Review of Magnetoelectric Sensors

Abstract

Multiferroic magnetoelectric (ME) materials with the capability of coupling magnetization and electric polarization have been providing diverse routes towards functional devices and thus attracting ever-increasing attention. The typical device applications include sensors, energy harvesters, magnetoelectric random access memory, tunable microwave devices and ME antenna etc. Among those application scenarios, ME sensors are specifically focused in this review article. We begin with an introduction of materials development and then recent advances in ME sensors are overviewed. Engineering applications of ME sensors were followed and typical scenarios are presented. Finally, several remaining challenges and future directions from the perspective of sensor designs and real applications are included.

Full text

Actuators 2021, 10, 109. https://doi.org/10.3390/act10060109 www.mdpi.com/journal/actuators
Review
Review of Magnetoelectric Sensors
Junqi Gao 1,2,3, Zekun Jiang 1,2,3, Shuangjie Zhang 1,2,3, Zhineng Mao 1,2,3, Ying Shen 1,2,3,* and Zhaoqiang Chu 1,2,3,*
1 Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China;
gaojunqi@hrbeu.edu.cn (J.G.); jjk95@hrbeu.edu.cn (Z.J.); zhangshuangjie@hrbeu.edu.cn (S.Z.);
maozhineng@hrbeu.edu.cn (Z.M.)
2 Ministry of Industry and Information Technology, Key Laboratory of Marine Information Acquisition and
Security, Harbin Engineering University, Harbin 150001, China
3 College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
* Correspondence: shenying@hrbeu.edu.cn (Y.S.); zhaoqiangchu@hrbeu.edu.cn (Z.C.)
Abstract: Multiferroic magnetoelectric (ME) materials with the capability of coupling magnetization
and electric polarization have been providing diverse routes towards functional devices and thus
attracting ever-increasing attention. The typical device applications include sensors, energy harvest-
ers, magnetoelectric random access memory, tunable microwave devices and ME antenna etc.
Among those application scenarios, ME sensors are specifically focused in this review article. We
begin with an introduction of materials development and then recent advances in ME sensors are
overviewed. Engineering applications of ME sensors were followed and typical scenarios are pre-
sented. Finally, several remaining challenges and future directions from the perspective of sensor
designs and real applications are included.
Keywords: multiferroic; magnetoelectric; sensors; object detection; magnetic localization; current
sensing; biological magnetic measurement; non-destructive testing; displacement sensing
1. Introduction
Multiferroic materials have been recently attracting ever-increasing attention be-
cause of the capability of coupling at least two ferric orders, i.e., ferroelectricity, ferromag-
netism, or ferroelasticity, and the vast potential for multifunctional devices applications
[1–5]. A control of polarization P by external magnetic field H (direct ME (DME) effect) or
a manipulation of magnetization M by an electric field E (converse ME (CME) effect) can
be realized in multiferroic magnetoelectric (ME) materials [6]. Compared with single-
phase ME material, ME heterostructures and ME laminates perform greatly enhanced
coupling capability, which is generally characterized by ME coefficient  [7–9]. After
a development of nearly half a century, tremendous progress regarding ME composites
and related device applications has been reported [1–3,6,10–19].
In this article, the focus is placed on magnetoelectric sensors and the corresponding
engineering applications. After an overview of materials fundaments, we present current
advances in ME sensors including DC, low-frequency and resonant magnetic field sens-
ing. Then we summarize typical engineering applications of ME sensors including object
detection and localization, speed and displacement sensing, current sensing and non-de-
structive testing, stress and strain sensing, and biological magnetic measuring. We will
also discuss some remaining questions of ME sensors and their engineering applications
at the end of the article.
2. Materials for ME Sensors
The ME effect was first experimentally demonstrated in single-phase multiferroic
material Cr2O3 in 1961 [20,21]. After that, diverse studies all over the globe were con-
ducted to further enhance the coupling capability of ferroelectric and magnetic orderings
Citation: Gao, J.; Jiang, Z.; Zhang, S.;
Mao, Z.; Shen, Y.; Chu, Z. Review of
Magnetoelectric Sensors. Actuators
2021, 10, 109. https://doi.org/10.3390/
act10060109
Academic Editor: Shuxiang Dong
Received: 26 April 2021
Accepted: 19 May 2021
Published: 24 May 2021
Publisher’s Note: MDPI stays neu-
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Actuators 2021, 10, 109 2 of 23
in a single-phase material system [20,22], but the low Curie temperature and the weak ME
coupling capability in single-phase ME materials, such as BiFeO3, BiMnO3 and LuFe2O4,
greatly limited their applications [1,23,24]. The proposal of a product effect in composite
ME materials by combining the piezomagnetic and piezoelectric effects of ferromagnetic
and ferroelectric materials then provided new routes towards improved ME coupling per-
formance. Early in 1986, Pantinakis et al. proposed 2-2 type ME composites based on the
aforementioned product effect [25] and giant ME coefficients were gradually realized in
laminated ME composites starting from the beginning of 21st century [1,6,10]. Compared
with single-phase or 0-3 typed ME materials, 2-2 typed ME composites, such as a bulk ME
laminates with piezoelectric phase (Pb(Zr,Ti)O3(PZT), Pb(Mg,Nb)O3-PbTiO3 (PMN-PT))
embedded in piezomagnetic materials (FeCoSiB, FeBSiC Terfenol-D, Ni or Fe-Ga) [8] and
a FeGaB/AlN thin-film ME heterostructure [26], exhibited enhanced ME coupling perfor-
mance benefitting from the removal of the leakage current and the improvement of the
interfacial strain transfer. At this section, we will first review materials advances in ME
sensors since 2002.
2.1. Bulk ME Laminates
It is highly desirable to design new connectivity structures for circumventing the lim-
itation of leakage current that occurs in 0-3 typed ME composites. Back in 2002, Ryu et al.
developed a laminated Terfenol-D/PZT/Terfenol-D ME composite (Figure 1a) with 2-2
type connectivity to solve the leakage current problem in 0-3 type ME composites, and the
obtained ME coupling coefficient at non-resonance frequency reached as high as 5
V/cm·Oe [27]. This was a significant event in the development of ME laminates and vari-
ous kinds of laminated structures were proposed afterwards [10,27]. For example. Dong
et al. reported 2-2 type ME laminates consisting of Terfenol-D ferrite and PMN-PT piezo-
electric crystal. These ME composites work with L-T mode and display relatively low ME
coefficients of 2.2 V/cm·Oe at non-resonance frequency [28]. In a bid to further improve
the ME voltage coefficient, Dong et al. in 2005 first proposed a push-pull mode that in-
creased the distance between electrodes and decreased the static capacitance of ME lami-
nates from nF to pF scale [29,30]. In such 2-2 type ME composites, the piezoelectric core
was symmetrically poled along its longitudinal direction and rgw d33 piezoelectric con-
stant of a piezoelectric material could be utilized. A giant ME voltage coefficient of 1.6
V/Oe at non-resonant frequencies was observed experimentally [30]. One year later, Dong
et al. further developed a multi-push-pull mode in 2-1 ME composites. The schematic
structure configuration and operation mode of such a 2-1 ME composite is presented in
Figure 1c. It consisted of a piezo-fiber layer laminated between FeBSiC alloys. For the first
time, the non-resonant ME coefficient at 1 Hz reached 22 V/cm·Oe, making such a struc-
ture especially suitable for low-frequency and passive magnetic sensing [31–35], but it
should be noted here that the mechanical quality factor for such a 2-1 type ME composites
is normally less than 100, so ultra-high resonant ME coefficients cannot be realized in this
case [29].
Another way to address the difficulty of fully polarizing the piezoelectric phase in 0-
3 type ME composites is replacing the particle phase with a 1-D piezoelectric fiber (form-
ing 1-3 typed connectivity). For example, in 2005 Nan et al. reported a 1-3 type ME com-
posite with ZT rod arrays embedded in a Terfenol-D medium via a dice-and-fill technique.
The non-resonant ME coupling coefficient reached 6.2 V/cm·Oe [36], which represented
great progress for ME composites. Two years later, Ma et al. simplified this 1-3 type ME
structure by just embedding one single PZT rod in a Terfenol-D/epoxy mixture [37]. The
single period element of the 1-3 ME composites is shown in Figure 1b. Although the non-
resonant ME coupling coefficient decreased by almost one order of amplitude, this simple
structure, low-cost fabrication process and sub-millimeter size made it attractive for mi-
cro-ME array applications [37].

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Figure 1. (a) Schematic structure (top) and photograph (bottom) of ME laminate composites using Terfenol-D and PZT
disks [27]. (b) 3D and crosss ectional schematic illustration of the single period of 1-3-type ME structure [37]. (c) Illustration
of the FeBSiC/piezofiber laminate configuration working on multi-push-pull mode [29,30]. (d) The schematic view for 1-1
laminated ME composite and a-(ii) the prototype snapshot of the 1-1 typed ME sample [8].
In 2017, Chu et al. reported a 1-1 type ME composites, which consisted of a [011]-
oriented Pb(Mg,Nb)O3-PbZrO3-PbTiO3 (PMN-PZT) single crystal fiber and laser-treated
amorphous alloy Metglas. The 1-1 type ME composite featured athe one-dimensional con-
figuration as shown in Figure 1d [8]. The laser treatment could decrease magnetic hyste-
resis loss of Metglas and thereby enhance the Q value of the ME resonator. In addition,
the fiber configuration effectively utilized the magnetic flux concentration effect occurring
in Metglas layers. More importantly, this 1-D configuration favored the longitudinal vi-
bration mode of ME laminates. A ME coupling coefficient of ~7000 V/cm · Oe, that was
nearly seven times higher than the best result published previously, was finally realized,
opening a door to develop new ME devices, e.g., resonant magnetic receivers in particular
[8]. In addition, a high ME coefficient of 29.3 V/cm·Oe at non-resonant frequency was also
achieved for our 1-1 type composites. Note, only one single crystal was consumed in this
case, while previous 2-1 type composites normally took five crystals. In 2020, the resonant
ME coefficient of 1-1 type ME composites was further enhanced to 12,500 V/cm·Oe by
using a hard piezo-crystal Mn-PMN-PZT [9]. A summary of the field coupling coefficient
of different ME laminates, i.e., 0-3, 2-2, 2-2.1-1 ME laminates, is given in Table 1.
With respect to ceramic-based thin film multiferroic laminates, Ryu et al. recently
developed a Pb(Zr,Ti)O3 film deposited on piezomagnetic materials, e.g., Ni and Metglas.
The crystallization of PZT film was implemented by laser annealing, which was able to
keep the piezomagnetic layer free from property degradation [38–41]. Readers can get
access to more detailed information concerning film-based ME composites in other review
papers [3,6,10].

Actuators 2021, 10, 109 4 of 23
Table 1. Some ME laminates and their ME coupling performances.
Composition Year Connectivity Working Mode


(V/cm·Oe)


(V/cm·Oe)
Terfenol-D/PZT [37] 2007 3-1 L-L 0.5 18.2
NiFe2O4/PZT [42] 2001 2-2 L-T 1.5 /
Terfenol-D/PZT [27] 2002 2-2 L-T 5 /
Metglas/PVDF [43] 2006 2-2 L-T 7.2 310
Metglas/P(VDF-TrFE) [44] 2011 2-2 L-L 17.7 383
Lanthanum gallium tantalite/
permendur [45] 2012 2-2 / 2.3 720
FeCoSiB/(Pt)/AlN in vacuum [46] 2013 2-2 L-T / 20,000
FeCoSiB/(Pt)/AlN [47] 2016 2-2 L-T / 5000
Metglas/LiNbO3 [48] 2018 2-2 L-T 1.9 1704
FeBSiC/PZT [30] 2006 2-1 L-L 22 500
Metglas/PMN-PT [31] 2011 2-1 L-L 45 1100
Metglas/PMN-PT without laser
treatment [8] 2017 1-1 L-T 29.3 5500
Metglas/PMN-PT with laser
treatment [8] 2017 1-1 L-T 22.9 7000
Metglas/Mn-PMN-PZT with laser
treatment [9] 2020 1-1 L-T 23.6 12,500
Note: Connectivity. We use different number to represent the connectivity of each individual phase. For example, 1-3 type
composite means one-phase fiber (denoted by 1) was embedded in the matrix of another phase (denoted by 3); 2-2 type
composite means laminated structure (each phase has a plane configuration denoted by 2); 2-1 type composite means one-
phase fiber was laminated with another phase plate; 1-1 type means both phases are in the form of fiber configuration.
Working mode. L-L, L-T means longitudinal vibrations with longitudinal magnetization and transverse polarization(L-L)
or transverse magnetization and transverse polarization (L-T).
2.2. MEMS and NEMS ME Laminates
In a bid to obtain miniaturized ME devices with enhanced ME coupling capability,
micro-electro-mechanical systems (MEMS) fabrication technology is a promising ap-
proach benefiting from the strong interfacial bonding force and the fine control over the
material composition. Greve et al. developed a thin film MEMS composite consisting of
AlN and amorphous Fe90Co78Si12B10 [49]. AlN is an ideal piezoelectric material compatible
with MEMS techniques, and amorphous soft magnetic alloy is a good candidate for the
piezomagnetic phase because of its high piezomagnetic properties. As shown in Figures
2a,b, two kinds of deposition flow could be used for MEMS ME composites. Conventional
process flow involves the deposition of a high temperature constituent (AlN). In Figure
2a, a reverse flow was then proposed, where FeCoSiB was deposited as the first layer on
the smooth wafer surface and AlN, including with the Pt seed layer, was deposited on top
of it without any substrate heating [47]. A giant ME coupling coefficient of 5000 V/cm·Oe
was measured in this case [47]. In Figure 2b, depositing the magnetostrictive layer and the
piezoelectric layer on two sides of a silicon substrate separately is another way to obtain
good MEMS ME films [50]. With respect to NEMS ME films, Sun’s group in Northeastern
University has contributed lots of works in this field [26,51,52]. As shown in Figures 2c,d,
the typical material is AlN and FeGaB film. As a ME resonator, both laterally-vibrating
(Figure 2c) or vertically-vibrating (Figure 2d) mode can be realized at different frequency
bands. Recently, a NEMS ME resonator has been successfully utilized for mechanical an-
tennas with miniaturized size compared with traditional antennas driven by RF current
[53].

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Figure 2. Sketch of ME MEMS cantilever with the functional layer deposited on one side (a) [47] and two side (b) [50] of
silicon substrate. (c) Scanning electron microscopy (SEM) images of the ME nano plate resonator. (d) Scanning electron
microscopy (SEM) images of the fabricated ME thin-film bulk acoustic wave resonators. The red and blue areas show the
suspended circular plate and AlN anchors. The yellow area presents the electrode [53].
3. Advances in ME Sensors
The giant ME coupling in ME composites provides the chances to be implemented as
diverse functional devices, such as sensors, energy harvesters, magnetoelectric random
access memories, tunable microwave devices and ME antennas, etc. Among those appli-
cation scenarios, advances in ME sensors will be reviewed in this section.
To assess the performance of a general magnetic sensor, several critical parameters
should be considered, i.e., limit of detection (LoD), sensitivity, working temperature, dy-
namic range, power consumption, size and the cost, but one should note LoD and sensi-
tivity should be given a high priority when taking the research stage of ME sensors into
consideration. With respect to the LoD of ME sensors, the ME coupling coefficient and the
voltage noise level should be considered equally. Table 1 summarizes the ME coefficients
of typical ME composites. The total noise level  comes from both internal and external
noise sources. The internal noise is dominated by the dielectric loss  and the leakage
resistance , which can be written as follows [32,33]:
=
+
=
 +
()

,
(1)
where k is the Boltzmann constant (1.38 × 10−23 J K−1), T is the temperature in Kelvin, Cp is
the static capacitance, tan δ is the dielectric loss, f is the frequency in Hz and R is the DC
resistance of the ME sensor. The total noise density  has a 1/f spectrum and makes the
magnetic field detection at low frequency much more difficult. On the other hand, ME
sensors are susceptible to external environment variations, e.g., temperature fluctuation
and base vibration, which typically occurs in low frequency as well [7,54]. We will discuss
the current advances in ME sensors focusing on the improvement of LoD in the following
sections.

Actuators 2021, 10, 109 6 of 23
3.1. Low-Frequency Magnetic Sensor
In 2011, Wang et al. reported the realization of an extremely low limit of detection
through a combination of giant ME coupling in 2-1 type ME composites and a reduction
in each noise source. Giant ME coupling was achieved by optimizing the stress transfer in
multi-push-pull mode, the thickness ratio of Metglas to piezofiber, and the ID electrodes
distribution on Kapton (Figure 3a). Experimental results showed that an extremely low
equivalent magnetic noise of 5.1 pT/√Hz at 1 Hz was obtained (Figure 3b) [33].
Figure 3. (a) Schematic diagram and the protype photo of 2-1 type ME composite working on multi-push-pull mode. (b)
Measured and estimated equivalent magnetic noise of the proposed sensor unit [33].
The problem in 2-1 type ME composites based on multi-push-pull working mode is
the difficulty to fully polarize the piezoelectric phase and the capacitance in this configu-
ration is usually small. In 2012, Li et al. further pointed out that the equivalent magnetic
noise could be reduced by a factor of √N through stacking some number N of ME sensor
units in parallel [32]. From the perspective of reducing the total noise level , connecting
N ME sensor units in series could be also effective to increase the detection capability. For
example, Fang et al. reported a 2-1 ME sensor based on multi-L-T mode, of which the
schematic is shown in Figures 4a,b [55]. In this case, the ME charge coefficient could be
kept at a high level while the static capacitance and the leakage current could be decreased
remarkably by increasing the number (N) of piezoelectric crystal. As a result, the meas-
ured equivalent magnetic noise (EMN) of the Metglas/Mn-PMNT composite was as low
as 0.87 pT/√Hz at 30 Hz for N = 7, which was 1.8 times lower than that for N = 1 (see
Figures 4c,d) [55].
In 2011, frequency conversion technology (FCT) was proposed to circumvent the
large 1/f noise for active ME sensors [56–60]. Quasi-static or extremely-low frequency
magnetic fields can be effectively detected in this case. For example, Chu et al. realized a
limit of detection of 33 pT/√Hz at 0.1 Hz by using amplitude modulation method com-
bined with FCT in 1-1 type magnetoelectric composites [61]. During the measurement, a
carrier signal and a modulation signal were both applied to the ME sensor.

Actuators 2021, 10, 109 7 of 23
Figure 4. 3D structure of Metglas/Mn-PMNT ME composite (a) and its cross-sectional diagram (b); (c) The EMN over the
frequency range of 8 Hz < f < 100 Hz. (d)The EMN and  of different Metglas/Mn-PMNT sensors at 30 Hz [55].
Figures 5a,b demonstrates the fundamental modulation phenomenon and the block
diagram of the correlation detection scheme with respect to an amplitude modulation sig-
nal SMod (t). The output voltage waveform was observed by a mixed signal oscilloscope.
The ME sensor was driven by 100 Hz carrier signal and the modulation frequency is 10
Hz. Once the low-frequency modulation field HAC with an intensity of 10−6 T was applied,
a clear amplitude modulation (envelope) signal was generated due to the intrinsic fre-
quency mixing characteristic in ME sensors, as shown in Figure 5a(ii).
In order to test the limit of detection by using this amplitude modulation method, the
time constant decreased to 10 ms and the demodulated signal from time domain wave-
form via a lock-in amplifier was analyzed. Figure 5c shows the measured output voltage
in response to an applied 100 mHz HAC varying from 0.1 to 10 nT. Clearly, a standard
linear-response to HAC within this range was obtained as given in the inset in Figure 5c.
Accordingly, the limit of resolution (LOR) of the ME sensor based on this amplitude mod-
ulation method was determined to be as low as 100 pT. To confirm this LOR, Figure 5d
further verified it by measurement. Considering an equivalent noise bandwidth
(ENBW)of 7.8 Hz corresponding to the given measurement system, the calculated LoD
was then calculated as 33 pT/√Hz at 0.1 Hz.

Actuators 2021, 10, 109 8 of 23
Figure 5. (a) The demonstration of fundamental modulation and frequency mixing phenomenon in ME sensors; (b) A
block diagram of the amplitude demodulation method with respect to amplitude modulation signal SMod (t). (c) The meas-
ured output waveform in response to an applied weak AC magnetic field at 100 mHz. (d) A linear-response to varying
HAC at 100 mHz with a step of 0.1 nT [61].
3.2. Resonant-Frequency Magnetic Sensor
ME laminates can be viewed as resonators from the perspective of mechanics and
resonant phenomenon is also able to enhance the ME coupling coefficient and thus to im-
prove the detection ability [10]. In this regard, ME sensors could be highly competitive
over other magnetic field sensors, e.g., fluxgate sensor and optical pump magnetometer.
Using a 2-2 ME composite, Dong et al. reported an enhanced LoR of 1.2 pT early in 2005
(see Figure 6a) [29]. As for MEMS ME magnetic sensor, Yarar et al. developed a low tem-
perature deposition route of very high quality AlN film, allowing the reversal process
flow as talked in Section 2.2. Correspondingly, the LoD was enhanced by almost an order
of magnitude approaching 400 fT/Hz1/2 at the electromechanical resonance, as shown in
Figure 6b [47]. Based on the giant resonance ME coupling coefficient in 1-1 type ME lam-
inate, a superhigh resonant magnetic-field sensitivity close to be 135 fT (see Figure 6c) was
further obtained by Chu et al. [8], which indicates great potential for 1-1 type ME compo-
sites in the field of eddy current sensing, space magnetic sensing and active magnetic lo-
calizing [8,62]. In 2018 Turutin et al. reported a new ME composite consisting of the y +
140° cut congruent lithium niobate piezoelectric plates with an antiparallel polarized
“head-to-head” bidomain structure and magnetostrictive material Metglas [48]. Based on
this 2-2 ME bimorph, the equivalent magnetic noise spectral density was only 92 fT/Hz1/2
and the directly measured resolution was found to be 200 fT at a bending resonance fre-
quency of 6862 Hz (see Figure 6d), but one should note that the bandwidth of resonant
ME sensors is normally below 1 kHz due to the high mechanical quality factor, which is a
major limitation facing practical engineering applications [8,48,63]. It should however be
noted that resonant ME sensors are greatly limited by the narrow bandwidth and specifi-
cally suited applications need to be considered.

Actuators 2021, 10, 109 9 of 23
Figure 6. (a) Magnetic field detection limit measurements at frequencies of f = 1 Hz and f = 77.5 kHz (resonance condition),
respectively [29]; (b)The measurement of LOD for MEMS ME sensor [47], (c) for 1-1 typed ME sensor [8] and (d) for a 2-2
ME bimorph [48].
3.3. DC Magnetic Sensor
DC or quasi-static magnetic sensors are promising for magnetic anomaly detection
uses, such as geomagnetic navigation, metal detection and magnetic medical diagnosis,
etc. Early in 2011, Gao et al. demonstrated the excellent detection ability for DC field using
2-1 ME composite [31]. As shown in Figures 7a,b, the magnetic resolution was found to
be 4 nT and 1 nT when driving the composite at non-resonant frequency and resonance
frequency, respectively [31]. In 2013, Nan et al. reported a self-biased 215 MHz magneto-
electric NEMS resonator consisting of an AlN/(FeGaB/Al2O3) multilayered heterostructure
(Figure 7c), for ultra-sensitive DC magnetic field detection [51]. A ultra-sensitive detection
level starting from 300 picoTesla was obtained experimentally (Figure 7d) [51]. The RF
NEMS magnetoelectric sensor is compact, power efficient and readily integrated with
CMOS technology, however, the measurement of the resonance frequency and the admit-
tance spectrum is not technologically convenient. Li et al. then further proposed to moni-
tor the reflected output voltage from the ME resonator directly [26]. The optimized detec-
tion sensitivity was determined as 2.8 Hz/nT for AlN/FeGaB resonator. An ultra-high fre-
quency (UHF) lock-in amplifier and a directional coupler were used to apply and test the
RF signal of this resonator. And the final limit of detection was measured to be around 0.8
nT.

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Figure 7. The measurement of LoD for Metglas/PMN–PT ME laminate at (a) f = 10 kHz and (b) resonance frequency of
27.778 kHz [31]. (c) Schematic representation and (d) the measurement of LoD for NMES AlN/(FeGaB/Al2O3) multilayered
heterostructure [51]; (e) Schematic representation of the conventional flux gate senor and the proposed ME flux gate sensor
[64]; (f) The measured results for DC magnetic field resolution [64].
Using the nonlinear resonance magnetoelectric effect in ME composites, Burdin et al.
fabricated a planar langatate-Metglas structure and employed the third harmonics of the
output signal to measure the DC magnetic field as low as 10 nT [65]. In addition, a broad
dynamic range from ~10 nT to about 0.4 mT was also successfully obtained using the non-
linear ME effect [66]. More recently, Chu et al. proposed a shuttle-shaped, non-biased
magnetoelectric flux gate sensor (MEFGS) for DC magnetic field sensing enlightened by
the design of conventional flux gate sensor [64]. Figure 7e shows both the schematic of
typical flux gate senor and the proposed magnetoelectric flux gate sensor. The flux gate
sensor based on Faraday’s Law of Induction is composed of a racetrack type magnetic
core surrounded by an excitation (first) coil and a detection (second) coil. With respect to
MEFGS, a similar differential structure, which can produce a longitudinal-bending vibra-
tion when applying a DC field, can reject in-phase vibration noise and enhance the out-
of-phase ME voltage signal simultaneously [54]. We note here that in [54] the authors
found that a ME flux gate sensor excited under a non-resonant high frequency field could
perform better detection ability. As shown in Figure 7f, the relative change of the ME volt-
age output signal in response to a LOD of 1 nT is around 0.2% and the output signal can
return to the reference level during the repeated test cycles when choosing a non-resonant
frequency of 48.5 kHz [64].
Performance summary of some typical magnetoelectric sensors was given in Table 2.
Table 3 further compares the LoD of passive ME sensors with some commercially availa-
ble magnetometers, i.e., magnetoresistive sensors, giant magneto-impedance sensors,
fluxgate sensors, optically pumped magnetometers and SQUID magnetometers. As it can
be seen in Table 3, ME sensor shows comparable and competitive performance with these
products. Specifically, the low power consumption and high detection ability are signifi-
cant advantages for ME sensors, while vibration interference still now greatly limits the
engineering applications. On the other hand, piezoelectric materials are normally suscep-
tible to the working temperature and the temperature stability of ME sensors is also a
critical issue. For example, Burdin et al. compared the temperature dependence of the res-
onant magnetoelectric effect in several kinds of ME composites and showed that the
widely studied PZT-Metglas ME sensor can only work in a narrow temperature range of
0 °C to +50 °C [67].

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Table 2. Performance summary of typical magnetoelectric sensors.
Composition Working Mode Sensing Mode

Low-frequency mag-
netic field sensing
Metglas/Mn-PMNT [55] Longitudinal vibration (Multi-L-
T) Passive sensing 0.87 pT/
√Hz
@ 30 Hz
Metglas/PMN-PT [33] Longitudinal vibration (Multi-
push-pull) Passive sensing 5.1 pT/
√Hz
@ 1 Hz
Metglas/PMN-PZT [61] Longitudinal vibration (L-T) Active Modulation 33 pT/
√Hz
@ 0.1 Hz
Resonant magnetic
field sensing
Metglas/ LiNbO3 [48] bending mode Direct Sensing 92 fT/√Hz
FeCoSiB/(Pt)/AlN [47] bending mode Direct Sensing 400 fT/√Hz
Metglas/PMN-PZT [8] Longitudinal vibration (L-T) Direct Sensing 123 fT/√Hz
DC magnetic field
sensing
langatate-Metglas [65] bending mode Nonlinear ME effect 10 nT
Metglas/PMN-PZT [9] Longitudinal vibration (L-T) Linear ME effect 1 nT
FeCoSiB/(Pt)/AlN [26] Lateral vibration Delta-E effect 0.8 nT
FeCoSiB/(Pt)/AlN [51] Lateral vibration Delta-E effect 0.4 nT
Table 3. Performance Comparison with commercially available magnetometer for 1 Hz magnetic field sensing.
Magnetometer Working
Temperature
Power
Consumption (mW)
Typical Size
@
(pT/
√
) Limitations
ME sensor [33] 0 °C to +50 °C  <1 80 mm × 10 mm
@ ME composites 5.1 Vibration
interference
Magnetoresistive sensor
 −40 °C to +125 °C ~0.02 6 mm × 5 mm × 1.5 mm
@ sensing element 100 Low
sensitivity
Giant magneto-
impedance
sensor  −20 °C to +60 °C 75 35 mm × 11 mm × 4.6 mm
@ sensing element 15–25 Low
sensitivity
Fluxgate magnetometer 
−40 °C to +70 °C 350 ø100 mm × 125 mm
@ system size 2–6 Power
consumption
Optically pumped magne-
tometer  −35 °C to +50 °C >12,000 175 cm × 28 cm × 28 cm
@ system size 4 Complex setup
SQUID magnetometer [68]
<−196 °C >1000 12.5 mm× 12.5 mm
@ chip size <0.005 Cooling
 Estimated from the data in ref. [65];  Based on commercial product TMR9001 in MultiDimension Technology Co., Ltd.
(Zhangjiagang Free Trade Zone, Jiangsu Province, China);  Based on commercial product MI-CB-1DH in AICHI STEEL
CORPORATION (Tōkai city, Aichi Prefecture, Japan);  Based on commercial product Mag03 from Bartington Instru-
ments Ltd (Witney, Oxon, OX28 4GG United Kingdom).;  Based on commercial product G882 marine magnetometer
from GEOMETRICS, INC (San Jose, CA, USA).
4. Engineering Applications of ME Sensors
As we summarized in Tables 2 and 3, ME sensors show competitive performance
with commercial optically pumped magnetometers, giant magneto-impedance sensors
and fluxgate magnetometers. In this regard, a large number of works that utilize ME sen-
sors for magnetic field sensing have been published and various applications have been
implemented. In this section, we will overview current advances in sensing applications
of ME sensors.
4.1. .Magnetic Target Detection and Localization
A metallic material can be magnetized by the geomagnetic field along each of its three
orthogonal directions, which in turn generates three magnetic signature vectors. In 2012,
Shen et al. proposed a triple-axis magnetic anomaly detection system based on
Metglas/Pb(Zr,Ti)O3/Metglas ME sensors. To compare the performance of ME sensor with
widely used fluxgate sensor, they placed a tri-axial ME sensor, a tri-axial piezoelectric
sensor (PE) and a fluxgate sensor on the ground in a line with the same closest path ap-
proach (CPA) as shown in Figure 8a. The obtained signals are given in Figure 8b. It can be
seen there was little vibration or acoustic contribution to the tri-axial ME sensor at 2.5 s,
and the response amplitude of ME sensor was obviously higher than that of the fluxgate

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sensor [69]. Then, they also modeled the magnetic field of metallic objects as a magnetic
dipole and designed a ME sensor array to analyze the magnetic signature. The orientation
and velocity of target were presented in the form of a characteristic magnetic waveform,
which provided the basis for magnetic anomaly detection and identification [70].
Figure 8. (a) Photograph of the vehicle detection system setup; (b) sensor output signals in terms of the X (blue curve), Y
(red curve) and Z (green curve) component in the ME sensor (top), PE sensor (middle) and fluxgate sensor (bottom) [69].
With respect to magnetic object localization, Xu et al. constructed a magnetic gradient
meter consisting of eight measuring points using 2-1 type ME sensors to locate the mag-
netic source in a 3-D cube [71]. Their experimentally obtained data that successfully
yielded 3-D vector outputs representing the distribution of the magnetic flux lines of the
tested source placed in the center of the cube. Based on a 1-1 type ME sensor, Chu et al.
also proposed a 2-D magnetic positioning and sketching system consisting of a 1-D ME
sensor array as shown in Figure 9a. Experimental results concerning the positioning of an
iron ball with a diameter of 5 mm are given in Figure 9b. The localization error was
roughly estimated as 2.4 cm in a scanning area of 70 cm (in length) × 50 cm (in height). In
addition, the posture and the length-diameter ratio of a metal bar could be also success-
fully recognized via the system [72].
Figure 9. (a) Prototype of the measurement setup using 1-D ME sensor array and imaging system. (b) the positioning
result of an Fe-ball [72].

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4.2. Geomagnetic Field Sensing
When it comes to applications, e.g., vehicle detection, maritime navigation and aero-
nautical magnetic exploration, it is necessary to obtain the orientation of a DC (or AC)
magnetic field. In 2007, Zhai et al. measured the value of both the Earth’s magnetic field
and its inclination based on Metglas/piezoelectric-fiber ME laminates [73]. This ME sensor
was working under an active mode without any bias field and it was found that DC mag-
netic field variations of less than 10−9 T and angular inclinations of less than 10−5 deg can
be detected. The voltage output measured when the ME sensor was rotated in the Earth’s
plane is shown in Figure 10. It could be clearly seen that the maximum voltage output
could reach −100 mV when the sensitive direction of the ME sensor was oriented along
the geomagnetic field in the Earth’s plane, but when the sensor was oriented along the
east and west directions in this plane, its output was essentially 0 mV, implying a high
single-axis directivity and the potential application in geomagnetic navigation.
In 2013, Duc et al. presented an integrated two-dimensional geomagnetic device
which consisted of two one-dimensional magnetoelectric sensors arranged in an orthogo-
nal direction. They also finished the circuit design and hardware implementation (Figure
10b). The obtained accuracy of angle measurement reached as low as ±0.5° (Figure 10c)
and the spatial angles can be automatically computed while rotating the sensor module
[74].
Figure 10. (a)Output voltage from the magnetoelectric sensor when it is rotated in the Earth’s plane [73]. (b) Photograph
of the experimental rotation system and (c) the accuracy measurement of spatial angles [74].
In 2018, Pourhosseini et al. presented a multi-terminal hexagonal-framed magnetoe-
lectric composite (HFMEC) to realize the same goal as mentioned above. The hexagonal-
framed ME composite (HFMEC) was fabricated by using three thickness poled [011]-ori-
ented PMN-PT single crystal fibers (Pb(Mg1/3Nb2/3)O3-PbTiO3) sandwiched between two
hexagonal-framed FeBSi alloys (Metglas).
Figure 11. (a) The structure of the HFMEC. (b) ME coupling response of the HFMEC as a function of the DC magnetic-
field, the signal exhibits a “V” shape and the knee point of the curve reveals the geomagnetic field [75].

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According to the threefold symmetric ME voltage responses of the HFMEC, a valid
formula for calculating the angular direction of the magnetic field was given and a high
angular resolution of about 0.1° was experimentally verified. In addition, the obtained
“V” shape as shown in Figure 11b in the output signal could also be used to determine the
absolute geomagnetic field intensity [75].
4.3. Current Sensing and Non-Destructive Detection
With respect to power grids and chips monitoring and protection, current detection
is urgently needed. Based on Ampere’s law, non-contact measurement is usually achieved
by magnetic sensors, such as current transformers (CTs), Hall devices, SQUIDs, and mag-
netoresistance elements. However, CTs and Hall devices are limited by low sensitivity
and narrow dynamic range; SQUIDs must work at extremely low temperatures and the
inherent 1/f noise also restricts the magnetoresistance elements’ sensitivity [76]. In this
case, researchers tried to achieve high-sensitivity current detection by using ME sensors.
For example, Dong et al. first proposed a ME current sensor based on a ring-type ME
composite consisting of a Pb(Zr,Ti)O3 core laminated between two Terfenol-D layers and
operated in a circumferentially magnetized and circumferentially polarized mode, which
featured a stable frequency response ranging from 0.5 Hz to 2 kHz [77]. However, it was
difficult to apply the magnetic bias along its easily magnetized axes with respect to a ring
type Terfenol-D and it was highly desired to design a self-biased ME current sensor. Then
Zhang et al. further proposed to construct a Fe73.5Cu1Nb3Si13.5B9 air-gapped high-permea-
bility flux concentrator to enhanced the ME response of SmFe2/PZT/SmFe2 self-biased
magnetoelectric (ME) laminate as shown in Figure 12a. In Figure 12b, they compared the
detection ability at 119.75 kHz (resonance) and 1kHz (off-resonance), respectively. A lin-
ear output response was obtained for both cases, and the output sensitivity measured at
resonance was roughly one order of magnitude higher [78].
Oil and natural gas pipelines are normally buried underground or distributed under
the sea, and are thus susceptible to corrosion and pressure damage. The eddy current test-
ing (ECT) technology is widely to monitor the working status of those pipelines [79]. In
2021, Chu et al. constructed an ECT probe, by integrating the exciting coil and a 1-1 type
ME sensor. During the experiment, they set the lift-off distance to 3 mm. Figure 12a shows
the measurement result for an aluminum pipeline with a 10 × 1 × 1 mm3 crack placed in
the center. The scanning signal displayed an obvious response to this crack. In order to
further compare the crack detection and localization performance, authors also separately
tested an aluminum pipeline and a steel pipeline both with a one-dimensionally distrib-
uted cracks labelled 1# and 2#, respectively. Specific response to different cracks was ob-
viously obtained and the location was also identified for both two cases as shown in Fig-
ure 12d. It should be noted here the power consumption of ME ECT probe was only 0.625
μW, which represents a 2–3 orders of magnitude improvement compared with magneto-
resistive (MR) sensors and represented a crucial step towards online low-power monitor-
ing of pipeline cracks [80].

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Figure 12. (a) Schematic and photograph of the current-sensing device; (b) Comparison of the sen-
sitivities measured at low frequency and resonant frequency [78]. (c) Measured ME voltage re-
sponse with respect to an aluminum pipe with a 10 mm crack in the center (the inset highlighted
by dashed line showed the structure of the ME ECT probe). (d) Crack identifying results for one-
dimensionally distributed cracks labelled 1# and 2# for an aluminum pipeline and steel pipeline,
respectively [80].
4.4. Velocity and Displacement Sensing
It is of great significance to monitor the position and speed of crankshafts in the field
of industrial automation. In 2018, Wu et al. fabricated an angle speed sensor based on a
ME sensor, which consisted of four PZT/FeGa/PZT magnetoelectric (ME) laminate com-
posites, a closed magnetic circuit composed by a magnetic accumulation (MA) ring and
four magnetic accumulation arcs with magnetostrictive layer embedded into the U-
shaped slots, a multi-polar magnetic ring (MPMR), and a holder composed of a shaft and
shells as shown in Figure 13a. The rotating shaft drove the MPMR, which applied alter-
nating magnetic field to ME sensor. As the speed enlarged, the output voltage increased
at first, and then reached to stable values, as shown in Figure 13b. In addition, the meas-
ured frequency of the generated alternating magnetic field presented a linear response as
a function of the rotation speed, as given in Figure 13c. The authors accordingly concluded
the sensor could distinguish a small step-change rotational angle of 0.2° under a rotational
speed of 120 r/min [81].
In 2021, Lu et al. found that during the rotation of the gear, the change of the perme-
ability between the tooth and the air will disturb the magnetic field produced by the mag-
net, which can be used to measure the rotational speed of gear as well. The proposed
system was composed of a ME sensor, a gear and a permanent magnet, as shown in Figure
13d, When the gear was rotating, the convex and concave teeth of the gear alternately
passed, which generated alternating magnetic flux density. As shown in Figure 13e, the
spatial magnetic field varied as the gear rotation angle changed. When the convex tooth
was parallel to the permanent magnet, high permeability of gear led to large magnetic
field at the position of ME sensor. On the contrary, the low permeability of air led to a
small magnetic field. Then, they determined the best distance of three parts of the system
in Figure 13d, and obtained the curve of measured speed (Gs) as a function of setting speed
(Sset), as shown in Figure 13f [82].

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Micro-displacement sensing is crucial for precise positioning applications, including
micro-manufacturing and biological engineering. Without the obstruction of fringe effects
occurred in capacitive sensors, and the limitations of complicated optical components re-
quired in optical sensors, the ME effect was recently proposed for micro displacement
measurement. In 2021, Yang et al. fabricated a ME sensor based on Terfenol-D/PZT com-
posites [83]. The change of displacement led to the change of air gap (δ(d)), which brought
variation to the magnetic field applied to Terfenol-D by the permanent magnet and thus
enabled an ME voltage output. Then, they investigated the dynamic displacement ampli-
tude and static position measurement performance of the prototype. The ME sensor
achieved its highest sensitivity in the case of resonant excitation and the measured dis-
placement resolution was less than 13.27 nm, which was comparable to and competitive
with commercial laser displacement sensors [83]. A magnetic proximity sensor was also
recently proposed by Pereira et al. based on the ME effect [84].
Figure 13. (a) Schematic view of the packaged sensor; (b) The peak-to-peak values under different rotational speed; (c)
The frequency of the output signal as a function of the rotational speed [81]. (d) Schematic layout of the gear, permanent
magnet and FeCoSiB/Pb(Zr,Ti)O3 sensor; (e) The magnetic flux density with the gear rotates one circle (f) the measurement
speed (Gs) under different rotational speed [82].
4.5. Stress and Strain Measurement
Strain measurement is essential for various applications, such as structural health
monitoring and medical diagnosis. Steel cables are widely used in bridges, ships, mining
and other engineering fields. It is very important to ensure the stress and structure integ-
rity of steel cable. However, the real-time stress monitoring of steel cables is still a difficult
problem. In 2014, Zhang et al. proposed an elasto-magneto-electric (EME) sensor based
on the elasto-magnetic (EM) and magneto-electric (ME) effect, which has advantages of
high sensitivity, fast response, and ease of installation compared with conventional detec-
tion devices [85]. With an exciting coil around the cable, the magnetic field generated by
the current would magnetize the cable and the surrounding area. The stress on the cable
would then change the magnetization strength of the cable, which led to the variation of
the secondary field induced by the cable as shown in Figure 14a. Figure 14b shows their
experimental results, where f was the load value under high stress as measured by the
load cell, and XEME was the normalized result of the signal output of the EME sensor. It
can be seen that a good linear relationship between the stress and the output signal was
obtained [85].

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In 2020, Chen et al. fabricated a strain sensor based on ME heterostructures, the meas-
urement setup of which was shown in Figure 15a [86]. The frequency shift of ferromag-
netic resonance occurred in NiCo film by applying an elastic strain generated by piezoe-
lectric single crystal PMN-PT was employed to detect the substrate’s strain status. When
excited at 9.4 GHz, the resonant field Hr decreased from 956.65 Oe to 802.83 Oe with the
strain ε increased from 0 με to 700 με, indicating a resonant frequency shift of about 430.7
MHz, as shown in Figure 15b. Accordingly, the calculated strain sensitivity S = (∆f/f)/ε was
determined as 65.46 ppm/με [86]. Considering the resolution of FMR spectra, the limit of
detection of the wireless strain sensor was around 0.54 με, which was comparable with
that of commercial metal-foil sensors that needed connection wires [86].
Figure 14. (a)Structure of the EME sensor; (b) Stress response of EME sensors [85].
Figure 15. (a) the schematic of the EPR cavity and FMR measurement setup; (b) the negative correlation between Hr and
ε of the NiCo film with a static strain range of 0 με–700 με by linear fitting [86].
4.6. Biomagnetic Measurement
Contactless imaging or monitoring of biological entities by using the magnetic field
components of biological currents, has become an emerging field of magnetoelectric sen-
sors [87]. Room temperature working and stringent spatial resolution are typical require-
ments for biomagnetic measurement [88]. Furthermore, the magnetic signals emanating
freely from humans are of very low amplitude compared with the Earth’s magnetic field.
For instance, cardiac magnetic signals are on the order of 10~100 pT, whereas brain mag-
netic signals are typically one to two orders of magnitude lower [89]. Therefore, the mag-
netic detection device needs a super-high sensitivity and wide dynamic range. Figure 16
shows the intensity and frequency distribution of various magnetic signals in human body
and the typical limit of detection of some representative sensors [90]. Compared with
widely used a superconducting quantum interference device (SQUID) requiring liquid

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nitrogen cooling and optically pumped magnetometers (OPM) suffering from bandwidth
and scalability limitations, ME magnetic field sensors offer passive and thus low-power
detection, high sensitivity, compact structure and also a large dynamic range [91].
In 2016, Hao et al. designed a kind of biomagnetic liver susceptometry (BLS) instru-
ment for assessing the liver iron concentration (LIC) based on ME sensors, which can be
operated under room temperature and in an unshielded environment [88]. In 2020, Lukat
et al. further successfully localized and mapped superparamagnetic iron oxide nanopar-
ticles (SPIONs) with a technique based on ME sensors [92].
Figure 16. Amplitude densities of magnetic signals generated by various sources of the human body [90].
The structure of MSPM is shown in Figure 17a. A rotating plate holder generating
periodic signal was used to enable an easy acquirement of useful signals from the sample
and to remove the environment drift. The permanent magnet and electrically shielded ME
sensor were placed on two sides of the plate holder [92]. Compared with other methods,
this system circumvents the difficulty to separate the magnetic field generated by the sam-
ple under excitation and the magnetic field superposition of the excitation source in mag-
netic particle imaging (MPI) [93] and magnetic particle mapping (MPM) [94]. The mag-
netic signal originating from different concentrations of SPIONs was measured to deter-
mine the performance of the system. As shown in Figure 17b, the signal strength linearly
depended on concentrations of SPIONs and the limit of detectable iron content was about
20 μg. With respect to the spatial resolution, different samples can be well distinguished
in a smallest distance of 5 mm as shown in Figure 17c [92].

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Figure 17. (a) Setup for measuring distributions of SPIONs. (b) Maximum magnetic field amplitude for different iron
content measurements. (c) Place the sample in different grooves (top), the measured field distributions of the two sample,
and the red line in the field distribution shows the location of the grooves (middle), the particle distribution reconstructed
from these measurements (bottom) [92]. (d) Measurement setup of cardiological magnetic detection. (e) Averaged result
of the R-wave measurement [95].
Reermann et al. proved the statement that thin-film magnetoelectric sensors could be
used for heart magnetic measurements. They successfully measured the R-wave signals
from the heart of a volunteer in a shielded room as shown in Figure 17d, and the inset
highlights the layout of the ME sensor used. The sensor was placed at a distance of about
10 mm above the skin. The result of two times measurement was shown in Figure 17e.
After several-times average of the collected data, a specific peak corresponding to the R-
wave of a human heart was obviously observed [95].
5. Future Outlook
In this review article, we have introduced the advances in ME sensors and their en-
gineering applications. Here, we end with some perspectives that we suggest should be
addressed in the coming future. First, continued efforts should be made to further enhance
the ME coefficient for both thin-film and bulk ME composites by improving the interfacial
stress transfer, looking for better component materials and optimizing the structure pa-
rameters. Considering the specific application for weak magnetic field sensing, the noise
contribution in ME composites should be emphasized as well. Secondly, the realization of
quasi-static and DC magnetic sensing with satisfactory sensitivity based on ME compo-
sites remains a big challenge. Compared with widely studied passive ME sensors, active
ones could be one possible scheme to address this problem. In this case, studies about the
packaging technology to keep a low damping and the corresponding circuit design should
be a priority. In addition, methods to eliminate the high influence from environment vi-
bration should be also considered in a bid to realize engineering applications of ME sen-
sors in relatively complex environment. Finally, we appeal to the industrial community
to get involved in the development of ME sensors for the applications discussed in this
article. Besides the LoD, other critical parameters as mentioned at the beginning of Section
3 should be studied as well. For example, efforts could be made to further improve the

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temperature stability, to enlarge the dynamic range and to guarantee the final linearity of
a ME sensor. This may create new dimensions for ME community and facilitate the indus-
trialization of ME products.
Author Contributions: Conceptualization, Z.C., J.G.; writing—original draft preparation, J.G., Z.J.;
writing—review and editing, Z.C., Y.S.; visualization, Z.J., Z.C.; supervision, S.Z., Y.S.; funding ac-
quisition, Z.C., Z.M. All authors have read and agreed to the published version of the manuscript.
Funding: This research work was funded by Fundamental scientific research business expenses of
central universities (3072021CFJ0501).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data presented in this study are available on request from the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the
design of the study; in the collection, analyses, or interpretation of data; in the writing of the manu-
script, and in the decision to publish the results.
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