Advanced Magnetic Microwires as Sensing Elements for LC-Resonant-Type Magnetoimpedance Sensors: A Comprehensive Review

J Supercond Nov Magn (2012) 25:181–195DOI 10.1007/s10948-011-1320-4

R E V I E W PA P E R

Advanced Magnetic Microwires as Sensing Elementsfor LC-Resonant-Type Magnetoimpedance Sensors:A Comprehensive Review

Anh-Tuan Le · Manh-Huong Phan

Received: 6 September 2011 / Accepted: 20 September 2011 / Published online: 15 October 2011© Springer Science+Business Media, LLC 2011

Abstract In recent years, all modern vehicles and trans-port means use a vast variety of sensors and transducers.The operation of all medical instruments is also based onsensors and transducers. Industry is also employing moreand more transducers for the monitoring and control of pro-duction lines. Therefore, the sensing technology has beendriven by the increasing needs for enhanced sensitivity, im-proved stability, high reliability, and lower costs. For thispurpose, we have proposed and developed novel two LCresonant-type magnetoimpedance (LCMI) sensor devicesutilizing soft magnetic microwires as a sensing element, giv-ing an emphasis on the use of resonance effect from LC-components and the rapid permeability change of the mag-netic microwires to significantly improve the sensitivity per-formance of sensors. This article aims to provide a compre-hensive analysis of the design and operation of these de-vices. After a description of magnetic core materials, circuitdesigns and fabrication techniques is given, the details of allexperimental measurements are presented. The characteriza-tions of constructed LCMI sensor devices are systematicallyanalyzed, and the physical origins of magneto-resonant phe-nomena, field, and frequency dependences in these LCMIsensor devices are addressed. Influences of processing pa-rameters on the sensing characteristics of LCMI sensors are

A.-T. Le (�)Department of Nanoscience and Nanotechnology, HanoiUniversity of Science and Technology (HUST), 01 Dai Co Vietstreet, Hanoi, Vietname-mail: [email protected]

M.-H. PhanFunctional Materials Laboratory, Department of Physics,University of South Florida, 4202 East Fowler Avenue, Tampa,FL 33620, USA

also discussed. This enables the optimal conditions to fabri-cate high-performance magnetic sensing devices.

Keywords Magnetic microwires · Multifunctionalcomposites · LC-resonant-type MI sensor · Giantmagnetoimpedance effect · High-frequency applications ·MEMS

1 Introduction

A magnetic sensor is a device capable of sensing a magneticfield and converting information from it. In practical appli-cations, the information related to the magnetic inductionsis converted by the sensor into an electrical signal [1]. Theoperation of a magnetic sensor is based upon many differ-ent physical principles, that in turn, leading to a wide rangeof magnetic sensor types such as inductive sensors, Hall-effect sensors, magneto-optical sensors, giant magnetoresis-tance (GMR) sensors, and giant magnetoimpedance (GMI)sensors [2–5].

Magnetic sensors have been also widely used in manymodern technological applications such as ultrahigh-densitymagnetic recording systems [6], automotive and automo-bile devices [7, 8], navigation [9], traffic monitoring systems[10, 11], industrial robots [12], medical electronics [13],and biomagnetic instrumentations [14, 15]. Read heads incomputers have magnetic sensors. Automobiles use mag-netic sensors to determine the position in several placessuch as the engine crank shaft and wheel braking. Facto-ries have higher productivity because of the precise stabil-ity and low cost of magnetic sensors. On the other hand, theadvanced integrated circuit technologies and consumer elec-tronics market have been growing very rapidly. The marketis forecasting the further-reduced minimum feature size and

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182 J Supercond Nov Magn (2012) 25:181–195

fabrication cost, while increasing density of devices in theapplications. Therefore, the magnetic sensor technology hasbeen driven by the needs for improved sensitivity, smallersize, quicker response, and lower prices [16–20]. In thiscontext, recently developed magnetic sensors utilizing gi-ant magnetoimpedance (GMI) effect, so-called GMI sensors[21, 22], are of great interest, because of their high sensitiv-ity, high flexibility, and cost-effectiveness. The GMI sensorshave advantageous features of high sensitivity of fluxgatesensors with the field detection resolution of about 1 mOefor AC uniform fields and about 100 mOe for a DC field,without a need for exciting and sensing coils [21]. The sen-sor head length of the GMI sensor is about 1 mm which isabout 1/20 of the fluxgate sensor head length due to beingfree from the demagnetizing field in the head. Therefore, theresolution for detection of localized magnetic-pole field ismore than 20 times higher in the GMI sensor than that in thefluxgate sensor [16, 17]. In addition, the GMI sensors havebeen found to be more field sensitive than the existing gi-ant magneto-resistance (GMR) sensors [23, 24]. The GMRmaterials generally involve large fields to obtain a responseof a few percent, whereas the GMI materials can produce afew hundred percent changes in the impedance at very smallmagnetic fields [25–30]. For instance, a GMR sensor has amaximum sensitivity of ∼10–20%/Oe, while the field sen-sitivity of a GMI sensor can reach an extremely high valueof 500%/Oe [31]. To date, the GMI technology is relativelynew and its development is still in progress; it is likely thatthe low prices and high flexibility of this technology willpromise wide-ranging applications in the near future.

Giant magnetoimpedance is a phenomenon that signifi-cantly changes the electrical impedance of a magnetic con-ductor with a small variation of magnetic field [32]. This ef-fect was initiated by the research group of Panina and Mohriet al. [33, 34]. That discovery has given rise to a new direc-tion in magnetic sensor technology, and has brought aboutthe rapid increase of research groups all over the worldto study about the GMI phenomena as well as its techno-logical applications [35–40]. It was well recognized thatthe very essence of GMI is mainly related to the depen-dence of the skin depth upon the effective magnetic per-meability of the material. As the permeability of materialchanges substantially with the static magnetic field or thefrequency, the impedance also changes as a function of theseparameters. Accordingly, any phenomenon which producesa large change in the permeability will give rise to a GMI ef-fect [41]. The further detailed analysis of GMI phenomenol-ogy and its characterizations can be found in some good re-view articles [42, 43].

So far, the most promising candidates for GMI sensor ap-plications are amorphous cobalt-rich ribbons, wires, glass-coated microwires and multilayers made of a metallic layer

sandwiched between ferromagnetic materials (with or with-out intermediate insulating layers) due to their displayed ex-cellent GMI behaviors [44, 45]. Some prototype sensors em-ploying these materials as sensing elements, i.e., magneticfield sensors [46–50], current sensors [51, 52], position sen-sors [53, 54], stress sensors [55, 56], torque sensor [57],biosensors [58–63], were proposed and successfully devel-oped. The current progress of GMI is thrusted toward the in-crease of magnetic-field sensitivity and the optimization ofthe signal-to-noise ratio in the GMI sensor devices [64, 65].

To improve the field sensitivity of GMI sensors, sev-eral attempts have been made by either the use of the fer-romagnetic resonance effect [41, 42] or of the electricalresonance from a LC-resonance electronic circuit [66–70].Both methods have proved useful for developing ultrasen-sitive magnetic sensors that can operate at very high fre-quencies [71–80]. In particular, Kim et al. [81] have recentlydemonstrated the superior features of LC filter-type magne-toimpedance sensors. The LC filter circuit showed the out-put changing ratio per 1 Oe of 5% at a high frequency of50 MHz. This value was 2.5 times larger than that expectedin a conventional bridge circuit with constant current excita-tion. In another work, Takezawa et al. [82] reported that theperformance of a microthin-film magnetic field sensor wassignificantly improved by making the use of LC resonanceof the sensor element as well as the impedance change dueto the permeability change of the magnetic film. This indi-cates that LC-type MI sensors can be ideally used for a widerange of technological applications.

This article aims to provide a comprehensive analysisof design and operation principle of novel LC-type magne-toimpedance (LCMI) sensor devices. New developments ofLCMI sensor circuits with glass-coated Cobalt-based amor-phous ferromagnetic microwires used as sensing elementsare presented that considers two types of LCMI sensorsinvolving magnetic microwires as either inductive elementof the circuit or a core material to the inductive element.The technological study in these LCMI sensor devices isalso addressed in our works. It is demonstrated that the fea-ture of novel LCMI sensor devices built in our works canbe used to develop a new series of highly sensitive GMI-based magnetic sensors operating at very high frequencies(UHF–VHF). Moreover, the LCMI sensor devices with fer-romagnetic microwires used as a sensing element could bepromising devices for microtechnological applications, andpresent an attractive option for advanced magnetic sensors,intelligent measurement and control systems. By employ-ing the resonance effects from a LC-resonance circuit andrapid change in magnetic permeability of sensing element,the field sensitivity of sensor devices were extremely im-proved that to be engaged in increasing specific engineeringrequirements of automobile and biomedical applications.

J Supercond Nov Magn (2012) 25:181–195 183

Fig. 1 Left: a self-patterned LCMI sensor device consisting of a mag-netic microwire as inductive element and two terminal conductive elec-trodes as capacitors. Right: a equivalent electronic circuit

2 Materials, Design and Fabrication Techniques

2.1 Materials

We used the amorphous glass-coated Co83.2B3.3Si5.9Mn7.6

(sample no. 1) and Co67Fe3.8Ni1.4B11.5Si14.6Mo1.7 (sam-ple no. 2) ferromagnetic microwires, which were fabricatedby the Taylor–Ulitovsky method [83], as sensing elementsto construct varying LCMI sensor devices. The diametersof the metallic core, measured in an optical microscope,were about 16 µm and 29 µm, and the thicknesses of theinsulating glass coating were about 5 µm and 3 µm forsamples no. 1 and no. 2, respectively. These microwiresamples were thermally annealed at different temperaturesTa = 50,100,150,180, and 200 °C for 1 hour in vacuum toimprove their soft magnetic properties. The annealing tem-perature range was selected, because the enhanced soft mag-netic properties could improve the GMI effect in the high-frequency range (∼several MHz), where magnetization isonly caused by rotation of magnetic moments [28].

2.2 LC-resonance Circuits Design

Our group developed a new LC-type resonance circuit, inwhich the sensor circuit is directly built on a magnetic mi-crowire by forming two capacitive terminal electrodes atthe ends of the microwire without direct contact to its fer-romagnetic core. In this case, magnetic microwires wereused as inductive element of the circuit, whereas the conduc-tive electrodes act as capacitors in the LC-resonance circuit[see Fig. 1]. The length of magnetic microwire was about5–15 mm and the width of the electrodes was about 2 mm,respectively. It is also worth noting that this new configura-tion of circuit can be adequate for possible practical mag-netic devices.

To develop the further compatibility with modern micro-electronic systems, a new class of LCMI microsensor de-vices was produced by means of microelectromechanicalsystem (MEMS) techniques. The new micro-LCMI deviceconsisted of a solenoidal microinductor with a bundle of

Fig. 2 Left: a micro-machined LCMI sensor device consisting of asolenoidal micro-inductor with magnetic microwire as a core materialto inductive element and an external capacitor connected in parallel tothe micro-inductor. Right: an equivalent electronic circuit

Fig. 3 Left: schematic representation of a solenoidal micro-inductor.Right: fabricated high-aspect ratio microinductors on a Pyrex glasswafer by using MEMS technique

soft magnetic microwires as a core and an external capac-itor connected in parallel to the microinductor [see Fig. 2].In this case, the magnetic microwires were used as a corematerial to the inductive element. The solenoidal microin-ductors were fabricated with the dimensions of 500–000 µmin length, 200 µm in width, 75 µm in height, and with 10–20turns [see Fig. 3]. The heat-treated magnetic microwireswere inserted into a microinductor as sensing core materi-als [see Fig. 4]. After connecting leads to microinductors ina set to external integrated circuit terminal socket, the in-ductor sets was molded to reinforce mechanical strength byepoxy. To form a LC-resonance circuit, the varying externalcapacitors from 1–100 pF were connected in parallel to themicroinductors.

2.3 Fabrication Techniques

The standard ultraviolet lithography (UV-LIGA) process,which is a cost-effective process, with UV-sensitive resistswas used to form thick polymer molds, and electroplatingtechnique to build three-dimensional (3D) micromachinedmetallic MEMS structures [84–87]. For low-cost MEMSfabrication, UV-LIGA process is available with photosen-sitive polyimide, a positive photoresist with high viscosityand high transparency, and an epoxy-based negative pho-toresist SU-8 with the compensation of lower resolution andlower aspect ratio compared to the LIGA process [88–92]. In


this work, the negative photoresist SU-8 was used to developthe UV-LIGA process for fabricating polymeric or metallicmold inserts [see Fig. 5].

3 Experimental Measurements

The inductance and impedance measurements were per-formed by a network analyzer (Agilent, 8712ET, 0.3 MHz–1.3 GHz) and an impedance analyzer (HP4191A, 1 MHz–1000 MHz), both connected to a computer controlled

Fig. 4 A solenoidal microinductor with inserted magnetic microwiresas a microcore

data acquisition system. A schematic view of experimen-tal method for conducting measurements was displayed inFig. 6. The impedance changes of constructed LCMI sen-sor devices was directly measured using the HP4191A withtwo contact terminals in a wide frequency range from 100–1000 MHz. Impedance measurements were conducted alongthe sample axis under a longitudinal applied dc magneticfield. The external dc magnetic field, created by a solenoid,was swept through the entire cycle equally divided by 800intervals from −300 Oe to +300 Oe.

The percentage change of magnetoimpedance, e.g., GMIratio, with applied dc magnetic field has been expressed as

GMI(%) = �Z/Z(%)

= 100% × [Z(H) − Z(Hmax)

]/Z(Hmax), (1)

and the dc magnetic-field sensitivity of GMI as

ξ = [�Z/Z(%)

]max/�H, (2)

where Hmax is an applied maximum dc magnetic field andHmax = 300 Oe in the present work. �H stands for the fullwidth at half maximum (FWHM).

4 Characterizations of LC-Type MI Sensor Devices

4.1 Self-patterned LCMI Device

4.1.1 Magneto-Impedance Characteristics

The GMI characterizations are strongly dependent on thefrequency of the ac current flowing along the sample and the

Fig. 5 A process diagram of theUV-LIGA technique: (a) seedlayer deposition, (b) bottomconductor mold, (c) bottom Cuconductor electroplating, (d) viamold, (e) via structureelectroplating, (f) top conductorformation, and (g) removingSU-8 and etching seed layers


Fig. 6 Schematic representation of experimental method for conduct-ing the MI measurements

applied magnetic field. We will analyze these dependencesin detail.

4.1.1.1 Field Dependence According to the MI theory[42], for a cylindrical magnetic conductor (e.g., wires), itsimpedance can be written as

Z = RdckaJo(ka)/2J1(ka), (3)

where Rdc is the dc resistance of the wire, Jo and J1 arethe Bessel function of the first kind, a is the radius of thewire, k = (1 + j)/δ with an imaginary unit j , and δ is thepenetration depth expressed as

δ = c√

4π2f σμφ

(4)

Here, c-the speed of light, σ -the electrical conductivity ofthe wire, f -the frequency of the ac current flowing alongthe sample, and μφ-the circumferential permeability.

To measure GMI effect, a dc magnetic field is usuallyapplied parallel to the ac current along the longitudinal di-rection of the sample [32]. At a given frequency, the appli-cation of a dc magnetic field (Hdc) changes the circumfer-ential permeability μφ and hence the penetration depth δ

which in turn alters the magnetoimpedance until the valueof δ reaches the radius of the sample (a). To achieve a largeGMI effect, the penetration depth should be as small as pos-sible in the absence of an applied magnetic field. Large cir-cumferential permeability along with a low value of the re-sistivity gives rise to a small penetration depth at high fre-quency range [43]. A large increase of the circumferentialpermeability can be achieved by applying an ac current ofthe frequency sufficiently high to excite the resonance of thesample. This large circumferential permeability at the res-onance strongly decreases the penetration depth and, there-

fore, increases the impedance of the sample [40]. In this con-text, amorphous Co-based ferromagnetic microwires usedare good candidates for GMI sensor applications, becausethey possess extremely high circumferential permeabilityarising from their circumferential domain structure [25, 26].

Figure 7 displays the magnetic-field dependences ofmagnetoimpedance GMI(%) for sample no. 1 measured atdifferent frequencies. It can be easily seen that the shape ofGMI curves varies dramatically as the frequency increases.GMI profiles show a single-peak (SP) feature, or a double-peak (DP) one, depending upon a certain frequency region.From the magnetic field dependence of GMI, we can cal-culate the field sensitivity of GMI ξ (%/Oe) as illustratedby (2). In practical, based upon the magnitude of ξ , theoperating regime and potential applications of a magneticsensing element can be determined.

4.1.1.2 Frequency Dependence As mentioned above,apart from the applied dc field, another parameter deter-mining GMI features is the frequency of a driving currentwhich generates the circular ac driving magnetic field [42].Depending upon the magnitude of frequency, the three mainmechanisms have been proposed for explaining GMI fea-tures, which can be distinguished as follows: (i) at relativelylow frequencies (f < 1 MHz), the changes of the impedanceare mainly due to the so-called magneto-inductive effectarising from the circular magnetization process; (ii) at in-termediate frequencies (1 MHz < f < 100 MHz), the GMIeffect is ascribed to variations of the magnetic penetrationdepth due to strong changes of the effective permeabilitycaused by an applied dc magnetic field. In this case, bothdomain walls motion and magnetization rotation contributeto the circular permeability and consequently to the GMI ef-fect, and (iii) at high frequencies (100 MHz < f < 10 GHz),a motion of domain walls is totally damped and the perme-ability rapidly decreases until the ferromagnetic resonancephenomenon is reached [42]. Since the measuring frequencyvaries from 100–1000 MHz in the present work, GMI resultswill be treated as the case (iii), where the domain walls areimmovable.

Figure 8 displays the frequency dependence of max-imum values of GMI(%) for sample no. 1, indicated as[GMI(%)]max. It is worth noting that a multiple-peak GMIbehavior appears to occur in the frequency range of100–1000 MHz. A similar behavior was found in self-patterned LCMI sensor device using the sample no. 2 (seeinset of Fig. 8). This is obviously different from what wasobserved for Co-based microwires [25, 26] in the interme-diate frequency range of 1–100 MHz, where GMI curvesoften showed a SP feature at low frequencies and a DP athigher frequencies, along with an appearance of the onlyone peak of the frequency-dependent GMI curve. This alsodiffers from what were observed in GMI curves relating to


Fig. 7 The magnetic-field dependences of magnetoimpedanceGMI(%) for sample no. 1 measured at different frequencies

Fig. 8 The frequency dependences of maximum value of GMI(%), de-noted as [GMI(%)]max, for sample no. 1 and sample no. 2, respectively

the ferromagnetic resonance in the high-frequency range of1–10 GHz, for typical Co-based microwires [27, 28]. In thepresent work, it should be noted that the appearance of amultiple-peak GMI behavior is not a common feature ofthe frequency dependence of the GMI. It is not only deter-mined by the LC-resonance circuit, but also is also related tothe formation of standing magnetic waves within the sam-ple [66]. This will be discussed in detail in Sect. 4.1.3.

4.1.2 Magneto-Resonant Effects

It is important to mention within the investigated frequencyrange that, the sharp magneto-resonant effects, i.e., for sam-ple no. 1 were observed at two frequencies of 518 MHz and889 MHz. Accordingly, the field-dependent GMI curves ob-served at these frequencies were shown in Fig. 9. Moreover,the sudden changes of the phase angle as large as 180° [seeFig. 10] are evidenced for the occurrence of resonance [80].This explains why the maximum GMI values of about 250%and 700% have been found at frequencies of 518 MHz and889 MHz, respectively. It is worth noting that, at the reso-nance frequency of 889 MHz, the maximum GMI value ismuch larger than that obtained at 518 MHz. This impliesthat the resonance at 889 MHz produced a larger circumfer-ential permeability when compared to that at 518 MHz. Thishypothesis can be acceptable because the ferromagnetic res-onance actually occurs around 889 MHz (∼1 GHz) result-ing in an increase of the permeability with respect to fre-quency. Therefore, a smaller dc magnetic field is requiredto excite the sample at 889 MHz and a larger GMI effectis consequently observed. This probably explains a shiftof the position of the resonance peaks toward lower val-ues of the applied field, when the resonance frequency in-creases from 518 to 889 MHz. As one can see from Fig. 9,at the frequency of 518 MHz, the resonance peaks appearat Hdc = ±24.6 Oe, whereas it occurs at Hdc = ±12.3 Oeat the frequency of 889 MHz. These values coincide withthose obtained from the magnetic field dependence of theangle phase as displayed in Fig. 10. It is therefore reasonable


Fig. 9 The field-dependent GMI curves for sample no. 1 measured atfrequencies of (a) 518 MHz and (b) 889 MHz

to claim that the sharp magneto-resonant effect in the self-patterned LCMI sensor device only occurs at certain valuesof the ac current and the dc magnetic field which satisfy themagneto-resonant condition [78–80].

It is also interesting to note that the ac current strongly in-creased at the resonance frequency. Such a large ac currentgenerated a large circumferential ac magnetic field, there-fore resulting in an increase of circumferential permeability.Consequently, a drastic rise of the magnetoimpedance in thevicinity of the resonance frequency was found [81]. This isalso the reason why the GMI effect is often observed at theresonance frequency. By adjusting the measuring frequen-cies at near the resonance point, the GMI ratio reached thelargest value of 400,000% and 270,000% at the resonancefrequencies of 518.51 MHz and 146.32 MHz for sample no.1 and sample no. 2, respectively, as displayed in Fig. 11. Itshould be noted in the present circumstance that contributionof ferromagnetic resonance (FMR) to GMI can be excluded,because the resonance frequencies were less than frequencywhere FMR occurs (∼1 GHz). From (2), we calculated thedc magnetic-field sensitivity of GMI (ξ ) and correspondingfield sensitivities of GMI obtained about 218,000%/Oe and135,000%/Oe for samples no. 1 and no. 2, respectively. Thisis the highest values of GMI field sensitivity reported untilnow in the research of GMI. These results are very ideal for

Fig. 10 The field-dependent phase angle curves for sample no. 1 mea-sured at frequencies of (a) 518 MHz and (b) 889 MHz

Fig. 11 The magnetic-field dependences of magnetoimpedance,GMI(%), measured at the resonance frequencies of 518.51 MHzand 146.32 MHz for Co83.2B3.3Si5.9Mn7.6 (sample no. 1) andCo67Fe3.8Ni1.4B11.5Si14.6Mo1.7 (sample no. 2) samples, respectively

developing ultrasensitive magnetic sensors operating at thehigh-frequency region.

4.1.3 Influence of Parameters

To obtain a better understanding of nature of the GMI effectobserved in the self-patterned LCMI sensor device, influ-ences of parameters such as material processing and samplegeometry on the GMI characteristics were investigated.


Fig. 12 The field-dependent GMI curves measured at different fre-quencies for the microwire samples (sample no. 1) annealed at (a)100 °C and (b) 180 °C. The inset (1a) shows the frequency dependenceof the maximum GMI value, indicated as [GMI(%)]max

Fig. 13 The variation of the maximum GMI value measured at518 MHz as a function of annealing temperature

To verify the effect of thermal treatment on GMI, wecarried out annealing the investigated microwires at differ-ent temperatures (Ta = 50–200 °C). These samples were an-nealed for 1 hour in vacuum to improve the magnetic soft-ness of material by reducing residual internal stress relax-ation induced during the fabrication process [83]. Note thatthe enhanced magnetic softness could improve significantlythe GMI effect at high-frequency range. As an evident exam-ple, Fig. 12 shows the field-dependent GMI curves measured

Fig. 14 The frequency dependence of the maximum GMI ratio withvarying microwire length

at different frequencies for the microwire samples (sampleno. 1) annealed at (a) 100 °C and (b) 180°C. It is worth not-ing that the frequency at which the LC-resonance effect oc-curred (∼518 MHz) is almost independent on the annealingtemperature. As can be seen clearly from Fig. 12, anneal-ing magnetic microwires significantly changed the magni-tude of the GMI effect but not the characteristic resonancefrequency. This evidently indicates that the GMI feature ob-served in self-patterned LCMI sensor device is attributedto the resonance of LC components. In addition, anneal-ing magnetic microwires in the range of Ta = 50–200 °Calso caused considerable changes of permeability and hencethe GMI effect [28]. Among the samples investigated, themaximum value of GMI ratio of about 900% was found forthe microwire sample annealed at 180 °C [see Fig. 13], dueto the softest magnetic property of this sample. This im-plies that the magnitude of GMI response in a self-patternedLCMI sensor device also depends on the soft magnetic char-acteristics of a microwire, besides the contribution of LCresonance.

As previously mentioned, the appearance of a GMImultiple-peak feature can be determined not only by theLC-resonance circuit, but also related to the existence ofstanding magnetic waves within the sample [66]. If this isthe case [66], any change in microwire dimension can causethe change of number of GMI peaks. To verify this, we usedthe microwires annealed at 180 °C to construct the differentLCMI devices with varying microwire length (d) from 2 to9 mm. In this case, the dimensions of terminal electrodeswere fixed (a = 5 mm and w = 2 mm). As expected, theincrease of microwire length resulted in an increase in thenumber of GMI peaks [see Fig. 14]. It can be seen that as themicrowire length increased from 2 mm to 9 mm, the numberof GMI peaks increased from 3 to 6. To further clarify this,if one pays attention to the variations of the GMI feature ofthe microwire samples with the same length, but differentmicrowire diameters (21 µm and 32 µm for samples no. 1and no. 2, respectively). It was realized that the number of


Fig. 15 Inductance ratios as a function of external magnetic field fora microinductor with 10 turns, 200 µm in width, 75 µm in height, and500 µm in length

GMI peaks remains unchanged as the microwire diameterchanges [see Fig. 8]. This evidently indicates the existenceof standing magnetic waves within the sample [81]. Here,other effects of coaxial wire on the formation of standingwaves in the transmission line could also be considered[66, 67]. In terms of these results, the multiple-peak GMIfeature observed in a self-patterned LCMI sensor device canbe attributed to the effect of the LC-resonance circuit andthe formation of standing magnetic waves within the sam-ple, while the magnitude of GMI is related to the soft mag-netic characteristics of the microwire and the LC resonance[80, 81].

4.2 Micromachined LCMI Device

4.2.1 Inductive Characteristics

Since the magnetic permeability of the microwires variesrapidly as a function of external magnetic field, the induc-tance of the microinductor can change drastically as theexternal magnetic field changes. Therefore, the variationsof inductance, called the inductance ratio, as a function ofexternal magnetic field in the microinductors were investi-gated [82].

Figure 15 displays the inductance ratios as a functionof external magnetic field measured at different frequenciesfor a microinductor with appropriately annealed microwirecores at 180 °C for 1 hour and with sizes of 10 turns, 200 µmin width, 75 µm in height, and 500 µm in length. As onecan see from Fig. 15 that the inductance ratio curves changedrastically as measuring frequency increases, the maximumvalue of inductance ratio reached an extremely high valueof 760%. This reflects the fact that the inductance of themicroinductor varies very sensitively with the external mag-netic field. It is, however, noted that the value of inductanceratio is strongly altered with the changes in dimensions ofthe solenoid.

We depict in Fig. 16 the inductance ratios as a functionof external magnetic field for a microinductor with 20 turns,200 µm in width, 75 µm in height, and 1000 µm in length.It can be seen clearly that the maximum values of induc-tance ratio are much lower when compared to the previousone. It is worth noting that the largest inductance ratio valuecan be obtained at optimal conditions for the dimensions ofsolenoid and annealing microwires at chosen frequencies.The different size of solenoid will give totally different spec-ifications such as inductance, Q-factor, etc. In the presentcase, the dimensions of solenoidal microinductors were var-ied from 500 to 1,000 µm in length with 10–20 turns. Inorder to illustrate the effect of varying dimensions on the in-ductance, a theoretical consideration for the microinductorwhich has different shapes of microinductor dimensions is


Fig. 16 Inductance ratios as a function of external magnetic field fora microinductor with 20 turns, 200 µm in width, 75 µm in height, and1000 µm in length

introduced. For a solenoid-type inductor, the inductance L

can be represented with [88]

L = N2μAc

lc(5)

where Ac is the cross-sectional area of the core, lc is the totallength of the core, μ is the permeability of the core, and N

is the number of coil turns.

Fig. 17 Measured frequency dependence of inductance values for amicroinductor with 10 turns, 200 µm in width, 75 µm in height, and500 µm in length

As it can be derived from (5), increasing the turns in-creases the inductance. But this increases the resistance ofthe microinductor, resulting in lower Q-factor [88]. Thus,the optimization of dimensions for the microinductor playsan important role in achieving good electrical properties.One notes that the inductance ratios in the figure are justchanges of inductance of the microinductor in percentagebetween maximum and minimum values. To estimate abso-lute inductance values of the microinductor, we measuredthe frequency dependence of inductance values and shownin Fig. 17. It can be seen that the inductance values variedfrom 281 nH to 110 nH as a function of measuring frequen-cies from 10 MHz to 100 MHz. The effect of the inductancefall off at higher frequencies [Fig. 17] is due almost entirelyto the dependence of the permeability of the magnetic corematerial on frequency [87].

4.2.2 Magneto-Impedance Characteristics

To form a LC-resonance-type sensor circuit, various externalcapacitors ranging from 1 to 100 pF are connected in paral-lel to the microinductors. Because the inductance of the mi-croinductors varied drastically with respect to the externalmagnetic field, therefore, the resonance frequency as wellas the impedance of the micro LCMI sensor devices can besensitively altered as the external magnetic field changes. Toclarify this, the magneto-impedance characteristics of fabri-cated micro LCMI sensor devices were studied as a functionof the external magnetic field and the driving frequency.

4.2.2.1 Field Dependence Figure 18 shows the field de-pendence of magnetoimpedance ratios (i.e., MIR) for amicro-LCMI device with an external capacitor value of39 pF measured at different frequencies. It can be seen thatthe shape and magnitude of field-dependent MIR curvesvaries drastically as the measuring frequency increases. Itis also worth noting that the MIR values changed sensitively


Fig. 18 Magnetoimpedance ratios as a function of external magneticfield measured at different frequencies for a micro LCMI device withan external capacitor value of 39 pF

with a small variation of external magnetic field, which maybe useful for magnetic field sensors detecting small fields.In our present case, the permeability of soft magnetic mi-crowires core varies rapidly as the external magnetic fieldchanges causing a large variation in the inductance and,hence the impedance of the micro LCMI sensor device [82].

To evaluate the performance of the micro LCMI sensordevice, from field-dependent MIR curves the maximum fieldsensitivity of the device can be calculated by using (2). Forinstance, as one can see from Fig. 18(c), at the resonancefrequency of 104 MHz the calculated maximum field sensi-tivity reached a large value of 40%/Oe. This value is of prac-tical importance in the development of highly sensitive mi-cromagnetic sensors. Nevertheless, the values of field sen-sitivity were considerably altered with a slight change ofoperating frequencies at the resonance point as well as ofexternal capacitor values. These will be discussed in detailin Sect. 4.2.3.

4.2.2.2 Frequency Dependence As observed, Fig. 18 givesus an outline view of frequency dependence of MIR. TheMIR first increases with increasing frequency, reaching amaximum value at the resonance frequency, and then de-creases at higher frequencies. A similar tendency was alsoobserved for all other samples. It is believed that this fre-quency dependence is related to the dependence of the per-meability of the magnetic microwire core on frequency.

4.2.3 Magneto-Resonant Effects

As one can see clearly from Fig. 18, for a micro LCMI de-vice with an external capacitor value of 39 pF, a large changeof impedance ∼80% was observed to occur at the frequencyof 104 MHz within the investigated frequency range. Thisoriginates from both the strong change in permeability ofthe microwires caused by external magnetic field and theLC resonance effect of the sensing elements. At a high fre-quency range, the sensing device can be considered as anequivalent LC-electric circuit, in which consists of a resistorwith an inductance in series and connected with a capacitorin parallel. Therefore, the resonance frequency of the circuitcan be given as follows [90]:

ω =√

1

LC−

(R

L

)2

(6)

Here, ω is the angular frequency of the ac-current flowingthrough the circuit.

It can be clearly seen that the resonance frequency ob-tained from (6) will decrease when the value of external ca-pacitor increases. Our experimental results also show thistendency, the resonance frequency of micro LCMI sensordevices decreases from 569 MHz to 72 MHz when the exter-nal capacitor value increases from 1 pF to 100 pF as shown


Fig. 19 The variation of resonance frequency (fr) and field sensitivity(ξ ) of micro-LCMI sensor devices as a function of external capacitorvalues

in Fig. 19. This indicates that by changing values of externalcapacitor, the operating frequency of the sensor device canbe precisely tuned for desirable purposes. It is worth to not-ing that the field sensitivity of micro LCMI sensor devicesalso alters as the external capacitors changes [see Fig. 19].Consequently, an appropriate selection of the external ca-pacitor for making a LC-resonant circuit is necessary for thedesign and fabrication of practical micromagnetic sensorswith desired sensitivity and operating frequency.

It is also interesting to mention that the impedance varia-tion of a micro-LCMI sensor device can be significantly im-proved by working at resonant conditions in a LC-electriccircuit. In our present case, the magnitude of impedancechanges was extremely enhanced by adjusting the measur-ing frequencies at near the resonance point. Even slightchange of measuring frequencies changed the MIR curvesto totally different shapes, magnitudes, sensitivity, etc. Themagnetoimpedance ratios for a micro-LCMI sensor devicewere measured at various frequencies to find sharp peaks formaximum sensitivity. In the present work, the largest MIRvalue up to 500% with very sharp peak was obtained at afrequency of 263.4 MHz for a micro LCMI device with anexternal capacitor value of 10 pF as shown in Fig. 20. Using(2) for calculation, the maximum field sensitivity of the mi-cro LCMI device reached as much as 420%/Oe. This resultreveals a great possibility for highly sensitive sensor devicesby making a LC-resonance circuit while selecting the fre-quency with the largest response.

4.2.4 Influence of Parameters

As stated above, the influences of microinductor dimensionsand external capacitors on the characteristics of device werediscussed. The aim of this section is to address how the mi-crowire core materials modify the sensing characteristics ofmicro-LCMI sensor devices. The obtained results revealedthat annealing microwire cores and numbers of microwire

Fig. 20 Magnetoimpedance ratio measured at 263.4 MHz for a mi-cro-LCMI sensor device with an external capacitor value of 10 pF

Fig. 21 The calculated sensitivity of micro-LCMI sensor devices in-creased as the number of core microwires increases from 1 to 5

had a noticeable influence on the MIR values as well as thefield sensitivity of device.

Because the great variations in MIR values of micro-LCMI sensor devices are due to strong changes in perme-ability of core material and the LC resonance effect of thesensing elements. Consequently, the property of core mate-rial is a crucial factor for the performance of device. In ourpresent case, thermal treatments on microwires affected themagnitude of the MIR values but not the characteristic res-onance frequency. It is important to note in the investigatedtemperature range of Ta = 50–200 °C that the highest MIRvalue was observed in a micro-LCMI sensor device with themicrowire core (sample no. 1) annealed at 180 °C, due tothe softest magnetic property displayed in this sample. Thisresult is good agreement with that observed in Sect. 4.1.3.

To further clarify the influences of core material, we ex-amined the effect of number of microwire cores on the sens-ing characteristics of device. Here, the dimensions of mi-croinductor and the external capacitor were fixed, while thenumber of microwires (n) was varied from 1–5. The experi-mental results showed that the sensitivity of device increasedwith increasing the number of microwire cores in the sens-


ing element. As one can see clearly from Fig. 21, the cal-culated field sensitivity increases from 40%/Oe to 92%/Oeas the number of sensing microwire cores increases from 1to 5. In our present case, the increase in sensitivity is likelydue to the dynamic magnetic interaction between the ferro-magnetic microwire cores in the sensing element under theinfluence of high-frequency excitation current [93–98]. Thisresult is of great interest for the practical application devel-opment of advanced micromagnetic sensors.

5 Summary

Novel classes of LCMI magnetic microsensors with the ad-vanced magnetic microwires as sensing element were suc-cessfully developed. It focused on giving an emphasis on theuse of resonance effect from LC-components to improve thesensitivity of sensors. A comprehensive analysis of the de-sign and operation of these devices was presented. The char-acterizations of LCMI microsensor devices were systemat-ically analyzed, and the physical origins of resonance phe-nomena, field, and frequency dependences in these LCMIdevices were addressed. Influences of processing parame-ters on the sensing characteristics of sensors were also dis-cussed. This also opens up a new opportunity to design highsensitivity sensor devices containing sensing magnetic mi-crowires for a variety of engineering and technological ap-plications

Acknowledgements This work was financially supported by theVietnam’s National Foundation for Science and Technology Develop-ment (NAFOSTED) through project number 103.02.96.09.

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Documents

Advanced Magnetic Microwires as Sensing Elements for LC-Resonant-Type Magnetoimpedance Sensors: A Comprehensive Review