microwires, their anisotropy consists of no shape anisotropybut the magnetoanisotropy coupled by the internal and/or external stress and magnetostriction. Theinfluence of internal stress and applied stress on GMI has been reported theoretically in Refs. [52,53].Regarding the glass-coated microwires, the following equations are held:

K ¼ K0 � 1:5kðrzz � r// þ rappliedÞ ð2:22aÞ

and

Hk ¼ 2K=l0Ms; ð2:22bÞ

where K and Hk are the anisotropy constant and field, respectively, rzz, r// and rapplied are the axial,azimuthal stress and applied stress, respectively, Ms is the saturation magnetisation and l0 the perme-ability in vacuum. Also the effective permeability depends on the ratio of Hk to Ms, which is deter-mined by K, expressed as [54]:

leff ¼Ms sin2ðhþ heÞ

Hk½h sin2ðhþ heÞ þ cosð2hÞ; ð2:23Þ

where the anisotropy field Hk = 2K/Ms and h = Hex/Hk. h is between the anisotropy angle he and p/2. Be-sides, the static magnetisation angle also changes with the static magnetisation angle, as indicated inthe equation for the magnetostatic energy Um based on the equivalent uniaxial anisotropy [55]:

Um ¼ �jeK j cos2ða� hÞ �M0Hex cos h; ð2:24aÞ

jeK j ¼ K þ ð3=2Þkra

cosð2~aÞ ð2:24bÞ

and

~a ¼ 12

tan�1 3jkrt jjK þ ð3=2Þkraj

; ð2:24cÞ

where a is the anisotropy angle which takes different values according to the relationship between theanisotropy constant K and the product of magnetostriction constant k multiplying the axial stress ra

[50].The tunable properties can be characterised by the free-space measurement. From what has been

discussed above the dependencies of effective permittivity through magnetoimpedance on the fieldand stress are well established. A note is in order here. Such metal-dielectric composites incorporatingwire-shaped inclusions have been treated theoretically and experimentally for decades [56]. Most re-cently, researchers have found that it is possible to obtain a negative permittivity and/or permeabilityat certain frequencies for this kind of composite and recognised its importance [57]. This brings aboutthe next important functionality of the wire-composite, i.e., metamaterial properties, which will bediscussed in the following section.

2.2.4. Metamaterial properties2.2.4.1. Fundamentals of metamaterials. Metamaterials are one of the most appealing subjects in mate-rials and physics nowadays (see, e.g. [57–62]). Any research, if connected to metamaterials, appears tobe absolutely fascinating and cutting-edge. To begin with, the basic question is elucidated as to what ametamaterial is.

A metamaterial is by definition an artificially engineered material that gains its properties from itsstructure rather than its constituents. The resultant properties are not encountered in naturally occur-ring materials, such as negative refractive index and negative stiffness [63]. First of all, a metamaterialmust be non-existent in nature, which accounts for the origin of its name as meta means ‘beyond’ or‘of a higher kind’ in Greek [64]. It is an extension to the conventional materials in terms of materialbehaviours. Second, the unique properties of metamaterials are not derived from their constituentmaterials but from their structure, which distinguishes them from conventional composite materials.Typically yet not essentially, a metamaterial boasts an ordered structure, realised by a periodicarrangement of the functional units, as schematically depicted in Fig. 7. Another implicit regulation

Fig. 7. Generic sketch of a volumetric metamaterial synthesised by embedding various inclusions in a host medium.


is that the physical dimensions of unit (scale) and neighbouring distance (periodicity) must be smallerthan the incident wavelength so that homogeneity can be ensured without which a material cannot berecognised as ‘material’ [63]. The collective responses (effective responses) of all units to the externalfield (stimuli) give the macroscopic properties of a metamaterial. By manipulating the scale and peri-odicity of these units one can tailor the properties of a metamaterial. The effective medium theoryfinds great use herein to study the behaviour of metamaterials as reviewed in Ref. [65], which in turncan be instrumental to metamaterial design and engineering for specific applications. In this sense,metamaterials can also be categorised into smart materials and multifunctional composites.

In this review, the metamaterials are restricted to electromagnetic metamaterials of our majorinterest. The metamaterial engineered by functional units as basic building blocks can be analogisedto the conventional materials out of atoms. Likewise, Maxwell equations can be transformed frommicroscopic to macroscopic form, making it possible to describe the electromagnetic response of ametamaterial via both an effective permittivity (e(x)) and permeability (l(x)). At the sub-wavelengthscale, these two parameters can be manipulated independently thanks to the decoupling of the mag-netic and electric field. It follows that some intriguing properties can be achieved for some appropriate

Fig. 8. Negative refraction. (a) An empty glass. (b) A glass filled with an ordinary medium with positive refractive index, such aswater; the straw inside the glass is refracted. (c) The water is replaced by a negatively refracting medium. Reprinted withpermission from [367], copyright 2006 OSA.


materials. For instance, magnetic responses can be realised in metamaterials consisting of mere non-magnetic constituents [66]. At certain frequencies, a negative refractive index material (NIM) can beobtained with both e(x) and l(x) being negative ðn ¼ � ffiffiffiffiffiffilep Þ, as depicted in Fig. 8. The exploitation ofNIMs opens up new prospects of manipulating light and produces revolutionary impacts on present-day optical technologies.

2.2.4.2. Classification of and approaches to metamaterials. Since e(x) and l(x) can be controlled inde-pendently, it is possible to obtain the unusual media with either only negative e(x) (ENG) or only neg-ative l(x) (MNG), and both of them negative (DNG) as against the conventional media with bothparameters positive. Such a classification according to the sign of e(x) and l(x) is shown in Fig. 9and each class is detailed in the below.

Fig. 9. Classification of materials in the el plane in terms of their signs. Reprinted with the permission from [59], copyright JohnWiley & sons.

Fig. 10. Arrays of SRR structure (a) and nanorods (b). Reprinted with the permission from [57], copyright 2005 OSA.

Fig. 11. A superlens capable of high-resolution imaging. Reprinted with the permission from [368], copyright 2007 NaturePublishing Group.


ENG Many plasmas exhibit this characteristic below plasma frequencies according to the Drudemodel. Veselago [67] initially proposed gaseous and solid plasmas. Decades later it was foundthat noble metallic wires (e.g., silver, gold) behave in this manner in the infrared (IR) and visiblefrequency domains [57]. This is theoretically proposed first by Rotman and Pendry [47,68];Smith et al. [61] and Shelby et al. [60] realised the idea using thin wires as the scattering ele-ments. Composites containing conductive sticks have also been intensively investigated to rea-lise negative permittivity by Lagarkov et al. [44,46] and Makhnovskiy and Panina [12].

MNG Typical materials of this kind are gyrotropic materials. The composite media with thin wiresenabling a resonance feature are also capable of giving negative values of effective permeabilitynear the resonance frequency.

DNG Also known as Veselago medium named after its discoverer [67], left hand material and NIM. Itwas realised by Smith and Shelby et al. [61] via split ring resonators (SRRs), as shown in Fig. 10a.It consists of two planar concentric conductive rings, each with a gap. Shalaev et al. [57] alsosuccessfully fabricated the NIMs using arrays of gold nanorods or thin wires as illustrated inFig. 10a.

2.2.4.3. Applications of metamaterials. The reason why metamaterials become a focus of intense studyis primarily that they afford a range of novel applications. Perfect lenses proposed by Pendry [58] areone of the most exciting applications. A lossless slab (Fig. 11) with a refractive index n = �1 projects animage of the object placed into the near field with subwavelength precision. This has profound im-pacts on biomedical imaging and subwavelength photolithography [69].

Metamaterials are a basis for building a practical cloaking device. The possibility of a working invis-ibility cloak was demonstrated in Ref. [70]. The cloak deflects microwave beams so they flow around a‘‘hidden’’ object inside with little distortion, making it appear almost as if nothing were there at all.Such a device typically involves surrounding the object to be cloaked with a shell which affects thepassage of light near it. Using FE simulations, Cai et al. [71] designed an optical cloaking device whichdeploys an array of metallic wires projecting from a central spoke that would render an object withinthe cloak invisible for red light.

Most recently, with a flooding study of metamaterials, more potentials are explored for industrialapplications. Sato et al. [72] reviewed the applications of metamaterials in automobiles as summa-rised in Fig. 12. Melik et al. [73] proposed a metamaterial-based stress sensor with exceptional reso-lution. Metamaterials are also applied to improve the performance of antennas as reported, e.g., by

Fig. 12. Applications of metamaterials in automobiles [72], reproduced courtesy of the Electromagnetics Academy.


Alici and Özbay [74]. The microwave-absorbing capacity of a conventional shielding material is en-hanced by the metamaterial coating recently reported by Zou et al. [75], implying the potential ofmetamaterials in electromagnetic interference shielding (EMI) applications. EMI will be discussed inthe next section.

Overall, there are still many unknown applications yet to be tapped into for metamaterials. In thepresent work, arrays of magnetic microwires are employed to obtain negative effective permittivity.Plus, the antiferromagnetic resonance features of ferromagnetic microwires suggest that a negativepermeability is also obtainable. In this sense, the microwire-composite could demonstrate the meta-material functionalities, for which corresponding applications are anticipated.

2.2.5. Electromagnetic interference shielding and microwave absorption2.2.5.1. EMI shielding. Electromagnetic interference (EMI) by definition is the process by which disrup-tive electromagnetic energy is transmitted from one electronic device to another via radiated or con-ducted paths or both. Suppression is the process of reducing or eliminating EMI energy. It may includeshielding and filtering [76]. EMI problems have impacted almost all electrical and electronic systemsfrom daily life to military activity, and to space exploration, for the following major reasons: (i) theproliferation of electronic equipment and various devices in both industrial and domestic environ-ments affords a good chance for EMI; (ii) miniaturisation of components in electronic systems and sys-tems themselves physically increases the potential of EMI; and (iii) new digital technology turns out tobe in favour of EMI [76].

EMI has been found not only detrimental to electric appliances but also harmful to human health asit may contribute to serious diseases such as cancer [77]. Effective shielding materials are thereforedesired to minimise the influence of EMI. To locate effective shielding materials, one has to understandforemost the EMI theory, or, what constitutes EMI and what material properties are desirable to arrestEMI.

EMI theory lies within the framework of electromagnetic wave theory. An electromagnetic waveconsists of two components, namely, a magnetic field H

!and an electric field E

!. They are normal to

each other and the prorogation direction of the wave is normal to the plane containing them. The ratioof E!

to H!

is termed as impedance. EMI shielding can be divided into the near field region and the farfield region according to whether the distance between the radiation source and the shield is smallerthan k/2p or not. It is the far field region that the EM wave theory is applicable, whilst the electric andmagnetic dipoles are responsible for the EMI occurring in the near field region [78].

EMI capacity is parametrised by the shield effectiveness (SE), which is defined as the ratio of theresidual energy to impinging energy. The EMI attenuation afforded by a shield relies on three mech-anisms as depicted in Fig. 13. The first is the reflection of the wave from the shield (R); the second isthe absorption of the wave when it passes through the shield (A); and the third originates from the

Absorption (A)Incident wave

Reflectionloss (R)

Secondreflection loss

Transmittedwave

Re-reflectedterm

Internalreflections

(M)

Fig. 13. Schematic representation of EMI shielding.


multiple reflections of the wave at various interfaces within the shield (M). The total SE can be given inthe form [79]:

SE ¼ �10 logpout

pin¼ SER þ SEA þ SEM; ð2:25Þ

where Pin and Pout are the incident power and transmitted power, respectively. The reflection shieldingeffectiveness, SER, can be approximated as SER = �10log(1 � R). Likewise, the multiple reflectionshielding effectiveness, SEM can be expressed as SEM = �10log(1 �M). Thus, the absorption shieldingeffectiveness, SEA, can be approximated as SEA = �10log[T/(1 � R �M)], where T representstransmission.

To suppress the increasing EMI, it is necessary to pursue new materials with enhanced EMI shield-ing capacity. Due to the skin effect (see Eq. (2.6)), high frequency EM radiation only occurs in the sur-face layer of an electrical conductor. Since a smaller skin depth results in larger attenuation, lowerresistivity and higher permeability are required for achieving a better shielding performance. In thiscontext, a wide range of candidate materials have been suggested for EMI shielding applications. Amost typical material among them is the polymer composite containing metallic fillers such as steel,nickel or silver in the form of powder fibre or flake [80–83]. It was reported that the shielding effec-tiveness (SE) exceeded 30 dB for steel fibre reinforced composites with a filler loading of 6 wt.% and athickness of 1.5 mm at 1–2 GHz [82]. An SE of more than 50 dB was also reported for the nickel pow-der-filled composites with a filler loading of 40 wt.% and a thickness of 2.85 mm [80]. While these fill-ers benefit the shielding properties of the resultant composites, the large density, physical rigidity andlow corrosion resistance of the metallic phase are disadvantageous. In addition, a relatively high load-ing of these fillers is required for achieving low resistivity and high SE. Recently, carbon fibre [84–87]and carbon nanotubes (CNT) [88–95] have been shown to be useful for EMI shielding applications. Inthe case of carbon fibres, it would be ideal if they could yield large SE as these materials are widelyused in the aerospace and automobile industry. However, when compared with metallic fillers, thehigher resistivity of carbon fibres imposes a stringent requirement of a larger loading of carbon fibresin order to achieve the same shielding effectiveness, thus raising the manufacture cost. While someefforts have been made to improve the conductivity of the fibres by coating them with a thin metalliclayer, the coating itself could be easily damaged during the coating processing [84]. For the case of thecarbon nanotubes-based composites, Li et al. [88] reported an SE of more than 25 dB for MWCNT/poly-acrylate composites with 10 wt.% CNTs and a 1.5 mm thickness at X-band (8–12 GHz). Park et al. [89]found that a 15 l m thin CNT bucky paper containing more than 50 wt.% CNTs reached the SE of 22 dBat 2–18 GHz. By catalysing the CNTs with magnetic particles such as Fe, Co, Ni and their compounds,the SE of the CNTs-based composites was significantly improved due to the increased absorption as aresult of the introduction of magnetic permeability [90–95]. However, the difficulty in dispersingnano-sized fillers and high fabrication costs hinder the CNTs-based composites from commercial


applications. Some conductive polymers have also been developed recently for EMI shielding applica-tions, but their poor mechanical properties make them undesirable for such applications [96–99].

2.2.5.2. Microwave absorption. Absorption, as mentioned above, occurs when the microwave interactswith the materials. The absorption or attenuation originates from the dielectric loss (polarisation andconduction loss) and the magnetic loss (ferromagnetic resonance, eddy current loss, hysteresis loss,etc.). The key to realise high absorption consists in not only a large loss factor but matching permit-tivity and permeability (impedance match) according to the transmission line theory [100]. For a sin-gle layer composite,3 the reflection loss (RL) is given by [100,104,105]:

3 Thediscuss[100,10

RL ¼ 20 log

ffiffiffile

qtanh j 2pfd

c

ffiffiffiffiffiffilep� �� 1ffiffiffi

le

qtanh j 2pfd

c

ffiffiffiffiffiffilep� �þ 1

; ð2:26Þ

where l and e are the relative permittivity and permeability of the absorbing material, respectively. jis the imaginary unit. f denotes frequency, c the light speed in free space and d the thickness of theabsorber. The attenuation constant a (real part of the propagation constant c) is then given by[100,106]

a ¼ ReðcÞ

¼ Rejx ffiffiffiffiffiffilep

c

� �¼ xffiffiffi

2p

c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil00e00 � l0e0 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðl02 þ l002Þðe02 þ e002Þ

qr: ð2:27Þ

Here one can see that the attenuation constant is dependent on complex magnetic permeability. Toobtain large attenuation constant at any frequency, it requires large l00, e00, tanEd and tanMd. However,this condition needs to be tempered with Eq. (2.26), whereby a matching condition must be satisfiedin order to obtain minimum reflection loss, expressed as [107–109]
ffiffiffiffi
le

rtanh j

2pfdc

ffiffiffiffiffiffilep� �

¼ 1: ð2:28Þ

Detailed calculation reveals that the absorption bandwidth and maximum absorption are actuallytwo offset parameters. For a dielectric absorber, the usual case is that larger e00 gives rise to larger losstangents and an optimised e00 and associated loss tangent can be expected to achieve the maximumabsorption condition (too small or too large e00 will not be in favour of absorption). For a magnetic ab-sorber, the matching frequency can be regarded as the ferromagnetic resonance frequency, which canbe given as

f ¼ r2p

Hk; ð2:29Þ

where c = 2.8 MHz/Oe is the gyromagnetic ratio. The anisotropy field Hk is given by [110]

Hk ¼2jK1jl0Ms

; ð2:30Þ

where K1 is the anisotropy constant and Ms is the saturation magnetisation. A larger saturation mag-netisation or smaller anisotropy field will redshift the resonance frequency, which also means an im-proved absorption bandwidth, since there exists a trade-off between resonance frequency andabsorption bandwidth [111].

aim of this section is to provides a basic understanding of MA theory relevant to microwire composite. More detailedion on the case of multilayer absorber and the design principle can be found in other review papers [101] or books2,103].


Since the implementation of carbon black and Al flakes as radar absorbing material in the airborneand seaborne vehicles during WWII [112], a plethora of absorbing materials have been developed andcommercialised including dielectric absorbing materials such as carbon black [104,113,114], carbonnanotubes [115–117], SiC fibres [118] and nanowires [119], short carbon fibres [120–122], and othernon-magnetic conducting particles; and magnetic absorbing materials such as M-type hexaferrites[123,124], magnetic nanoparticles [106,125] and magnetic particles filled nanotubes [90,91,126].Although the nanomaterials have attracted much attention as promising absorbing materials, themost widely used absorbing materials are still magnetic ferrites [127–129], carbon black and carbonyliron powder [130–132]. In comparison with the magnetic powders, the ferromagnetic microwires areadvantageous in their unique shape anisotropy that aids wave attenuation, a capability to overcomethe limitation of Snoek’s law, and superior tailorability of electromagnetic properties through wiregeometry and concentration [133,134]. In this context, in spite of their relatively large diameter,the ferromagnetic microwires with superior electromagnetic properties and mechanical propertiesare investigated as structural absorbing materials in quite a few studies, which will be discussed inSection 6.2.

3. Techniques for processing microwires and their composites

3.1. Amorphous metallic wires

Based on the conventional techniques for fabricating amorphous alloys, a variety of fabricationtechniques have been advanced for microwires fabrication, including melt spinning [135–139], in-rotating water spinning [8,140–145], electrodeposition [146–151] and the most popular technique,the Taylor–Ulitovskiy method [8,152–159]. For details of these processing techniques, one can referto the previous reviews on GMI [7,31] and microwires [6,9,160,161]. Here we just discuss the melt-extraction technique that is absent in previous reviews.

Melt-extraction (MET) was first applied to prepare metallic fibres as long as four decades ago [162].It was further developed to find wide use in the fabrication of amorphous wires, ceramic fibres such ascalcium aluminate [163] and high resistivity alloy wires such as MgZnCa [164]. Recently, it is increas-ingly used in the fabrication of magnetic microwires [165–169]. The basic principle of MET is to applya high-speed wheel with a sharp edge to contact the molten alloy surface and then to rapidly extract

Fig. 14. Schematic of melt-extraction facility.

Fig. 15. Morphology of polymer composite plate sample (a) and arrangement of the short-cut microwires in it (b). Reprintedwith permission from [172], copyright 2010 Elsevier.


and cool a molten layer to be wires, as schematically shown in Fig. 14. There are three main advanta-ges of this technique: (i) MET gives a higher solidification rate of 105–106 K/s than any other method,which is in favour of the form of amorphous phase. (ii) The wires produced by this method possessextraordinary mechanical properties due to the quality faultless surface and circular geometry[164,170]. (iii) The soft-magnetic properties of the materials are significantly improved by fabricatinginto microwires via MET; this is believed to be attributed to the considerable quenched-in stress [167].The main drawback of this method is that it has loose control on the diameter of the produced wires.The typical diameter range for the magnetic wires is about 30–60 lm [165–167,171] depending on theprocessing parameters. Apparently, it is not suitable for preparing ultra thin magnetic microwires.

3.2. Microwire composites

Loosely defined, microwire composites can be any form of material consisting of wires and a matrixmaterial, while in engineering parlance, microwire composites conforming to the above definitionmay not be able to serve general structural purpose and hence cannot be categorised as compositematerials. In the section, the scope will be extended to any form of microwire composite with a par-ticular note of its application range. The emphasis is placed on the microwire composites that meetthe quest for both functional and structural use.

3.2.1. Microwires-epoxyEpoxy is believed to be the most extensively used as the matrix material for all kind of composites

and coatings for engineering applications. Zhang et al. [172] prepared a microwire composite coatingon the surface of aluminium plate using polyamine dissolved by alcohol. The resultant composite andmicrowires arrangement are shown in Fig. 15. Liu et al. [173] also used epoxy to cast the toroidal sam-ples for microwave characterisation. Starostenko and Rozanov [30] fabricated the composite mat bycoprecipitation of glass fibre and wire pieces in a dilute solution of polystyrene. It should be noted thatthe wire pieces are used in these works are in the range of 5–10 mm. If the wires are too long, it wouldbe challenging to realise a good dispersion of wire pieces and receive the 2D plane-isotropic compos-ite. If the wires are too short, the demagnetising effect would be too strong and ruin the overall elec-tromagnetic properties of the microwire composite.

3.2.2. Microwires-elastomersCompared to epoxy, elastomers usually have much smaller Young’s modulus (2 MPa) and hence

will appropriate strain when subject to even a relatively small force. Thus rubber-based compositesare suitable for characterising their responses to the stress.

Qin and co-workers [174,175] used two pieces of transparent silicone rubber sheets to prepare theplanar composites with periodically arrange continuous wires. The procedure schematically shown inFig. 16 is as follows:

Fig. 17. Schematic structure of toroidal composites: (a) Isotropic samples; (b) anisotropic sample. Reprinted with permissionfrom [171], copyright 2007 Nonferrous Metals Society of China.

Fig. 16. Schematic of the preparation of continuous-wire composites based on silicone rubber for free-space measurements;the final dimensions of the resultant composite are 520 � 500 � 1.5 mm.


(1) 500 mm long microwires were laid out in a periodical manner with a fixed wire spacing on thewhite sheet.

(2) Around 80 g thoroughly stirred and vacuumed liquid silicone rubber/hardener mixture wereuniformly cast on the surface as the adhesion layer, which was followed by covering the trans-parent layer right on the top. An aluminium plate and heavy weights were then placed on thetop of the preform to assist the curing process in the ambient air.


(3) After 24 h when the resin was cured, four surface-roughed glass-fibre tabs of 10 mm � 500 mmwith two drilled holes of 6.35 mm were attached on both sides normal to the longitudinal direc-tion of the sheet. The holes were designed for load bearing.

(4) The sample was then sent to an oven to cure the resin used for gluing the tabs at 70 �C for 1 h. Asa final step, the holes in the tabs were further pierced through the sample and strings werepassed through the holes as well for fastening the weights in the study of stress tunable effect.

For the case of short-wire composites, Marin et al. [176] dispersed 40 g 1 mm Fe-rich microwiresinto the silicon resin to receive a composite sheet for microwave absorption application. Di et al. [171]and Zhang et al. [172] used rubber dissolved by acetone to prepare the composite of the toroidal ringshape, in that it can fit the sample holder specific for the measurement by a vector network analyser.The wire arrangement can be made either regular or random as shown in Fig. 17, which determines ifthe composite is isotropic or anisotropic. Yet this kind of composite (inner diameter of 3 mm, outerdiameter of 7 mm and height of 3.5 mm) is very small and has limited application.

3.2.3. Microwire E-glass prepregsE-glass prepregs have been widely used in the industry and are themselves excellent structural

composites. Naturally, using it as a matrix to make microwire composite secures the structural func-tion even with a very small amount of microwires.

Ref. [177] detailed the preparation of short-wire composites and continuous-wire composites withE-glass prepregs as matrices. For example, the preparation work of the short-wire composite was donein the following steps:

(1) Five centimetre wire-pieces were laid out at zero degree along the glass-fibre direction betweenthe two layers of prepregs with in-plane size of 50 cm � 50 cm (the size may vary to fit differentmeasurements). The wire spacing was controlled at fixed values of the order of centimetres(comparable to the wavelength at gigahertz range) in perpendicular and parallel directions asshown in Fig. 18a. Note that the wire length and spacing are selected within the resolutionrange of the microwave measurements at gigahertz.

(2) Another two layers were laid up on the top and bottom of the wire-embedded layers in thesame direction, giving a layup of four prepreg layers containing short wires.

(3) After bagging the composite on an aluminium plate with air sucked out to the required vacuumof 94.6–104.7 kPa, the material was cured in an autoclave. The curing conditions are as follows:the temperature was raised at a rate of 2 �C/min to 127 �C and kept for 80 min before coolingdown naturally to room temperature. At a rate of 69 kPa/min the pressure was increased to206.7 kPa (30 psi) and kept at this level for 30 s and then 690 kPa for 600 min before decreasingat a rate of the 20.7 kPa/min.

A typical cross-sectional view of prepreg based wire composite is shown in Fig. 18b.On the exterior surface, one can see several ridges of different colours from other regions (indicated

by arrows), which is attributed to a non-uniform distribution of the resin and glass-fibre in the pre-pregs [28], as revealed in the scanning electron microscope image of the cross-section (Fig. 19b). It

Fig. 18. Schematic of the continuous-wire composite,where b is the interwire spacing (left-panel) and short-wire composites(right panel), in which a denotes the wire radius, l denotes the wire length.

Fig. 19. (a) In-plane view optical micrograph of composite surface and (b) a cross-sectional SEM image of the composite whereboth the single metal wire with glass coating and glass fibres in the composite are shown. Reprinted with permission from[197], copyright 2010 Elsevier.

Fig. 20. Comparison of magnetic hysteresis loops of a single magnetic microwire and its as-prepared composite. Reproducedwith permission from [186], copyright 2007 AIAA.


is the microwire, which is slightly larger than the glass-fibres in diameter, that results in the non-uni-form distribution of the resin in the region close to it. However, such influence from the microwires islimited to the near-wire region only and is comparable to the inherent defects in the prepregs. Besides,since the wire-composite is intended to contain a very small number of wires that are separated in aspacing of a few millimeters to a few centimetres, which is three to four orders of magnitude higherthan the diameter of the microwires, the disruption of microwires to the composite integrity isminimal.

4. Basic magnetic and mechanical properties of microwire composites

4.1. Magnetic properties of composites

Due to the inclusion of magnetic fillers, the polymer composite becomes magnetic, i.e. responsiveto the external static or dynamic magnetic field. Although most studies are devoted to the dynamicresponse of these kinds of heterogeneous composite media [178], i.e., complex permeability, it isworthwhile exploring the static magnetic properties of microwire composites for two reasons: (i)the composite with wire arrays could be of some application interest in the magnetic sensing field


as quite a few studies are devoted to the microwire arrays [179–184]. (ii) AC permeability is associatedwith the static magnetic properties such as saturation magnetisation and the anisotropy field accord-ing to the modified model based on Snoek’s law proposed by Acher and co-workers [111,185]
Z F
0l00ðf Þf df 6

p6sð�c4pMsÞ2; ð4:1Þ

where l is the imaginary part of complex permeability, f is the frequency, s denotes the volume frac-tion of magnetic fillers, c is the gyromagnetic factor with a value of 2.8 MHz/Oe, Ms is the saturationmagnetisation. In this connection, this section addresses some of the static magnetic properties ofmicrowire composites.

Phan et al. [186] prepared E-glass prepreg-based composites with bundles of microwires and mea-sured their magnetic properties were measured in comparison with those of the single wires. Fig. 20shows the M–H curves of the single microwire and composite. It is interesting to note that, for both lon-gitudinal and transverse measurements, the coercivity of the as-prepared composite is much smallerthan that of the single microwire. This indicates better soft magnetic properties for the microwire com-posite than single wires. It is also shown that the effective anisotropy field for bundles of microwire isstrongly increased as compared to the single wire [171]. Such changes of magnetostatic and magneto-elastic characteristics are due to the long range dipolar interactions [184,187] between neighbouringwires as well as the interfacial stress between microwires and matrix. The dipolar interactions havea strong impact on the magnetic properties in a similar way to classical spins interacting throughoutlong-range interactions, resulting in the changes in the hysteresis loop. Equally, interfacial stress ofthe order of hundreds of MPa [175,188], resulting from the different coefficient of thermal expansionbetween the microwire and polymer matrix, will have significant effect on the magnetoelastic featuresof the wires according to Kme = 3/2k(ri + rapp), where Kme is the magnetoelastic energy component, k isthe magnetostriction constant, ri and rapp are the internal stress and applied stress on the wire, respec-tively [189,190]. In the case of Fe-based wire of a length greater than critical length, due to the dipolarinteractions, the coercivity and anisotropy field is supposed to be increased with number of wires. Onthe other hand, the coercivity is decreased with increasing stress and anisotropy presents an oppositetrend [188,189,191]. The combination of these two mechanisms results in the observed contrast be-tween the microwire composites and monolithic wire. The presented magnetic properties indicate thatthe microwire composites are promising for magnetic sensing applications [8].

Due to the involvement of polymer, magnetic filler and multi-interfaces, the temperature plays animportant role in regulating the magnetic behaviour of composites. The glass transition temperature(tg) of the composite samples is evaluated for one to gain a better understanding of their magneticproperties (see Fig. 21). Phan et al. found that, by annealing in the vicinity of the glass transition tem-perature, there exists a critical temperature of 177 �C. Before the temperature reaches it, the coercivitydecreases while afterwards the opposite trend is shown. This is contrary to the conventional case thatthe coercivity should decrease with the stress relaxation due to the thermal annealing below crystal-lization temperature [192]. Clearly, such a complex annealing temperature dependence of coercivityinvolves multiple mechanisms at different interfaces, viz, the structural relaxation in the wire, thestress relief in the polymer-wire interface. The competitive and interdependent relationship betweenthese two mechanism vary sensitively with the temperature. At low temperature relative to glasstransition temperature, the second mechanism prevails and could result in a rearrangement of micro-wires, i.e, regulation of the composite mesostructure. Thus the coercivity could be increased due to theenhanced interaction between the wires [193]. Subsequently, the decrease of coercivity should resultfrom the stress relief contributed by both glass-transition and wire structural relaxation. The gradualdecrease of remnant magnetisation can be accounted for by the reduction of the volume of the axiallymagnetised area as an effect of stress relief due to the positive magnetostriction constant [189,191].

4.2. GMI effect

As with wires, their composite also presents a significant GMI effect. It has been shown by Phanet al. [186] that, at a given frequency of 10 MHz, the GMI ratio and its field sensitivity reached the

Fig. 21. Magnetic hysteresis loops of as-prepared composite annealed at Ta = 375 K, 405 K and 435 K.The glass transitiontemperature is 449.5 K. Reproduced with permission from [186], copyright 2007 AIAA.


highest values of 450% and 45%/Oe for those composites containing four wires, while the compositecontaining only one wire gave 14% and 1%/Oe, respectively (see Fig. 22). The wire addition effect onthe GMI is believed to be attributed to the reduction of resistivity as one of the causes. Another causeis the combination of the high circumferential permeability of the microwire and a multiwire-parallelconfiguration is likely to cause a magnetic flux closure and hence resulted in an extremely high effec-tive permeability [193,194]. It is worth noting both GMI and anisotropy field are enhanced, which ishighly desirable for realising high-performance sensing entailing large sensitivity and broad workingrange. In addition, compared to single wire, the existence of polymer matrix could accommodate aversatile and judiciously designed multi-wire system, which provides more possibility to extend itsapplications. However, the GMI presented in Ref. [186] is very weak, with suitable optimisation of sin-gle wires via advanced annealing techniques such as stress-joule-annealing [195] and recently re-ported multi-angle annealing techniques [196], the GMI of wire composite could be further improved.

Qin et al. [197] also demonstrated the pronounced improvement of maximum MI effect with increas-ing wire inclusions, attributed to the effective response of all the wires. The microwire composite is

Fig. 22. Frequency dependence of GMI profiles with varying wire number n = 1,2,3,4 mm. Reproduced with permission from[369], copyright 2007 Elsevier.


shown to yield a larger GMI at higher frequencies but with minor increase of energy loss, which is desir-able for sensing applications. The multi-wires in the parallel manner constitute an increase of the totalcross sectional area of the wires, resulting in a stronger skin effect when considering the ratio of radiusand penetration depth. Consequently the GMI effect is improved. In addition, if the wire is simply dealtwith as a single domain substance, the interactions between wires in the multi-wire composites inducea magnetic closure to make the whole structure more stable, albeit the total internal energy is increased[187]. These results differ significantly from those reported by Garcia et al. [198], who demonstrated amulti-wire system exhibiting a reduced GMI effect with the number of wires, which is explained by theauthors as an effect of shielding between wires. This difference should be ascribed to the functions of thematrix and the curing process for our composite media. The wire-sample underwent annealing in thecuring stage and the domain structure were significantly modified. It is suggested that, the confinementof the matrix also helps maintain the modified configuration, giving rise to the peculiarity of the GMIbehaviour. Of note is that the involvement of polymer matrix opens up new routes to modulate GMI per-formance, although limited study has been reported thus far. A particularly important aspect is inter-face. The homogeneities of interface would be critical to the GMI characteristics, it is thereforenecessary to study the detailed interfacial conditions. Surface treatment using chemical agents suchas silane or nanotubes [199] could also be considered to enhance both interfacial bonding and GMIproperties. Another aspect of practical interest [200] is to develop superior bonding technology toaccommodate multiple wires so that a high stability of GMI signal output can be ensured.

It is well established that GMI effect of microwires associated with the magnetic properties isstrongly influenced by the length of wires [180,201–204]. The argument holds true for the microwirecomposite system. It has been revealed that the GMI ratio increased from 15.5% to 268% as the micro-wire length decreased from 4 to 1 mm [186]. This is attributed to the decrease of the electric resistivityin the multi-wire system compared to the single wire, in spite of the increase of the demagnetisingeffect [180] for single wire. Based on the outstanding magnetic properties of microwire composites,it shows a promising application perspective. Indeed, the polymer matrix provides a ‘platform’ toassemble the microwires and exhibit the properties that is significantly different from the single wire,which is exactly what composites are for [205].

4.3. GSI effect

As mentioned above, the stresses can play an important role in investigating the GMI materials, andthese can be treated in two respects. One concerns the stress influence on the GMI behaviour, and anumber of works have been published on this topic for various materials including ribbons[206–208] and microwires [209–211]. Second is the so-called giant stress-impedance (GSI) effect,

Fig. 23. GMI profiles of composites containing single wire as a function of applied stress. Reproduced with permission from[188], copyright 2011 Elsevier.


which refers to a stress-induced variation of impedance in magnetic materials. This effect in the inter-mediate frequencies has been evaluated on amorphous wires and ribbons. Shen [212] reported thatthe GSI effect of a CoSiB microwire reached about �35% for stress r = 140 MPa, which is five to sixtimes more sensitive than a conventional semiconductor stress sensor. One kind of Fe-based ribbonswas also found to possess an SI ratio of 20% for r = 84.8 MPa with the stress perpendicular to the geo-magnetic field [213]. In this regard, the wire-based composite is expected to be a good candidate forstudying the GSI effect over a wider stress range, since it can be treated as a multi-layer medium con-sisting of a metallic core, a glass coat and a composite matrix. Such a hierarchical structure would en-able a sensitive response to the applied stress for the composite media, where the coupling of internaland external stresses is likely to be able to manipulate the GMI and GSI behaviour. Both aspects of theGSI effect of microwire composites were investigated by Qin et al. [188].

Fig. 23 illustrates the magnetic field dependence of the GMI ratio taken at f = 1 MHz under variousapplied tensile stresses for the single-wire composite of four layers obtained by the method describedin Section 3.2.1. Here the tensile stress was applied along the microwire axis. It can be seen from thefigure that the maximum GMI ratio decreased as the applied stress was increased. While the GMI ratiodecreased gradually with the applied magnetic field (Hdc) for the unstressed composite, the case is dif-ferent for the stressed composites. With increasing Hdc, the GMI ratio first increased, then reached amaximum, and finally decreased for the stressed composites. The magnetic field at which the GMI ra-tio reached maximum can be considered as the circular anisotropy field (Hk) induced by the appliedtensile stress.

Fig. 24a illustrates the tensile stress dependence of the maximum GMI ratio and the anisotropyfield. Clearly, the GMI ratio decreased slightly from 255% for r = 0–253% for r = 150 MPa and drasti-cally reduced to 151% for r = 600 MPa by more than 100%. An opposite trend was observed for the rdependence of Hk. A subtle increase of Hk by 8 A/m for r = 150 MPa was followed by a further increaseof 112 A/m for r = 600 MPa. The r dependence of longitudinal coercivity (Hc) was also measured andthe result is shown in Fig. 24b. The drop of Hc was observed at r = 600 MPa. For the case of theunstressed composite, the gradual decrease of the GMI ratio with Hdc is likely to be caused by decreas-ing circular permeability due to the rotation of magnetic moments. However, an opposite effect

0

1

2

3

4

5

6

0 100 200 300 400 500 600

0 100 200 300 400 500 600

0

20

40

60

80

100

120

(b)

Hk(A

/m)

(a)

Hk=5.98+1.2×10-7σ+5.0×10-10σ2

140

160

180

200

220

240

260

[ΔΖ/Ζ]max %

Longitudinal

Ηc(A

/m)

Applied tensile stress, MPa

Fig. 24. (a) Tensile stress dependences of anisotropy field (Hk) determined from GMI profiles and maximum GMI ratio. (b)Longitudinal coercivity vs. applied tensile stress. Reproduced with permission from [188], copyright 2011 Elsevier.

Fig. 25. GMI profiles for the wire composites of four prepreg layers and eight prepreg layers in as-prepared and annealed statestaken at f = 1 MHz. Reproduced with permission from [188], copyright 2011 Elsevier.


observed for the stressed composites arises from the fact that the application of tensile stress to themicrowire with a negative magnetostriction strengthened the circular magnetoelastic anisotropy field,giving rise to the occurrence of a maximum in GMI that shifted towards higher Hdc as r was increased.The occurrence of such a maximum in GMI for the stressed composites can be attributed to the com-petition in the rotational magnetisation processes between Hdc and Hk. The decrease of the GMI ratiowith r at Hdc = 0 is attributed to a reduction in the circular permeability due to the domain walldisplacement.

Furthermore, it should be noted that, since the microwires were embedded in a polymer matrix,any heat treatment or variation coming from the polymer matrix is expected to have a significantinfluence on the GMI properties of the microwire and hence the composite. To gain insight into this,the influences of annealing treatment and the number of layers on the GMI properties are studied. Theresults are shown in Fig. 25. For the case of as-prepared samples, the four-layer composite exhibited ahigher maximum GMI ratio (255%) when compared with the eight-layer composite (216%). Mean-while, the annealed composite samples (treated at 100 �C for 3 h) exhibited higher maximum GMI ra-tios (282% and 248% for the four-layer and eight-layer composites, respectively) than the as-preparedones. These findings are explained as follows. In this kind of composite, a higher stress will be inducedas the number of composite layers increases. In the present study, the eight-layer composite may im-pose more stress in the through-thickness direction than the four-layer composite. As a result, the GMIratio decreased and Hk increased for the as-prepared composite of eight layers when compared withthe as-prepared composite of four layers. On the other hand, the annealing treatment is believed tohave relieved the stress between the microwire and matrix produced during the curing process. Thisexplains consistently the larger GMI ratio and smaller Hk obtained for the annealed composite samplesrelative to the as-prepared ones.

It is also interesting to see that the GMI behaviour observed for the as-prepared eight-layer com-posite is similar to that of the four-layer composite subject to a tensile stress of 450 MPa. This clearlysuggests that the applied tensile stress and residual stress imposed by the composite matrix on themicrowire could affect its GMI behaviour in a similar fashion. To understand this quantitatively,the contribution of the applied stress and the matrix-induced residual stress to the anisotropy fieldwere calculated, respectively.

In a cylindrical coordinate system (z,r,/), there exist three components for the residual stress in z(along the wire axis), r (radial direction) and / (azimuthal direction): rzz, rrr and r//, respectively. Themagnetoelastic energy density is given by [214]:

Ume ¼ �32

ks rzza2z þ rrra2

r þ r//a2/

� �; ð4:2Þ


where ks is the saturation magnetostriction constant. ai denotes the component of the unit magneti-sation vector. The residual stresses are assumed to be a function of x(r/a) only, a being the wire radius.

The anisotropy field can then be deduced by the following equation [214]:

Fig. 26.at f = 1

Hk ¼3jksjMs

rzz � r// þ1

ð1� kÞp2 þ krzz

� �; ð4:3Þ

where all symbols have the same meaning as in Eq. (4.2).Taking into account the residual stress imposed by the composite matrix, which is primarily along

the negative radial direction ðrrrÞ, Eq. (4.3) can be modified to:

Hk ¼3jksjMsðrzz � r// þ rrr þ frzzÞ; ð4:4aÞ

frzz ¼1

ð1� kÞp2 þ krzz: ð4:4bÞ

For four-layer composite, when rzz ¼ 450 MPa, given k = 0.5 and p = 0.67, one can receive the effec-tive contribution to Hk, frzz ¼ 619 MPa. For the eight-layer composite, according to the difference of itsanisotropy field relative to that of unstressed four-layer composite (DHk = 0.5 Oe), the concernedstress rrr is given by:

rrr ¼DHkMs

3jksj: ð4:5Þ

Given the typical numerical values: Ms ¼ 400 G; ks ¼ �10�7;rrr ¼ 667 MPa is received. The similarnumerical values of rrr and frzz explain the roles of applied stress and residual stress on influencingthe magnetoelastic properties and GMI properties. This result affords significant technical applicationsin the composite industry in terms of probing the residual stress and tailoring the related manufactureconditions.

The GSI effect in the microwire and the microwire-based composites with four and eight layers wasinvestigated. The results are shown in Fig. 26. It can be readily seen that the stress-impedance ratio[DZ/Z] decreased monotonously with stress for all the samples. Interestingly, while the maximumstress impedance ratio ([DZ/Z]max) is 38.1% for the single microwire, it is reinforced for the compositesamples (41.5% and 43.0% for the four-layer and eight-layer composites, respectively). These resultsindicate that the prepared composites are very appealing candidates for stress sensing applications.In the composite, in addition to the residual stress frozen-in between the glass and metallic core, thereexists residual stress at the interface between the microwire and polymer matrix. The enhancement of

GSI profiles for amorphous wire, four-layer wire-composite and eight-layer wire-composite in as-prepared states takenMHz. Reproduced with permission from [188], copyright 2011 Elsevier.


the GSI effect in the composites clearly points to the important coupling between internal and exter-nal stresses that coexist in these materials.

4.4. Mechanical properties

Since the fabricated composite is intended for structural applications, its mechanical properties areone of the major concerns. Also, the influence of microwires on the mechanical integrity of the com-posite is a key issue for the success of such sensor-embedded technology. Therefore, it is necessary todiscuss the mechanical properties of the composite matrix influenced by the embedded wires[197,215–217].

Qin et al. [197,217] found that, in the dilute composite with glass-fibre reinforced epoxy as a ma-trix, the fibre shows little effect as shown in Fig. 27, which displays the stress–strain curves obtainedfor blank composite samples, 10-wire, and 50-wire samples under a maximum force of 30 kN [197].The tensile strengths are summarised in Table 1. It is observed that all the mechanical parametersare very close to each other for the different types of samples. In terms of the tensile strength, the coef-ficients of variation (CV) for each type of sample are 6.3, 5.6 and 3.8. Upon performing cross compar-ison of their average properties, the CV is 3.7. The negligible wire effect can be understood from thebasic law of mixture that postulates a considerable volume fraction of fillers needed to realisereinforcement.

Back to 1980s, Goto and co-workers [215,216] had done excellent work in this regard. Goto andNishio [215] studied the reinforcing effect of metallic wires with and without glass coats on the epoxymatrix and reported that the mechanical properties of epoxy is strongly enhanced for the wires with-out glass-coat, the tensile strength reaching 600 MPa at 30 vol.% wire volume. While the glass-coatedwires do not show as good reinforcing effect due to the poor bonding between metallic core and glasscoat. These effects are readily demonstrated in the fracture morphology images (Fig. 28) Apparently,the quality of interfaces play a critical role in determining the ultimate mechanical performance of the

Fig. 27. Stress–strain curves of blank composites (free of wires), composites containing 10 wires and 50 wires measured by a30 kN load cell. Reproduced with permission from [197], copyright 2010 Elsevier.

Table 1Mean values and coefficients of variation (CV�) of tensile strength for each set of samples.

Blank sample 10-Wire sample 50-Wire sample

Young’s modulus (GPa) 14.22 (3.1⁄) 14.48 (1.1) 14.97 (3.0)Tensile strength (MPa) 951.48 (6.3) 935.18 (5.6) 1003.80 (3.8)

Fig. 28. Fracture morphology of microwire (glass coat removed)/epoxy composite (a) and glass-coated microwire/epoxycomposite (b). Reproduced with permission from [215], copyright 1987 Springer.


wire composites. These fine wires after removing glass coats are also found capable of improving thethermal properties of the composite by increasing the glass transition temperature as the wires canhinder the molecular motion.

Although the microwires can reinforce the polymer materials with adequate concentration andproper orientation, a trade off is often inevitable if one tend to integrate the structural function andother functionalities which favour not necessarily the large concentration or unidirectional fillers.For the designers of such multifunctional composites, it is necessary to maximize the most desirablefunction for targeted application but with a cost of other functionalities as low as possible.

5. Microwave tunable properties of microwire composites

Further to the understanding of the GMI/GSI behaviours of microwires and their composites, this sec-tion targets the microwave tunable properties of the microwire composites, i.e. tunable electromagneticproperties by magnetic field [12,30,41,43,51,197,217–222], stress [12,50,51,55,175] and temperature[41,218]. The tunable property is actually the so-called cross-variable response unique to multifunc-tional composites, i.e., a given field could control two or more variables, or a variable can be switchedby two or more external fields. To achieve such tunability or adjustability is essential for microwaveapplications such as tunable microwave devices [12] and remote interrogated sensors [223]. It will alsobe called for to realise reconfigurable local network environment, beam-steering antennas, and micro-wave remote sensing and control. Most proposed methods have been based on biased ferroelectric, fer-rite or magnetic composite substrates and reconfigurable resonant elements implementing activedevices or a system of micro actuators [224–226]. These technologies each have their advantages andlimitations such as high power consumption, low operational speed, limited frequency band and highcost. The dilute composites with ferromagnetic microwires were proposed in this context by Paninaand co-workers [12,51]. Together with following studies [30,174,175,197,219,221,222], the possibilityof tailoring the collective dielectric response of the wire media by changing the local magnetic proper-ties with external stimuli without changing the structural parameters has been demonstrated.

In what follows the tunable properties will be discussed in three categories: magnetic field tunableproperties, stress tunable properties and temperature tunable properties. In each section, both thewires and their composites will be discussed. Note that all the composites under discussion hereare non-percolating due to either the periodical arrangement of the wires with fixed spacing or theexistence of glass coat for random wire composites. Thus there is no concern that the formation ofconductive network will hinder the interactions with the microwave.

5.1. Field tunable properties

5.1.1. Field effect on the impedance of single wireThe static magnetic field is essential to generate the GMI effect. With our focus on the gigahertz

frequency, the numerous studies on the megahertz frequency (see [7] and references therein) will

Fig. 29. Real component of impedance for a FeSiB glass-coated microwire as a function of frequency for selected values ofapplied field. Reprinted with permission from [229] copyright 2009 Elsevier.


be skipped. At high frequency, the GMI effect is believed to be caused by the natural ferromagneticresonance in the outer layer of wires occurring at a relatively small ac field [26,28,29,227]. The reso-nance frequency is dependent on the anisotropy field, anisotropy angle and external field (if it exists)[50,55,197,228,229]. At around resonance frequency, the field sensitivity could reach maximum [230].The typical field effect is shown in Fig. 29. Note that the real (imaginary) part of Z corresponds to theimaginary (real) part of circumferential permeability [28]. Similar effects are also shown elsewhere[18,231–233].

5.1.2. Continuous-wire compositesFor continuous-wire composites, the dependence of effective permittivity on the external filed is

established via the field dependence of plasma frequency according to Eq. (2.21). As plasma frequencyis dependent on the interwire-spacing and wire diameter following Eq. (2.16), these two geometricalparameters are critical in governing the effective response of the composite to the external field. Actu-ally this is quite reasonable since these two parameters constitute the basic mesostructure, and aredecisive in the dielectric heterogeneous composites [234–236]. Also the tunable properties are largelydetermined by the local magnetic properties of the wires. Therefore, the following discussion of tun-able properties of continuous-wire composites is carried out from these three critical influencing fac-tors, i.e., interwire spacing (also known as cell parameter, periodicity), wire diameter and localmagnetic property of wires.

5.1.2.1. Influence of wire periodicity. Fig. 30 displays the dependence of complex effective permittivityon the frequency with magnetic field as a parameter for composites with wire Co68.7Fe4Ni1B13Si11-

Mo2.3 with different periodicity. The dependence of the effective permittivity is well displayed in bothgraphs below the corresponding plasma frequency.

It can also be seen that, with increasing wire periodicity from 7 to 15 mm, the frequency dispersionof effective permittivity on the magnetic field is remarkably depreciated as the tunability (defined asthe ratio of variation of the electromagnetic parameter to that of the corresponding field [224]) re-duced from 0.16 m/A to 7.7 � 10�3 m/A. This means that a small wire periodicity is preferable for afield-tunable property. However, a decrease of wire periodicity will increase the plasma frequencyand hence the skin effect. If the skin effect is too strong, the field effect will be rather weak. Therefore,the wire diameter may also need to be decrease to compensate the decrease of skin depth. Thereby,there exists an optimum value of wire periodicity matching the diameter for the microwave tunableproperties. This is consistent with the theoretical prediction that for b = 0.5 mm, the best tunabilitywill be achieved for a wire radius of 5–10 l m [237] (see Figs. 31 and 32).

Fig. 33 shows the frequency dependence of the reflection parameter (S11) taken at different mag-netic fields for the composites with b = 3 mm, 7 mm and 9 mm. It can be seen that the shape of thecurves varies remarkably as the wire periodicity increases from 3 mm to 9 mm. For the b = 3 mm sam-ple, the spectra can be divided into two frequency zones at 7.6 GHz. Below 7.6 GHz, the reflectivity

(a) (b)

Fig. 30. Frequency plots of the real and imaginary part of effective permittivity for composites containing long continuouswires with the external field as a parameter. (a) wire spacing b = 7 mm; (b) b = 9 mm. Reprinted with permission from [365]copyright 2012 Elsevier.


decreases as the magnetic field is applied. This is due to the absorption effect. However, the oppositetrend is observed for f > 7.6 GHz. For the b = 7 mm and 9 mm samples, one more zone is found forf > 16.3 GHz and f > 14.4 GHz. The frequency at which the signal of S11 changes with magnetic fieldis considered the characteristic frequency. It is worth noting here that as b increases from 3 mm to9 mm, the characteristic frequency decreases from 7.6 GHz to 3.8 GHz (between zones 1 and 2).One can also see that the characteristic frequency (between zones 2 and 3) decreases from16.3 GHz for the b = 7 mm sample to 14.4 GHz for the b = 9 mm sample. For the b = 3 mm samplethe characteristic frequency cannot be determined due to the limited measurement frequency range,

Fig. 31. Effective permittivity, real part, as a function of external field for composites containing continuous wires with differentwire periodicity b = 7, 9 and 15 mm. Reproduced with permission from [365] copyright 2012 Elsevier.

(a)

(b)

Fig. 32. Field tunability of transmission parameter S21 as a function of external field for composites containing continuous wireswith different wire periodicity b = 3, 7 and 9 mm at (a) 4 GHz and (b) plasma frequencies for each wire periodicity. The ordinateprofiles are divided by the factor 0.001. Inset graphs are the corresponding field dependence of S21. Reprinted with permissionfrom [219] copyright 2010 AIP.


but it appears to be higher than those for the b = 7 mm and 9 mm composites. This finding points to animportant consequence that the characteristic frequency shifts to a lower value for composites withlarger wire periodicity in the reflection spectra.

Fig. 34 shows the magnetic field dependence of the reflection parameter (S11) taken at 900 MHz.The sensitivity of S11 to the magnetic field is positively correlated to b. For the composites withb = 9 mm, S11 falls from �1.8 dB at Hex = 0 to �7.5 dB at Hex = 500 A/m.

5.1.2.2. Influence of wire diameter. It is well known that the wire diameter has a strong impact on theGMI properties of microwires [157,159,238,239]. Fig. 35 shows that composites containing wires witha larger diameter presents a higher field tunability than the other with a smaller diameter, which can

Fig. 34. Reflection parameter as a function of external field for composites containing continuous wires with different wireperiodicity b = 3, 7 and 9 mm at the initial frequency of 0.9 GHz.

(a) (b)

(c)

Fig. 33. Experimental reflection spectra (S11) for composite sample of 640 l m thick and 50 cm � 50 cm in-plane size withcontinuous amorphous wires spaced at 3 mm (a), 7 mm (b) and 9 mm (c). Reprinted with permission from [365] copyright 2012Elsevier.


be explained by the wire geometry dependence of the GMI effect and associated skin effect. It has al-ready been demonstrated that, the GMI effect is positively correlated to the wire diameter [240].Accordingly, the dielectric response of the composite containing wires of larger diameter is strongerthan otherwise [43].

Fig. 35. Frequency dependence of real part of effective permittivity with external field as a parameter for composites containingwires of different radius a. Reproduced with permission from [365] copyright 2012 Elsevier.

(a) S21 spectra for CP3 (b) S21 spectra for CP4

(c) S11 spectra for CP3 (d) S11 spectra for CP4

Fig. 36. Frequency dependence of S-parameters with external field as a parameter for composites containing wires of differentradius. Reproduced with permission from [365] copyright 2012 Elsevier.


A comparison between the transmission spectra (cf. Fig. 36) reveals that the diameter of the wirehas a profound impact on the intensity of S21 but much less effect on the tunability. The variation ofdiameter of several microns has a negligible influence on the plasma frequency of 5 GHz, and the


frequencies at which S21 reaches the minimum are about 3 GHz for both of them. It follows that theplasma frequency probably decides the patterns of transmission spectra.

The phase shift of S11 in the presence of an external field (cf. Fig. 37) suggests a promising sensingapplication of the composite. For CP3, the phase going through ±p is completely suppressed when it isunder a small field of 25 A/m. For CP4, the concerned phase shifts to a lower value from 3.7 in the ab-sence of a field to 3.0 in the presence of a field of 70 A/m. These considerable changes suggest the fer-romagnetic microwires enable their composite with a self-monitoring capacity: any stress change thatoccurs to the wire through the composite can be detected via the microwave tunable spectra.

5.1.2.3. Influence of wire composition. Following from the very strong dependence of the GMI propertyon the composition of microwires [6,7,157,159], the change of local magnetic properties with the com-position is expected to vary the field effect. Fig. 39 shows a comparison between the composites con-taining wires of same geometry but different composition. Both wire-composites present rather gooddispersion properties but differing field effect. This is attributed to the difference in soft magneticproperties as shown in the magnetisation curves of the two wires (Fig. 38).

The scattering spectra for the two composites with periodicity of 7 mm are presented in Fig. 40. Inthe spectra of S11, the two composites possess almost the same characteristic frequencies but differing

(a) a = 8 (b) a = 6.8

Fig. 37. Frequency dependence of phase of S11 with external field as a parameter for composites containing wires of differentradius. Reproduced with permission from [365] copyright 2012 Elsevier.

Fig. 38. M-H curves of Co68.7Fe4Ni1B13Si11Mo2.3 (a) and Co67.05Fe3.85Ni1.44B 11.53Si14.47Mo1.66 (b) measured in the field along thewire axis.

Fig. 39. Frequency plots of the effective permittivity, real part, for composites containing long continuous wires(Co68.7Fe4Ni1B13Si11Mo2.3 and Co67.05Fe3.85Ni1.44B11.53Si14.47Mo1.66) with the external field Hex as a parameter. Wire radiusa = 10 l m; wire periodicity b = 7 mm (upper plot) and b = 9 mm (lower plot).


field tunability. Comparison of spectra S22 shows that both the shift of resonance and resonance fre-quency are smaller for CP1.

5.1.3. Short-wire compositesIn a short-wire composite, short wire pieces may be uniformly dispersed in a random manner

[30,221,222] or in a periodical manner [174,175,177,197,219,241,242]. In this section the magneticbias (field) effects of short-wire composites are presented and discussed within the theoretical frame-work detailed in Section 2.2.3.

(a) (b)

(c)

Fig. 40. Frequency dependencies of magnitude of S-parameters for composite containing amorphous wires Co67.05Fe3.85-

Ni1.44B11.53Si14.47Mo1.66 spaced at 7 mm. (a) S11, (b) S21 and (c) S22.

(a) Real part (ε ) (b) Imaginary part (ε )

Fig. 41. Effective permittivity spectra of a short-wire composite with varying magnetic field in relative to anisotropy field(500 A/m). The material parameters are given in the graph: l is the wire length, a is the wire radius, nc is the ratio of wire numberto the area containing them.


Fig. 41 shows the dispersion of effective permittivity for a short-wire composite with the param-eters (l,a,nc) detailed in the graph. The value of e0 is rather small due to the low concentration ofthe microwires (Fig. 41a). Nevertheless, a dependence of e0 on the applied magnetic field is


demonstrated. The transformation of resonance to relaxation can be inferred from the frequency evo-lution of these curves. The anisotropy field can be used as a critical value to distinguish the frequencydependence of e0 at the studied frequency range (1–5 GHz). The same trend is also observed in the fre-quency plots of e00 (Fig. 41b). This is explained as follows. When Hex < Hk, the impedance is increasedwith Hex. Therefore, the internal loss increases and the relaxation dispersion occurs. The relaxationbehaviour is fully achieved when Hex = Hk, whereby the impedance reaches a maximum. Further in-crease of Hex results in a reverse trend. Note that the dielectric response to the magnetic field is notseen until the field is 250 A/m; this can be attributed to the relative insensitivity of magnetoimped-ance for this range of magnetic field.

As with the complex permittivity spectra, the transmission is increased as the field increases with aconcomitant resonance–relaxation change, as seen in Fig. 42a. Strikingly, the transmission spectrapresent a large transmission of ca. 90%, which corresponds to a very large return loss (see Fig. 42b).With the same spectra zoomed at 1–5 GHz (Fig. 42c), the resonance–relaxation transformation wasclearly observed with increasing magnetic field. The resonance/relaxation frequency shifts to highervalue with increasing magnetic field. The phase shift U is also shown in the reflection spectra as de-picted in Fig. 42d.

By decreasing the wire periodicity from 20 mm to 5 mm, the area concentration of wires is greatlyincreased from 0.06 cm�2 to 0.24 cm�2. As a result, the values of measured S-parameters are largelyincreased while their field dependencies remain unchanged (Fig. 43a–d). Inasmuch as the wire geom-etry (length, diameter and aspect ratio) remains unchanged, there will not be significant changes in

(a) Transmission. (b) Reflection.

(c) Reflection. (d) Reflection phase.

Fig. 42. (a) Transmission and (b) reflection spectra of a short-wire composite with the magnetic field as a parameter; (c) part of(b) at 1–5 GHz; (d) the phase of reflection coefficient. The phase reversal shift is indicated in the graph with coordinate valuesgiven. The material parameters are given in the graph by the same symbols as in Fig. 41.

(a) Real part of permittivity. (b) Imaginary part of permittivity.

(c) Transmission. (d) Reflection.

(e) Reflection phase.

Fig. 43. Experimental dispersion of (a) real and (b) imaginary part of effective permittivity; (c) measured transmission and (d)reflection spectra of the short-wire composite with the magnetic field as a parameter; (e) presents the phase of reflectioncoefficient. The material parameters are given in the graph by the same symbols as in Fig. 41.


the dispersion behaviour as far as the composite mesostructure is concerned. It should be noted that,although the phase shift remains unchanged when the field increases from 500 A/m to 1000 A/m, a


reduction from 500 A/m to 100 A/m is found to cause a phase reversal between � p and p in thereflection spectra (Fig. 43e).

5.2. Stress tunable properties

Due to the stress effect on the impedance of amorphous wires, the stress will have significant im-pact on the prorogation of microwave when they pass through the microwire(s). This is characterisedby the variation of electromagnetic parameters (reflection,transmission, permittivity and permeabil-ity) with stress. This is the basic working principle for microwave NDT methods [243–249]. Comparedto other NDT methods employing ultrasound [250,251], infrared thermography [251–253], radiogra-phy [254,255], radioactive computed tomography, and ground-penetrating radar (GPR) [256,257],microwave proves to be advantageous due to the fact that microwaves can penetrate deep insidethe composite, scatter little compared to acoustic waves, offer excellent contrast between matrixand reinforcing fibres, have good resolution, are not hazardous, cost-effective compared to radioactivemethods, and robust to environmental conditions unlike infrared methods [243–249]. Both near-field[258,259] and far-field free space [243] characterisation of composite structure have been proved tobe useful in detecting the debonds and delaminations of composite structure, demonstrating the use-fulness of microwave NDT technology in structural health monitoring applications. However, withoutembedding sensors, it is hard to detect the local damage. Most recently, the potential of using carbonfibres themselves as antenna and sensors to precisely detect the damage in CFRP has also been dem-onstrated [260]. However, the interactions of CFRP and microwave are limited by the high conductionloss of CF due to the high volume fraction. The use of micowires as sensor elements is advantageousfor their strong interactions with microwave and high sensitivity to external fields. In what follows,we will discuss the stress effect on the wire impedance and the stress tunable effects of microwirecomposites at gigahertz frequencies.

5.2.1. Stress sensing based on microwiresThe stress influence of GMI or stress-impedance effect has been mostly discussed in the megahertz

frequencies due to the application interest [211,261–266]. Interested readers are kindly referred to[7,160,6] and the references there. The focus here is on the stress effect of GMI behaviour in the giga-hertz frequency.

At gigahertz frequencies, the skin effect is very strong with a small skin depth (e.g. around 1.2 lmat 1–10 GHz [51]. The permeability is contributed by the outer layer of the microwire. For Co-basedmicrowire with the circumferential domain structure in the outer layer, the permeability is deter-mined by the natural ferromagnetic resonance [227]. According to the Landau–Lifshitz–Gilbert(LLG) equation, the permeability is strongly dependent on the anisotropy field of the wires. Consider-ing the significant stress impact on the anisotropy field of wires [52,214,239,267,268] and anisotropyangle [50,55,228], the permeability (or impedance) spectra can be regulated by the variation of inter-nal stress due to that of geometry [268–271] or glass-removal [272]; and external stress [197] asshown in Fig. 44a. The resonance frequency can be regulated by the parameter of the microwiresand the number of wires. Therefore, this effect could be utilised, beyond stress sensing, for detectingand locating damage in the microwire-based composites [260], which is of much interest in engineer-ing applications. In Fig. 44b and c, the sensing resolution is obtained from the shift of resonance withstress/strain with values of 1.06 MHz/MPa and 134.5 kHz/microstrain, respectively. These results leadto an important revelation that the microwires can be used as stress sensors in a wide frequency rangeprovided the permeability can be obtained. Compared with the newly proposed SRR-based sensorwith a sensitivity of 5.148 kHz/microstrain [73], the microwires are much more cost-effective andpossess a higher Q factor and sensitivity. The susceptibility of permeability to stress can be tailoredeither by tuning the composition, geometry, and microstructure of the microwires [268] or throughdeveloping composites containing magnetic fillers [273] and non-magnetic fillers [274].

It is worth mentioning that the stress sensitivity of impedance for single wire can be modulated bythe dc bias field. When the external magnetic field is equal to the value of the anisotropy field, thestress sensitivity reaches maximum. This is demonstrated in Fig. 45 [275], where the maximum sen-

(a)

(b) (c)

Fig. 44. (a) Calculated absorption spectra under varying rapp according to LLG formula [24] l ¼ 1þ l0cMs ½l0cðHdcþHk Þ�jxa�x2þx2

FMR�jxal0c½2ðHdcþHk ÞþMs

;

and Hk ¼ 3jks jMsðrzz � r// þ rappÞ [214,267] with the material parameters obtained from magnetisation test: Ms = 106 A/m,

c = 2.21 � 105 mA�1s�1, a = 0.02, Hs = 880 A/m and l0 = 1. (b) Applied stress dependence of resonance frequency shift. The slopeof fitted line represents the stress sensing resolution. (c) Resonance frequency dependence of microstrain. The slope of fittedline represents the strain sensing resolution. Reprinted with permission from [197] copyright 2010 Elsevier.


sitivity is shown at 15 Oe. The reason for this is well explained by the dependence of permeability onthe anisotropy angle, formulated as [228]:

l ¼ 1þ 4pcos2ðhÞv: ð5:1Þ

The application of magnetic field along the wire axis increases the circumferential magnetic perme-ability by rotating the magnetisation vector towards the wire axis. On the other hand, when a stressis applied along the microwires with a negative magnetostriction, the magnetisation vector rotatesaway from the axis direction. As a result, the circumferential magnetic permeability is decreased[50]. It is expected, therefore, that the application of longitudinal stress will compensate the effectof the magnetic field. The influence of stress is more obvious with a high magnetic field. Indeed, withreference to Fig. 45, the maximum applied stress of 1263 MPa encourages the absorption back to theoriginal value by offsetting the effects of the magnetic field. The magnetic field along the wire axis isdesirable for the absorption of microwires and can also be utilised to increase the stress sensitivity ofabsorption. Similar results were also reported in [50,55]. Upon analysing the data in Fig. 45, it can beobtained that the sensitivity of absorption to stress increases by ca. 39 times when the field increasesfrom 0.75 Oe to 15 Oe. This has profound implication in designing wire-based stress sensors.

(a) (b)Fig. 45. (a) Axial field dependence of absorption in presence of varying stress at 9 GHz for a Co67Fe3.9Ni1.4B11.5Si14.5Mo1.7 wire oftotal diameter 30.6 lm and glass coat 5.2 lm. (b) Tensile stress dependence of absorption (impedance) at varying magneticfields for the same wire. Reprinted with permission from [275] copyright 2011 Elsevier.


5.2.2. Stress tunable properties of composites5.2.2.1. Stress tunable properties of composites in free space. Fig. 46 [175] shows the complex permittiv-ity spectra for as-prepared intact rubber-based composite prepared by the method described in Sec-tion 3.2.2 and after being damaged with the occurrence of wire breakage. There are pronouncedchanges for both the real part e0 and the imaginary part e00 of effective permittivity. In particular, adrastic change of e0 is seen with a reversal of sign from negative to positive when the wire breakagehappened to the composite in question.

For the composites containing Fe4.84Co56.51B14.16Si11.41Cr13.08, there is no response at all for thecomposite subjected to a load range from 0 to 4 kg (not shown here). However, a stress tunablebehaviour parallel to the field tunable behaviour is observed in the transmission spectra (Fig. 47).Interestingly, the composite shows a similar response to stress and magnetic field, although the evo-lution of transmission with magnetic field is steadier than that with stress. To gain a deeper insightinto such stress tunable characteristics, Fig. 48 is plotted to show the calculated stress (resp. magneticfield) tunability versus stress (resp. magnetic field) at 1, 4.8 and 8 GHz, which are lower, equal andhigher in relative to the plasma frequency (fp), respectively. The overall evolution of tunability remainsthe same trend at all three frequencies. In comparison with the single peak feature displayed in themagnetic field dependence of tunability (Fig. 48b), both a maximum and a minimum appeared inthe stress dependence of tunability.

The primary principle pertinent to the stress tunable phenomenon is as follows. For composite con-taining ferromagnetic wires exhibiting giant magnetoimpedance effect at microwave frequencies, theeffective permittivity may depend on a dc magnetic field via the corresponding dependence of the sur-face impedance. The surface impedance can also be changed by applying a stress which modifies themagnetic anisotropy and domain structure in wires. Thus, the effective permittivity may also dependon the external stress or strain. It follows that the stress-impedance (SI) property of microwires is crit-ical to the susceptibility of the whole composite to the stress. SI depends strongly on the magnetoelas-tic characteristics of the microwire, which are conditioned by a number of factors: composition,domain structure, geometry, etc. This accounts for the observed insensitivity and sensitivity of themicrowire composites in terms of their permittivity to the external stress when one deals with differ-ent wires. Although, all these amorphous wires can be expected to show a drastic change when break-age occurs in the composite, the choicest wires have to be evaluated when it comes to a more delicatestress sensing application.

The single peak presented in stress tunability of S21 nfS21ðHÞ

� �is associated with the anisotropy

field. By contrast, a more complex relationship of nfS21ðrÞ merits more discussion. It is well


established that the Co-based microwires with a negative magnetostriction have a bamboo-like do-main structure, consisting of an inner core and an outer shell [7]. The surface impedance dependson the circumferential anisotropy at the outer shell. When a stress is applied along the axis of a micro-wire with negative magnetostriction, a magnetoelastic field is induced in the circumferential directionand this drives the spins rotating toward that direction. As a result, the circumferential magnetic per-meability is decreased and hence the surface impedance is also reduced. It is expected, therefore, thatthe application of a longitudinal stress will compensate the effect of the magnetic field. This explainsthe maximum that occurred at around 13 kPa (Fig. 48a). Afterwards, with increasing stress, the welldefined circumferential anisotropy may remain unchanged and hence the surface impedance showsvery little variation to the incremental stress, giving rise to a minimum of tunability at 40 kPa. Largerstress than 40 kPa may depreciate the circumferential anisotropy and increase the surface magne-toimpedance, which accounts for the recovery of the increased tunability with stress.

It should be noted that tens of kPa imposed on the composite yields hundreds of MPa on each wire,according to a simple calculation as follow. As the present case meets the isostrain condition, the fol-lowing equation holds

Fig. 46.from [1

ec ¼rc

Ec¼ ew ¼

rw

Ew; ð5:2Þ

where ec and ew denote the strain for composite and microwires, respectively; rc and rw the stress ex-erted on the composite and microwires, respectively; Ec and Ew the Young’s modulus of the compositeand microwires, respectively. Using the law of mixture, the stress each microwire experiences isgiven by

(a)

(b)

Complex permittivity spectra of as-received composite and after damage by tensile stress. Reprinted with permission75] copyright 2011 AIP.

(a)

(b)

Fig. 48. (a) Stress and (b) field dependence of tunability at 1, 4.8 and 8 GHz, plasma frequency fp = 4.8 GHz, The ordinate profilesare normalised by 10�4 and 10�5, respectively. Reprinted with permission from [175], copyright 2011 AIP.

Fig. 47. Effect of stress (left) and magnetic filed (right) on transmission spectra of microwire composite containingFe4Co68.7Ni1B13Si11Mo2.3 microwires. Reprinted with permission from [175] copyright 2011 AIP.



rw ¼rc

ðEm=EwÞfm þ fw; ð5:3Þ

where fm and fw are the volume fraction of the matrix and microwires, respectively. Due to the signif-icant difference between the Young’s modulus of rubber matrix (2 MPa) and of microwires (100 GPa).10 kPa on the composite can result in 500 MPa on the microwires. This is within the reasonable stressrange as commonly discussed in literature, in terms of the stress effect on GMI properties of micro-wires (see, e.g. [53,239]).

5.2.2.2. Stress influence of electromagnetic properties measured by spectroscopy. For composite contain-ing ferromagnetic wires exhibiting giant magnetoimpedance effect at microwave frequencies, theeffective permittivity may depend on a dc magnetic field via the corresponding dependence of the sur-face impedance. The surface impedance can be changed by applying a stress which modifies the mag-netic anisotropy and domain structure in wires. Thus, the effective permittivity may also depend onthe external stress or strain. Following the stress tunable theory proposed by Makhnovskiy and Panina[12], Qin and co-workers [174,276] approached the strain effect on the electromagnetic responsesfrom the technological aspects of the multifunctional composites.

Co56.51Fe4.84B14.16Si11.41Cr13.08 glass-covered magnetic microwires having a total diameter of29.4 mm and silicone rubber were used for the preparation of composite materials. Continuous micro-wires with the same length of 70 mm were embedded in a parallel manner into the silicone rubbermatrices, which were bonded by silicone resin (see Section 3.2.2 for further details). The number(n) of the microwires in composites varied with n = 6, 12, 17 corresponding to the wire spacingd = 2, 1, 0.8 mm. For comparison, copper wires with a diameter of 60 mm were also used as fillers.The resultant composites are of uniform dimension of 70 mm � 13 mm � 1.8 mm.

The electromagnetic measurement was carried out with a wave vector of the electromagnetic fieldperpendicular to the wires using a modified microwave frequency-domain spectroscopy. The quasi-TEM transverse electromagnetic mode, which is the only mode that propagates in the structure, makesthe analysis of the complex transmission and reflection coefficients relatively simple. Using the Nicol-son-Ross procedure for the transformation of the load impedance by a transmission line, are deter-mined by the transmission S21 and reflection S11 parameters. A vector network analyser (Agilent,model H8753ES) with SOLT calibration was used to measure the S parameters of the cell containingthe sample under test within the frequency range between 300 MHz and 5 GHz. Details of the instru-mental were discussed in Section 2.2.2.2. All measurements were done at ambient temperature.

Fig. 49 shows the permittivity spectra for composites containing different amount of microwiresand 12 copper wires. For the unstressed sample, the real component of permittivity e0 increases withthe wire amount. For the same amount of wires, composite containing copper wires displays a larger e0

than that with ferromagnetic microwires. The same trend remains when the strain reaches 2.4% as thetensile stress is applied along the longitudinal direction of the composite. Noticeably, there appears abroad relaxation peak at about 4 GHz for n = 12 sample when k = 2.4% and, with the same strain, asharper peak occurs at around the same frequency for the n = 17 sample. A similar evolution of per-mittivity spectra with strain is also shown in the imaginary component (e00). But such a phenomenonis not observed for the n = 6 sample and the sample with copper wires. It is also interesting to notethat e00 of the sample with copper wires is smaller than those with magnetic microwires.

Fig. 50 summarises the strain dependence of e0. The sample without wires shows expected responseof e0 to stress. After adding fillers into the composite, its e0 starts to show relatively stronger stress sen-sitivity, which increases with the wire amount. The sample with copper wires presents similar stresssensitivity of e0 to that containing the same amount of magnetic microwires.

Fig. 51 summarises the e00 spectra for all samples with strain ranging from zero to 2.8–3.2%. Notethat the strain discussed herein are nominal values. Overall, there is a significant influence of micro-wire amount on e00. The strain effects also vary with the wire amount. For the n = 6 sample, e00 is almostindependent of the strain. For the n = 12 sample, there is a remarkable dependence of e00 on strain, fea-tured as an evolution of symmetric resonance peak at 4.5 GHz. As n increases to 17, the peak positionand the evolution trend with the strain remain unchanged, the shape becomes asymmetric, though. Incontrast, the sample with the copper wires exhibits a complex evolution of the resonance peak with


the strain, which is the resonance peak occurring at the unstressed state increases with a small strainof 2% but disappears at larger strains. To exclude the influence of geometrical factors of the compositesand the microwires, Fig. 52 was plotted to show the frequency dependence of tand (ratio of e00 to e0),and the evolution of peak features with strain remains the same trend as in Fig. 51.

Strain dependence of effective permittivity is quantitatively analysed by the Gaussian molecularnetwork model (GMNM) [277]. Fig. 53 shows k dependence of D with varying amounts of wires, whereD = (e0(k) � e0(k = 0))/e0(k = 0). This relationship is well fitted by a functional form k(1 + k � 1/(1 + k)2),where k is a constant, the value of which varies with the wire amount as shown in Fig. 53.

The effective permittivity (e) is dependent on the wire concentration (pv) and the averaged polar-isability (hai): e = em + 4ppvhai, where em denotes the permittivity of matrix [12], Thus, increasing thewire amount improves the effective polarisation and hence the permittivity. The polarisability is pri-marily dependent on electric excitation. For the present composite configuration with microwires per-pendicular to the electric field vector, although the sample is aligned with the tensile axis of thedeformation apparatus, an axial component of electrical field still exists due to the inevitable mis-alignment of the wires within the sample and/or the possible inhomogeneity of the electrical fieldin the cell which may affect the electric excitation of the wires. This accounts for the observed dielec-tric response of the composite samples due to the polarisation and the induced circumferential mag-netisation of the wires. For the magnetic microwires, the strain modifies the magnetisation processand hence the circumferential permeability, resulting in the changes of e0. However, since the exper-imental data were obtained using the same protocol and measurement cell, the changes of permittiv-ity can be solely attributed to strain.

It is also shown that more microwires induce a sharper peak at ca. 4 GHz, indicating an increasedstress sensitivity. However, this argument does not hold true for the composites with n = 6 and copperwires which can be understood as follows: for n = 6, the wires concentration is not high enough to

Fig. 49. Effective complex permittivity spectra for unstressed composites (k = 0) and stressed composites with 2.4% straincontaining varying amount of microwires.

Fig. 51. Spectra of e00 for composites containing ferromagnetic microwires n = 6, 12, 17 and 12 copper wires with strain k as aparameter.

Fig. 50. Strain dependence of e0 for composites with n as a variable.


satisfy the response of a noticeable peak to the external stress; for copper wires, they have no responseto the induced circumferential magnetic field and therefore the composite does not show any stress-induced peaks. Overall, the effective permittivity of wire composites increases with the strain, whichis further discussed later based on the GMNM approach. It is worth pointing out that, owing to the

Fig. 52. Frequency dependence of loss tangent with strain as a parameter. Reprinted with permission from [174] copyright2010 AIP.


higher concentration of copper wires as a result of larger diameter than that of ferromagnetic micro-wires, the composite sample with copper wires shows a larger permittivity than that with the sameamount of ferromagnetic microwires.

From the application point of view, it is important to find ways to improve the stress sensitivity.Obviously, this can be approached by increasing the amount of microwires in the composite. However,it should be noted that it does not necessarily mean that more is better. In this work, the sensitivity ofpermittivity to stress showed little change between the n = 12 and n = 17 samples. Somewhat surpris-ingly it is found that the samples containing magnetic microwires and that containing non-magneticmicrowires appear to yield a similar stress sensitivity of e00. This observation suggests an independenceof the stress sensitivity in wire composites to the conductivity and magnetic permeability of the wiresfor a sufficiently high concentration of wires, although the reason for this result is not obvious.

The most striking feature shown in Fig. 51 is the evolution of the peak with the stress for n = 12 andn = 17 samples. It is proposed that the gradual spectral change from relaxation to resonance at 4.5 GHzcan also be attributed to the influence of stress on wire magnetisation as discussed above, which mod-ifies the eddy current loss and contributes to the steady evolution of the e00 resonance due to the cir-cumferential ferromagnetic resonance.

The loss tangent (tand) retains the same changing trend with the strain as e00(k), indicating thatsuch a strain effect is independent of any geometrical factors [278]. It should be noted that such a

Fig. 53. Variations of D with strain for composites with differing amount of wires as shown in the open symbols at 4 GHz. Thebest fitted lines to the function of k(1 + k � 1/(1 + k)2) and values of k corresponding to different n are also shown. Reprintedwith permission from [174] copyright 2010 AIP.


transformation of relaxation to resonance is absent for the n = 6 sample and composite with copperwires in the spectra of complex permittivity. This suggests the exclusivity of ferromagnetic microwiresand the requirement of wire concentration to realise a steady evolution of the peak feature defined bythe stress [221].

Now we discuss the strain-permittivity relationship. Basically the GMNM approach is related to theelasticity network of the composite material. Excellent agreement between the experimental resultsand the GMNM model is observed for all samples (Fig. 53), which suggest the applicability of the mod-el at measured strain range. By introducing more microwires (n 6 12) into the rubber matrix, a higherstress sensitivity (characterised by k value in this case) and a closer experimental-model match is ob-tained. But when n increases to 17, k is decreased and a relatively larger mismatch is observed. Thiscan be attributed to the enhanced complexity of the composite mesostructure arising from the largeramount of embedded microwires [277]. Nevertheless, due to the periodical topology of the microwireswithin the composite, GMNM gives fairly good predictions for all samples.

The significance of wire patterns is manifested in Fig. 54a, in which a nonlinear dependence of e00 onthe strain is shown. In this case, the wire starts to snap when the strain exceeds 2.8%. Due to the un-even interfacial properties, each single wire may experience different stress, which results in partialbut not total fracture of all wires. We then receive a similar resonance response for two patterns(Fig. 54b). This indicates that the increase of dielectric loss with the stress is compensated with theopposite effect resulting from the reduction of strained wires. There are two possible mechanisms in-volved in this phenomenon. First is the stress effect: the stress changes the current distribution in thewires and induces higher dielectric loss, and release of stress results in the opposite effect. Second isthe shape effect: the wires are fractured to relatively shorter pieces and the anisotropy field of the wirebecomes non-uniform and results in the reduction and broadening of resonance linewidth. This leadsus to a striking revelation in a larger context that the for functional fillers enabled heterogeneous com-posites, the macroscopic behaviour is dependent on the collective response of the fillers on one hand,and each single filler on the other hand. This then poses the challenge of how to manipulate some, ifnot each, of the fillers. In so doing, we will have greater control of the properties of the composite pre-sented to meet specific applications.

5.3. Temperature tunable properties

By analogy with stress, the temperature tunable properties are derived from the temperaturedependence of GMI properties. Because the magnetic permeability is sensitive to temperature,the GMI changes rapidly as a function of temperature, especially in the vicinity of the curie tempera-ture Tc. In general, for Co-based microwires, the GMI effect first increases with increasing measuringtemperature due to the internal stress relief and reaches a maximum value near the Curie temperatureof the material, then finally decreases at higher temperatures [279,280]. The dramatic change of GMI

(a) (b)Fig. 54. Spectra of complex permittivity for microwire composites with strain k as a variable. (b) Schematic models of the wirecomposites under tension: (upper panel) elongated sample without wire fracture; (lower panel) partial of wires are broken toshorter pieces. Reprinted with permission from [344] copyright 2011 AIP.


at temperatures above the Curie point was attributed to the collapse of the magnetic coupling in thematerial [281], which has been exploited for the development of temperature sensors [282].

In terms of composites, the magnetic phase transition at Tc will lead to a large transformation ofdispersion of effective permittivity as well as the reflection and transmission coefficients [41].Fig. 55 shows the theoretical permittivity spectra and transmission/reflection spectra for T < Tc andT > Tc. By analogy with the influence of stress or magnetic field, there is an anomalous dispersion ofe0(f) and relaxation-resonance transformation when T exceeds Tc. All these features demonstratestrong temperature effects, which can be exploited for temperature sensing. A very promising appli-cation is to embed these microwires into the preform of polymer laminates. The microwires can thenserve as self-regulating heating elements in the microwave curing process, which is believed to bemuch more efficient than conventional curing methods [283]. Meanwhile, with proper choice of com-position and tailoring, the wires can be made highly sensitive [284] to the temperature to be appliedfor process monitoring, which remains a challenging issue in composites manufacture [285]. In addi-tion, the wires remain as stress sensing elements in the cured composites for various kinds of struc-tural application. With increasing use of advanced fibre-reinforced composites in industry [286], theaddition of microwires may well renovate the composite industry to some extent.

(a)

(b) (c)Fig. 55. (a) Calculated dispersion spectra of resonance complex effective permittivity in the vicinity of antenna resonance underthe influence of temperature, the inset shows the schematic configuration of the composite. (b) Typical transmission andreflection spectra under the influence of temperature. (c) Typical reflection phase spectra under the influence of temperature[41].


6. Metamaterial and microwave absorption characteristics

6.1. Effectuation of microwire composite metamaterials

Thin conducting wire structures are common building blocks for preparing metamaterials withnegative permittivity of a range of unusual properties. This has generated a considerable interest inwire media and vast literature is devoted to the subject (see,e.g. [287–294]). The negative electricalresponse also suggests that the wire medium is characterised by a low frequency stop band from zerofrequency to the cutoff frequency which is often referred to as plasma frequency [295,296]. For thewire radius in micron scale, and lattice constant in millimeter scale, the plasma frequency is in thegigahertz range. In this frequency band, a strong dispersion of the effective permittivity may be usedto engineer a specific electric response. However, a single array of non magnetic wires cannot providenegative magnetic permeability, so to obtain simultaneously the negative permittivity and permeabil-ity, non-magnetic wires are often combined with another array of SRRs [61]. Such a design suffersfrom the drawback of having relatively large dimensions and is not suitable for making into a complexshape when required, e.g., to be made into a coating on a curved surface. Another disadvantage is thatsuch design is anisotropic and the negative refraction is limited to only a couple of polarisations ofincident plane electromagnetic wave [297–300], impeding interesting applications such as perfectlens [58], where isotropic metamaterial is needed. Most recently, alternative approaches have beenproposed capitalising on the magnetic properties of magnetic materials such as ferrites [301,302],yet a combination of non-conducting wires and magnetic materials is still needed. In this context,to pursue the most simplified design, single ferromagnetic wire or their array is proposed to providesimultaneous negative permittivity and permeability, in that the negative permeability can be ob-tained at frequencies between natural ferromagnetic resonance and antiferromagnetic resonance[231–233,303,304], while the negative permittivity can be obtained below the normalised plasma fre-quency ~f ¼ fp=

ffiffiffiffiffiffiemp

[48,12]. Thus, as long as the ferromagnetic resonance frequency is not higher thanthe plasma frequency in the continuous-wire case, or the anti-antenna resonance in the short-wirecase, the simultaneous negative permittivity and permeability can be obtained. With a square net con-figuration, the microwire composite will present isotropic performance.

Theoretically, a calculation is given here to illustrate the possibility of obtaining negative permeabil-ity and permittivity. For the configuration shown in Fig. 57a, the permeability can be expressed as [305]

leff ¼12ðx0 þxmÞ2 �x2

x0ðx0 þxmÞ �x2 1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirxe

2p ab

� �2 �2

þ 1

s0@ 1A ð6:1Þ

where x0 = cHdc with c the gyromagnetic constant and Hdc the external field. xm = 2p(2pa/b)2cM withM the saturation magnetisation of wires of radius a and interwire spacing b and a bulk conductivity r.For typical values of Co–Fe–Cr–B–Si wire, r = 1016c�1, M = 500 Gs, when a = 10 lm, b = 1 mm,Hdc = 10 Oe, the ferromagnetic resonance is 704 MHz according to fr ¼ l0r

ffiffiffiffiffiffiffiffiffiffiffiffiffiHdcMsp

=2p [108]. The nor-malised plasma frequency is 38.9 GHz, when the matrix permeability is 2. In this case, both negativepermittivity and permeability are obtained at 1.9–21.7 GHz [305]. It should be noted that by regulat-ing a, b (within the limit) and magnetic bias, the negative index range can be tuned. This could be ofgreat use from the application point of view.

The capability of microwires to realise metamaterial features is demonstrated amazingly in a singlewire. Labrador et al. [231] tested a single wire of nominal composition Fe77.5Si12.5B10 in a waveguideby paralleling it with the electric field vector on slices of Rohacell foam under a dc magnetic field. Bothnegative permeability due to the natural FMR and negative permittivity as an effect of interactionswith the waveguide are realised in the X-band. Note that different from the case of short-circuitedmicrowires with waveguide, the electrically isolated microwire behaves as capacitive-loaded, respon-sible for negative values of the effective permittivity. As the natural FMR occurs at zero magnetic field,magnetic field is then not an essential element in this metamaterial system, which greatly simplifiesits structure. On the other hand, application of magnetic field could also add the tunable functionality.


Such a self-contained and versatile fine element is hence established as promising metamaterial build-ing block to configurate a series of metamaterials, which are discussed below.

Different approaches were developed to realise the metamaterials based on ferromagnetic micro-wires. Adenot-Engelvin et al. [306,307] fabricated the wire composite as schematically shown inFig. 56a using CoFeSiB wire with a small negative magnetostriction coefficient of total diameter9 lm and core diameter 4 lm. The volume fraction of the wires is within the range of 6–11%. Themicrowave permeability for this composite is shown in Fig. 56b fitted by a model based on the sole-noid approach with a unique set of values for resistance (R), inductance (L) and capacitance (C).

The permeability is also found, in this configuration, to be dependent on the loops, in terms of theresonance frequency by analogy with the magnetic field effect [229,232] or stress [197]. Such field ef-fects can be readily explained by the LLG model for computing the magnetic dynamic susceptibility.

In another configuration (see Fig. 57a) [232] constituted by wire arrays of CoSiB with a diameter of2 � 3 lm, the transmission spectra were obtained as shown in Fig. 57b exhibiting the rise of transmis-sion with the dc field due to a double negative condition obtained. Although there is no matrix in-volved, such wire arrays demonstrate the potential to make metamaterials from these wires.

Liu et al. [173] proposed a metamaterial configuration by combining the long conductive fibresalong the electric field and microwires along the magnetic field as shown in Fig. 58a. As expected,the negative refraction index is shown at a certain frequency range as shown in the numerical results(Fig. 58b), although the significant resonance loss remains a problem for its application.

In comparison to the composites mentioned above, the prepreg-based composites possess muchbetter mechanical properties in addition to the metamaterial particularities [177]. Indeed, regardlessof the matrix, the wire arrays alone [232] or simply bonding the wire arrays on the paper [237,241] areable to show negative permittivity (see Fig. 59). But the sine qua non for composites in engineeringapplication is their structural function. In this sense, the proper choice of matrix, fabrication andthe resultant structural performance need to be addressed carefully to obtain a truly applicable mul-tifunctional composite.

A very important sine qua non for realising the metamaterial feature at microwave frequency isthat the diameter of microwire is comparable to the skin depth, too large a diameter will cause hugereflection [47,237,304]. This argument generally holds true for any functions based on microwave–material interactions other than EMI shielding dominated by reflection. For typical ferromagneticmicrowires, r = 1016 s�1 (105 S/m), l = 20, the calculated skin depth d at 10 GHz is about 1 lm [49].Since the permeability decreases with the frequency, d changes little. This is larger than even very thinmicrowires with typical radius of few microns. Although it is still possible to penetrate into most ofthe inner core in the Fe-based wire [171] or outer shell in the Co-based wire [308], the submicronwires [309–314] or nanowires [315–326] would be preferred in this case. On the other hand, reducingthe wire diameter will reduce the volume fraction of wires and hence the permittivity and permeabil-ity. One may have to accept that such an unavoidable loss is typical for metal metamaterials [327].

Fig. 56. (a) Schematic view of a sample with 11 metamaterial blocks. (b) Measured permeability and model with R = 0.1OX,L = 0.09 nH, C = 9.5 pF for the eight-loops wire composite. Reprinted with permission from [306] copyright 2006 Elsevier.

Fig. 58. (a) Schematic view of the configuration of microwire composite. (b) Negative refractive index of the microwirecomposite obtained by HFSSTM [173].

Fig. 57. (a) Schematic view of the configuration of wire arrays and measurement setup. (b) Measured transmissioncharacteristics on an array of two layers of three wires each one, as a function of the applied magnetic Hdc. Reprinted withpermission from [232] copyright 2009 AIP.


Another restriction is set on the ‘dilute’ condition, i.e., b a, which is necessary to have a relativelysmaller carrier density and large effective carrier mass, such that the plasma frequency can be regu-lated in the 1–10 GHz of application interest. The band stop or band pass filter, for example, can bedesigned based on the criticality of plasma frequency on transmission [47,305]. Also, it is argued thata large number of wires is deleterious since it will absorb most of the electromagnetic wave [197,304].This issue must be addressed before the microwire composites can find metamaterial applicationssuch as cloaking. On the other hand, it is desirable for microwave absorption application. As such,these two functionalities cannot be pursued simultaneously, but this would greatly extend the free-dom of tailoring the electromagnetic properties of the microwire composites.

6.2. Microwave absorption capacity of microwire composites

The high-frequency absorption behaviour of amorphous ferromagnetic materials, among others, isof sufficient interest for microwave absorber applications [229]. Since amorphous glass-coated micro-wires possess small dimension (1–30 lm in diameter), high electrical conductivity (�6 � 105 S/m),high magnetic permeability (�104), and high mechanical strength (�103 MPa), they can be incorpo-rated into polymer-based composites for creating high-performance microwave absorption[171,172,176] or EMI shielding [328] composite materials. It should be noted that, for microwire

(a)

(b)Fig. 59. Effective permittivity spectra of Co66Fe3.5B16Si11Cr3.5 continuous wire arrays deduced from the scattering spectra withthe external magnetic field as a parameter (wire radius a = 10 lm, spacing between wires b = 5 mm). Reprinted with permissionfrom [314] copyright 2011 John Wiley & sons.


composites, the EMI shielding of interest to us is absorption-dominated shielding [328]. In this sense,we will focus on the discussion of microwave absorption of microwire composites, which is deter-mined by its electromagnetic constitutive parameter, namely, permittivity and permeability throughthe intrinsic properties of microwires and the mesostructure. The following discussion is carried outbased on the different absorption mechanism, i.e. dielectric loss dominated and magnetic loss domi-nated absorbing.

6.2.1. Dielectric loss dominated absorbingIn the case of dilute composites, the microwire composites exhibit high complex permittivity but a

close-to-unity permeability with negligible magnetic loss at gigahertz frequency [12,172,221]. It fol-lows that the absorption feature is mainly determined by the relaxation polarisation.

The concentration of wire amount plays an important role in this case. It has been shown that anincreasing amount of wires will improve the absorption [328]. However, it is reported that rather thansimple linear dependence of absorption on filler content, there exists a threshold value at which thepercolation network is formed if the glass coats at the end of wires were spalled, which is often thecase [172] (see Fig. 60a). This is common in the percolating composite systems (see, e.g.[114,329,330]). In detail, when the wire content is smaller than the percolation threshold, the loss


tangent increases but without significant increase of dielectric loss as the wire content is increased,whereas further increase of wire concentration gave a sharp increase of dielectric loss due to the wavereflection rather than absorption. This effect overshadows the contribution of increasing loss tangentto the microwave absorption and results in the decrease of microwave absorption. Note that the tun-nelling effect is responsible for the conductivity of the composite before the percolating threshold,which is highly desirable for microwave absorption. It should be mentioned that, at this point, micro-wires are not as good as ferrite due to its much higher conductivity, which otherwise would free ourconcerns on the concentration limitation to preserve the dipole nature [331]. To address the conflictbetween increasing wire concentration and percolating network, superior glass quality is the key.Therefore, it reveals to us, in addition to the quality of the metallic core, good glass quality is necessaryfor further improving the microwave absorption. Indeed, it is shown that the percolation threshold de-creases due to the decrease of the length of naked metallic core via annealing but the level of maxi-mum absorption is retained. It can then be expected that with a further increase of annealed wireconcentration, the absorption can be increased.

6.2.2. Magnetic loss dominated absorbingIn the case of microwire composites with heavy loading, the ferromagnetic resonance may shift to

gigahertz frequency due to the enhanced effective anisotropy field via the long range dipolar interac-tions between wires [171,305]. In this case, the ferromagnetic resonance for the planar microwirecomposites is given by [305]

fr ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4pMsðHk þ HnÞ

p; ð6:2aÞ

Hn / iMsða=lÞ2; ð6:2bÞ

where Hn is the created field by neighbouring wires of total number i, or it can be simply understood asan additional anisotropy field induced by wire interactions [180]. Thus, any factors that can influencethe anisotropy field should be considered tuning parameters. Directly from Eq. (6.2), it is obtained thata larger aspect ratio (l/2a) will reduce the resonance frequency and increase the absorption accordingto Snoek’s law; and that the increasing number of wires will enhance the permeability and neighbour-ing field, and hence the resonance frequency. For Co-based wires, the decrease of metal-to-total diam-eter ratio p will elevate the internal stress and consequently the anisotropy field [160,332], thus theabsorption should be shifted to a higher frequency. This has been very well analytically explainedby Baranov [333]. The dependence of resonance frequency can be expressed as

f � f0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� p2

1þ 1:5p2

� �sðGHzÞ ð6:3Þ

where

f0 ¼ 1:5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik� 106

pðGHzÞ ð6:4Þ

Three kinds of microwires of typical positive, negative and vanishing magnetostriction constantwith correspondingly different composition [334] are chosen here to shed light on the usefulness ofthis theory. By using Eq. (6.3), the metal-to-total diameter ratio (p) dependence of resonance fre-quency is calculated for these three wires. The result confirms the role of wire cross-sectional geom-etry on the natural ferromagnetic resonance frequency and also reveals that the iron-based wires aremore suitable for absorption purpose at relatively higher gigahertz frequencies. It should be, however,noted that the resonance frequency can be shifted to higher frequency if a large enough neighbouringfield is yielded with a good number of wires added into the absorbing media or tailored wire geometry(Fig. 61). Another proved method is to make a multilayer structured microwire film that will enhancethe anisotropy field [335] and give an improved initial permeability as high as 6000 at 1 MHz. Withreduction of the wire length, the demagnetising field increases, and the anisotropy field are reducedaccordingly [171,180,204,328], resulting in reduction of absorption via the collaborative effect with

Fig. 60. (a) Fig. 7. Morphology andmetal core contact of the short-cutmicrowires: (a) as-cast; (b) annealed at 450 �C; (c)annealed at 530 �C; (d) metal core contact (as-cast). (e) Calculated reflection losses of planar composites filled with as-cast andannealed microwires (with filling ratio of 15% and thickness of 1.5 mm.) Reprinted with permission from [172] copyright 2010Elsevier.


the influence on the neighbouring field Hn. In general, optimal dimensions for excellent absorptionperformance requires a metallic core of diameter 1–3 lm and length of 1–3 mm comparable to thehalf wavelength [336] for microwires.

Before closing this session, several important aspects of implementation of microwires on absorb-ers should be highlighted. First, as the anisotropy constant of microwires can be conveniently modu-lated by the magnetostriction constant that is subject to wire composition and stress conditions(either internal stress from different geometry or external stress applied), tuning of natural FMR res-onance and associated absorption features such as absorption maximum and bandwidth is thereforereadily accessible. Second, the dispersion of microwires (i.e., mesostructure control) is critical to meetthe requirement of suitable dimensions for maximum absorption. This has been experimentallyproved in Ref [336]. Tunable absorption can be realised in the absence of magnetic field and prefersa ultra-thin metallic core, making the wires attractive for miniaturization of microwave devices basedon these fine elements. The last important aspect meriting our attention is the usage of wires withoutglass coats. Although they are inferior in terms of as-cast wire quality due to the fabrication limitation

Fig. 61. Theoretical curve (continuous line) of FMR frequency as a function of x according to Eq. (6.3) for three wires withpositive, negative and vanishing magnetostriction, respectively.


as compared to glass-coated wires, it is the metallic core rather than glass coat that interacts effec-tively with the microwave. As such, applying metallic core only into the absorbing matrix would im-prove the packing density of the wires [335] and hence the absorbing rate and efficiency.

7. Potential applications

The ultimate goal of developing new materials is for practical applications. Based on the structureand properties of microwires and their composites presented and analysed in previous sections, it isnow possible to propose relevant applications. As early as 1991 when the GMI was not defined, a re-port on the application of GMI was published [337]. From then on, GMI materials have been under ide-alisation and development for sensor applications taking advantage of their high sensitivity toexternal field, driving current frequency and tensile stress. Many new types of sensors using GMI ef-fect have been proposed, increasingly widening the application of the GMI. Hitherto, a variety of de-vices based on GMI microwires, such as magnetic field sensors [338–341], stress sensors [145,211],current sensors [342] and position sensors [340,343], have been commercialised. The detailed mech-anism of microwire-based GMI sensors has been detailed in Refs. [7,31,160,161]. Here we briefly sum-marise the sensing application of microwires as shown in Table 2. In this Chapter, some potentialapplications are proposed for microwires composites as mapped in Fig. 62.

Thanks to a remarkable microwave tunable dispersion of the electromagnetic parameters by exter-nal magnetic fields, stress and temperature, microwire composites find a wide range of applications in,to name but a few, smart coatings, microwave absorbers, non-destructive testing (NDT), stresssensing, structure monitoring, process monitoring and implant accessories (see, e.g.,[12,41,174,308,314,328,344]). They are discussed in the following sections.

7.1. Microwave applications

By analogy with the waveguide system containing ferromagnetic wires, the microwire compositeshave wide application as microwave electronic components [345]. Owing to their metamaterial prop-erties, the microwire composites can be used for general applications of left-hand materials such ashigh-performance frequency selective surface (FSS) and quality band stopper. Based on the remark-able tunable effect, they can also be applied as tunable filters and phase shifters [43,51]. Their low costand susceptibility to mass production, combined with their exceptional absorbing capacity in relativeto low volume fraction, mean that they can be designed into various shapes of absorber for civil uses,for example, to improve the electromagnetic compatibility of electronic devices and protect them andhuman bodies from EM and noise pollution, and also for military use as a means to realise camouflage

Table 2Applications of GMI sensors.

Applications Types of GMI sensors Features and/or functions

Target detection and trafficcontrol

Position sensors [370] Low fabrication cost and simple setting; superior to opticalbased monitoring devices

Wireless magneticfield sensors [371]

Remote control of industrial process

Nano-GMI sensor[372]

Measure electric field in high speeds for automobiles

Aerospace research andapplication

Magnetic field sensors Measure ambient magnetic field vector in space

Gear-tooth sensor Control speed and position of gears; improve flight safety[373,374]

Electronic compasses andinformation equipment

GMI electroniccompasses [371]

Small size and low power consumption

G2 motion sensors Detect both geomagnetism and gravity [375]Magnetic field sensors Superior to GMR in terms of sensitivity [376]

Non-destructive crackdetection

GMI amorphous wiresensor

Capture crack regions [377]

Biomedical and health control Brain position sensors[378,379]

Examine function of brain and detect tumour, if any

Biological detectionsensor [380]

Fast identification and diminution of direction threshold ofpathogens or other targeted biomolecules

Stress sensor applications GMI torque sensor[381]

Simple construction, high accuracy, low power consumptionand easy installation

SI-CMOS-IC multi-vibrator [382]

Very high sensitivity, sense seismovibration of bridges due tocars passing


of aircrafts or ships by absorbing radar waves. Their military application has been successfully per-formed by Micromag (Spain), who commercialised the excellent reduced radar cross section (RCS)technology in air, land and sea vehicles. In 2009, a mixed coating consisting of the wires within regularpaints, was implemented on the surface of a patrol ship of Spanish navy (see Fig. 63) and achieved sig-nificant reduction of RCS leading to increased suvivability from 45% to 90% at best [346].

Fig. 62. Application map of ferromagnetic microwires and their multifunctional composites [218]. Courtesy of Dr. Makhnovskiyof Plymouth University.

Fig. 63. Application of coating containing microwires on a patrol ship of the National Homeland Security Agency, Spain [346].Courtesy of Micromag Inc.


The targeting operation frequency range could be met by regulating the wire geometry and pat-terns. Yet it should be noted that the diameter of microwire also limits its application for higher fre-quencies. At terahertz (THz), for example, one has to resort to nanoparticles for any microwaveapplication.

7.2. Structural reinforcement and health monitoring

In civil and aeronautical engineering, the microwire can be used as reinforcing elements to makepolymer matrix composites with enhanced mechanical and/or thermal properties as discussed in Sec-tion 4. In addition, they can also be applied to reinforce glass matrix [347]. Due to its achievable highductility as demonstrated by Donald et al. [348] (Fig. 65), the microwire glass-matrix composite is ex-pected to meet the requirement of specific application where high toughness and resistance to spall-ing is necessary.

Another promising application for microwire composites is the evaluation of structural materialsby detecting the invisible structural damages or defects. According to the varied scattering responseof the defects and main structure to the waveguide, the contrast dielectric images can be established.The sensitivity to the stress of the composite also affords it full credibility in stress-monitoring. Withthe wires as sensing elements inside the composite, the stress distribution can be imaged vividly. Forinstance, the composites are treated as being made of a number of blocks, and each block has a sen-sitive yet different response to the stress exerted on it, which is reflected on the resonance spectrum.This kind of technology is called microwave imaging technology (Fig. 64). Note that the principal

Fig. 64. Proposed microwave contrast imaging technique for stress monitoring and structural interrogation [218]. Courtesy ofDr. Makhnovskiy of Plymouth University.


advantage of this technology is that it not only has the ability to monitor or detect the condition of thematerials at service, but can also be used at long range, which means remote monitoring can beachieved with data communication. This can greatly expand the capability of the current microwaveNDT technique. A lucrative target to practice this technology is wind turbines, a critical element forwind energy harvesting. By implementing the thin coating layer containing microwires onto the sur-face of the existing turbines or embedding the wires into the turbine structure to be produced, themicrowires would be able to function as dipolar antennas to monitor the health condition of turbines.They are also capable of identifying the approximate location of damages with the wire failure draw-ing on the length effect on the resonance frequency. In addition, the rotating blades is notorious incausing significant unwanted doppler returns to the illuminating radar, which could be somewhatdetrimental to the radar operations as it is a formidable task to filter these unwanted signals [349].Introduction of microwires can resolve this conflict of interest between the desire to encourage wideuse of renewable and green energy and that to maintain the effective operation of those important hu-man safety associated radars used for air traffic control, weather monitoring and marine navigationaids. The last but not least benefit is the attenuation of lightning impacts, which will severely influencethe electronic systems in a wind turbine [349]. The threefold benefits will surely avail a niche formicrowires being applied in energy sector.

It should also be noted that the research in SHM of composite structure is not without limitations.To date all work only deals with the dielectric matrices such as non-conductive polymer matrices orglass-fibre reinforced composites but not the carbon-fibre composites, in that the conductive carbonfibre is likely to result in huge conduction loss at a high volume fraction (60–70% for commercial car-bon fibre composites), making it a formidable task to quantify the effect of microwires, if any, throughthe results, for example, from the free-space measurements. This is however not unsolvable, and themicrowires could be set on the top of carbon fibre prepregs during the preform preparation or simplyserve as functional coat or tape attached on the surface of carbon fibre composites. In this way, how-ever, one may only be able to dectect a surface crack but not the inner damage. On the other hand, themicrowires coating on the carbon fibre could form a double-layer absorber capitalising on the absorb-ing properties of microwires and the quasi-reflective manner of carbon fibre composites [350]. How toimplement the microwires into carbon fibre composites is an intriguing topic worthy of further study.

7.3. Other applications

Combining the remote stress control with the advantage of the small size, the wire inclusions canbe made into micro antennas embedded into implants for biomechanical applications [218]. As an

Fig. 65. Micrographs exhibiting the high ductility of bended NiSiB amorphous microwire, which has been tied into a knot.Reprinted with permission from [348] copyright 2010 Springer.

Fig. 66. Proposed biomechanical application: a stereotype prosthetic device with microwires embedded into implants [218].Courtesy of Dr. Makhnovskiy of Plymouth University.


example, microwires have been proposed to be deployed in a prosthetic device as shown in Fig. 66.They are expected to meet the needs of immediate diagnosis of interfacial conditions at the micro leveland to analyse the elastic deformation inside the materials. Yet such application remains at a concep-tual level. Development of the relevant device has to rely on a full knowledge of the wire propertiesunder different conditions, precise control of wires in the device design, and robust processing of sig-nals. Compounded by the strict requirement of medical devices, this is non-trivial task but, without adoubt, is a promising direction for exploitation of microwire-based materials and devices.

Other possible applications rely on the combination of microwires and other functional materials,for example, carbon nanotubes. As is known, carbon nanotubes can be used as gas sensors owing totheir affinity to gas molecules resulting from extremely high surface-to-volume ratio. They are capableof detecting explosive gases such as hydrogen or toxic gases. The mechanism behind is the dc resis-tance of CNTs changes sensitively with absorption of analytic molecules. However the low sensitivity(typically 2–10%) calls for a significant improvement by modifying this technique. Phan et al. [199]reported the CNT casted on magnetic ribbon could enhance the impedance of original ribbon and var-ies sensitively with the content. Futhermore, with enhanced GMI effect, the advanced microwires/CNThyrbid filler can then be incoporated into polymer matrix to develop a multiscale hybrid composite formicrowave tunable and absorption applications. Therefore, development of microwire/CNT filler couldbe very useful to extend the sensing capability of microwires.

Another example is fibre-Optic magnetometer made from a magnetostrictive element attached to alength of optical fibre, capable of detecting external field via a phase change produced [351–353]. This


technology makes good use of the magnetomechanical effect (DE effect) addressing the magnetic fielddependence of Young’s modulus of magnetostrictive microwires. This effect can also be used for bio-sensing application [354]. It is interesting to note that on the one hand optical fibre and magneticmicrowire tend to be competitive in the sensing market; on the other hand, they can be coupled torealise sophisticated functionalities.

8. Summary and directions for future research

8.1. Concluding remarks

Both fundamental and technological aspects of microwire composites have been thoroughly re-viewed in this article. The primary conclusions arrived at as follows:

1. The multifunctionalities of microwire composites stem from the wire inclusions, which can act asboth reinforcement and functional fillers. According to the effective medium theory, the effectiveelectromagnetic properties of wire-composites are determined by the topology of the wire patterns(mesostructure) and the local properties, i.e., the intrinsic properties of microwires, includinggeometry, dielectric and magnetic properties. By tailoring the microwires and regulating the com-posite mesostructure, the electromagnetic properties which characterise the microwave interac-tions with the composite can then be modulated to realise a variety of functionalities such astunable properties, metamaterial properties and microwave absorption.

2. The microwire composites can be fabricated through different means from hand lay-up to open-mould casting, depending on the choice of materials. The selection of matrix draws on the struc-tural requirement, ranging from elastomer to epoxy to glass-fibre prepreg with distinguishedYoung’s modulus. Mass production is limited by the wire patterns and geometry; it remains a tech-nical challenge to realise industrial scale fabrication with precise control of composite structurefollowing the optimised design.

3. Microwire-composites present significant GMI and GSI effect enabled by the wire inclusions. TheGMI effect can be regulated via extremely small loading of wire fillers, which is desirable for thesensing applications. An enhanced GMI performance was obtained in the multi-wire compositesthrough the collective response of the microwires in the presence of an external magnetic field.The wire-composite also shows superior stress-sensing resolution and the GSI effect of the wire-composite can be well optimised by the number of composite layers and annealing. As evidencedby the structural examination and tensile tests, the extremely small volume fraction of microwires(�0.01 vol.%) allows the wire-composites to retain their mechanical integrity and performance.

4. The field-tunable properties of the composites in the microwave frequency range were found tovary remarkably with changing wire periodicity, wire geometry and composition. It is possibleto optimise the microwave dielectric properties and transmission/reflection patterns of the com-posites through modulating these wire parameters and the mesostructure constituted by the wiretopology. This can be utilised to manipulate the composite architecture and extend the limitationof the effective frequency range.

5. For a microwire composite panel, when the wire breakage occurs due to the applied stress, thereappears a significant change in the sign and magnitude of the effective complex permittivity belowplasma frequency. The magnetoelastic characteristics defined by the composition are critical to thestress sensitivity of dielectric response. When comparing the stress tunability and magnetic fieldtunability, much more complex dependencies of tunability on external stimuli were observed atthe measured frequency range. The high frequency-domain spectroscopy characterisation furtherreveals that, with increasing wire concentration, the composite exhibits larger permittivity andstrain sensitivity. There is a pronounced dependence of permittivity spectra featured as relaxationto resonance transformation with increasing strain and further confirmed with evolution of losstangent. The relative variation of e0 versus strain follows the Gaussian molecular network modelvery well.


6. Ferromagnetic microwires offer a solution to realise isotropic double negative medium e < 0, l < 0)with relatively simple structure consisting of only wire arrays, as opposed to the conventional com-plex structure constituted by the conducting wires and magnetic materials or SRRs. By regulatingthe wire diameter, the wire spacing and magnetic bias, the negative index frequency range can bewell tuned, which has been demonstrated in a number of configurations.

7. The microwave absorption of microwire composites originates from the dielectric loss and mag-netic loss, the domination of which seems to depend on the filler content. For dilute composites,the glass-coat quality plays a vital role in reducing the reflection loss by impeding the formationof a fully conductive network. For heavy-loaded wire composites, the absorption feature is closelycorrelated with the FMR. Therefore, the local static magnetic properties and the effective staticmagnetic properties as well as the size effect determine the dynamic magnetic response of the wirecomposites and hence the absorption characteristics. As such, sufficient freedom is available forone to modulate the EM parameters and control the absorption features (absorption maximumand bandwidth) for the targeted applications. As concerns the EMI shielding, the absorption isidentified as the main contributor. Rather low filler loading yields high shielding efficiency forthe microwire composites and make it superior to other shielding materials.

8.2. Outlook for future research

The present review detailed the multifunctionalities of microwire composites. Inspired by currentactive study on this subject, some relevant directions are proposed as follows:

� The interfacial properties of the microwire composites require more detailed study, which isabsent as yet. Chemical coupling agent such as silane can be applied to improve the interfacialstrength between the glass coat of microwires and polymer matrix. Varying pull-out test meth-ods (see e.g., [355]) and Raman spectroscopy can be used to perform a precise measurement ofthe bonding strength and interfacial stress transfer [356].

� Field/stress tunable properties of composites containing short or long continuous wires witheither helical or circumferential anisotropy should be investigated with or without an externalstress by varying the geometry of the wire and permittivity of matrix within a reasonable rangeusing the flexible planar coil, which may indicate a variety of options for designing the micro-wave tunable structure under the external magnetic field [12].

� Considering the sensitivity of the MI of microwires to temperature [160], the temperature tun-able properties would be of great use in composite process monitoring. The possibility of micro-wires serving as temperature sensing elements in composites manufacture realises the addedvalues of microwires in the preform process. This would make such microwire compositesmore useful and promising for industrial applications. Analytical results of typical dispersionof effective permittivity and transmission/reflection spectra with temperature have beenshown in Ref. [41]. It is promising therefore to direct efforts into this direction. Further, in viewof the efficiency of microwave in activating cross-linking for polymers [357,358], the micro-wave–material interactions can also be exploited for the microwave curing of the polymer com-posites [359]. Although a fluoroptic thermometer is immune to microwave [360], it would bemore convenient for microwires to serve as both heating and sensing elements in processing.

� To maximise the functionality and add more values to the resultant composite, a plausibleapproach is to develop hybrid composites incorporating both microwires and other functionalfillers such as carbon nanotubes. Because they serve quite a few similar purposes, e.g., mechan-ical reinforcements [2], metamaterial units [361], and EMI shielding elements [362], they arelikely to enhance the relevant performance of a hybrid composite. Further, their electromag-netic functions apply to different frequency ranges [363], and the combination of them maygreatly extend the applicability of the resultant hybrid composite. In addition, magnetic nano-particles can also be considered to coat on the surface of microwires to realise biphase magneticfiller with improved soft magnetic characteristics, which is desirable for some microwaveapplications hinged on high permeability and low hysteresis.


� Since the impedance match of the front absorber can be improved by the non-zero surfaceimpedance of carbon fibre composites as the substrate [364], design of a multilayer structureabsorber based on microwires and carbon fibre composites could be very promising with theincreasingly heavy use of carbon fibre in all kinds of vehicles. The manipulation of arrangementof carbon fibres and glass-coated microwires in normal manner could also realise metamaterialfeatures [173], which can be exploited for cloaking application.

� The objective of demonstrating the stress tunable properties is accomplished. However, such atechnique is not instrumented yet. A lot of work needs to be done in order to realise a visualdevice with high-definition tomography. Hopefully such an instrumentation will renovatethe composite industry in the pertinent aspects.

Overall, the ultimate goal is to devise a smart composite that is highly susceptible to a range of en-ergy signals and capable of an efficient and effective transformation to electric signals. The functionalfillers are expected to maximise the all-round performance of the resultant compositeindiscriminately.

Acknowledgements

The authors wish to acknowledge their collaborators: Prof. Larissa Panina, Mr. Nick Fry and Dr.Dimitry Makhnovskiy of the University of Plymouth, Dr. Manh-Huong Phan of the South Florida Uni-versity, Drs. Arcady Zhukov, Valentina Zhukova and Mihai Ipatov of the Universidad del Pais Vasco,Spain, Prof. Christian Brosseau of the Université de Bretagne Occidentale, France, Mr. Slava Popov ofTaurida National University, Ukraine, Dr. Nikolay Pankratove now at Moscow State University, Russia,Dr. Jie Tang of the National Institute for Materials Science (NIMS), Japan, Prof. Lu-Chang Qin of the Uni-versity of North Carolina at Chapel Hill, USA, Prof. Jianfei Sun, Mr. Huan Wang and Mr. Jing-shun Liu ofHarbin Institute of Technology, China. The authors are indebted to the Microfiber Technology Industry(MFTI) (http://www.microwires.com) for the provision of some magnetic microwires. F.X.Q. wouldalso like to acknowledge the financial support from the Conseil Général du Finistère Post-doctoral Fel-lowship Program and EPSRC Institutional Sponsorship. H.X.P. is the Deputy Director of Bristol Centrefor NanoScience and Quantum Information (NSQI) and he is also a visiting professor of Harbin Instituteof Technology, Harbin, China. A thank you also goes to those who kindly authorised permission to useor reproduce figures and drawings; corresponding references are duly indicated. Last but not least, theauthors are indebted to the anonymous referees for their constructive comments, which make the cur-rent paper even better.

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