Magnetoelectric Vortex Magnetic Field Sensors Based on the Metglas/PZT Laminates

This paper describes the route, from simulations toward experiments, for optimizing the magnetoelectric (ME) geometries for vortex magnetic field sensors. The research is performed on the base of the Metglas/Piezoelectric (PZT) laminates in both open and closed magnetic circuit (OMC and CMC) geometries with different widths (W), lengths (L), and diameters (D). Among these geometries, the CMC laminates demonstrate advantages not only in their magnetic flux distribution, but also in their sensitivity and in their independence of the position of the vortex center. In addition, the ME voltage signal is found to be enhanced by increasing the magnetostrictive volume fraction. Optimal issues are incorporated to realize a CMC-based ME double sandwich current sensor in the ring shape with D × W = 6 mm × 1.5 mm and four layers of Metglas. At the resonant frequency of 174.4 kHz, this sensor exhibits the record sensitivity of 5.426 V/A as compared to variety of devices such as the CMC ME sensor family, fluxgate, magnetoresistive, and Hall-effect-based devices. It opens a potential to commercialize a new generation of ME-based current and (or) vortex magnetic sensors.


Introduction
In principle, a multiferroic device has been defined as a combination of two or more primary ferroic ordering phenomena in the same application, such as ferroelectric, ferromagnetic, and ferroelastic. Among its combinations, the ferroelectric-ferroelastic forms the basis of piezoelectric transducers, while the ferromagnetic-ferroelastic is used as piezomagnetic devices. The conventional term "multiferroic" is primarily applied to materials that combine ferroelectricity and ferromagnetism (or in general, magnetism). At present, multiferroics can function with more external stimuli and novel effects, among these, the direct magnetoelectric (ME) effect represents an electric polarization response to an applied magnetic field. This has been employed for technological applications including (AC and (or) DC) magnetic field sensors, transducers, filters, oscillators, phase shifters, transformers or gyrators for voltage gain devices, current sensors, other power conversion devices and electric field tunable microwave magnetic strip line devices. The information on these applications can easily be found in   Figure 3 vividly demonstrates a mechanical system for investigating the dependence of the ME effect in the fabricated samples on the vortex magnetic field strength and the center displacement. In the setup, the two straight electrical conductors/wires are placed inside the ME ring. Among these wires, one of which (with an AC current of 0.385 A supplied by the Lock-in amplifier 7265 (Ametek Scientific Instruments, Berwyn, PA, USA) to generate an AC magnetic field for the ME composite operation) is fixed at the ring center, while the vortex magnetic field is created by a DC current from the other wire supplied by the other 2400 Keithley source (Keithley Instruments, Cleveland, OH, USA). The position of the vortex center (or the DC current-carrying wire) can be precisely adjusted by using a linear mechanical mover (Rack and Pinion stage, Edmund Optics Inc., Barrington, NJ, USA). The ME voltage signal is finally measured by the same Lock-in amplifier.   Figure 3 vividly demonstrates a mechanical system for investigating the dependence of the ME effect in the fabricated samples on the vortex magnetic field strength and the center displacement. In the setup, the two straight electrical conductors/wires are placed inside the ME ring. Among these wires, one of which (with an AC current of 0.385 A supplied by the Lock-in amplifier 7265 (Ametek Scientific Instruments, Berwyn, PA, USA) to generate an AC magnetic field for the ME composite operation) is fixed at the ring center, while the vortex magnetic field is created by a DC current from the other wire supplied by the other 2400 Keithley source (Keithley Instruments, Cleveland, OH, USA). The position of the vortex center (or the DC current-carrying wire) can be precisely adjusted by using a linear mechanical mover (Rack and Pinion stage, Edmund Optics Inc., Barrington, NJ, USA). The ME voltage signal is finally measured by the same Lock-in amplifier.  Figure 3 vividly demonstrates a mechanical system for investigating the dependence of the ME effect in the fabricated samples on the vortex magnetic field strength and the center displacement. In the setup, the two straight electrical conductors/wires are placed inside the ME ring. Among these wires, one of which (with an AC current of 0.385 A supplied by the Lock-in amplifier 7265 (Ametek Scientific Instruments, Berwyn, PA, USA) to generate an AC magnetic field for the ME composite operation) is fixed at the ring center, while the vortex magnetic field is created by a DC current from the other wire supplied by the other 2400 Keithley source (Keithley Instruments, Cleveland, OH, USA). The position of the vortex center (or the DC current-carrying wire) can be precisely adjusted by using a linear mechanical mover (Rack and Pinion stage, Edmund Optics Inc., Barrington, NJ, USA). The ME voltage signal is finally measured by the same Lock-in amplifier.

ME Geometrics Simulation Design
Considerable efforts have been undertaken to elaborate on a phenomenological description of the magnetoelectric voltage coefficient Although results are still diverse in

ME Geometrics Simulation Design
Considerable efforts have been undertaken to elaborate on a phenomenological description of the magnetoelectric voltage coefficient (MEVC), α ME = dE/dH. Although results are still diverse in detail, the MEVC can be generally expressed on the basis of the product of the piezomagnetic and piezoelectric coefficients as follows: In this formula, λ represents the magnetostriction of the ferromagnetic phase and ∂λ/∂H is the so-called piezomagnetic coefficient (or magnetostrictive susceptibility χ λ ) of the material; ∂E ∂λ = χ p εε o is the piezoelectric coefficient (or piezoelectric susceptibility χ p ). Inserting these relations into Equation (1), one obtains: where k c is a coupling factor (0 ≤ k c ≤ 1), which is of the value between the two (magnetic and electric) phases [3,15]. Thus, the sensor MEVC is directly related to the field dependence of the magnetostriction constant χ λ . Indeed, the (force) magnetostriction is almost quadratically proportional to the magnetization M (and thus, the magnetic flux density or magnetic induction B) of the magnetic phase, i.e., λ~M 2 ) [21]. The ME-based sensor performance and MEVC can be therefore understood partly through the information of the magnetic flux distribution on the Metglas material.
The simulation of the magnetic flux distribution was carefully conducted using the finite element method Ansys Maxwell 3D (Version 16, USA). The measured B(H) data of Metglas (VSM model 731, Lakeshore Cryotronics, Inc., Westerville, OH, USA) were used as the input parameter in the Magnetostatic mode [22]. In the simulation, the maximum number of elements of 400,000 points and the accuracy of 0.05% were set. The effective magnetic flux taken over the Metglas volume was calculated by: . The wire carrying a current of 1 A is located at different (x,y) positions with respect to the sample center (x = 0, y = 0). Clearly, the magnetic flux is inhomogeneously distributed over the magnetostrictive layers for both OMC and CMC. However, the effective magnetic flux calculated over the whole sample volume exhibits different behaviors. While the B eff value of the I-type is strongly dependent on the location of electric wire, that of the O-type remains almost stable. Actually, the variation of the normalized value of B max eff − B min eff /B max eff is only~0.7% for the O-type (see the circle plate in Figure 4b). For the rectangular bar; however, this difference varies from 16.6% to 67.7% depending on the position of electric wire close to or far from the center along the xand y-directions, respectively (see the saddle horse-type bending in Figure 4b). In addition, B eff in the ring shape is about 1.5 times higher than the maximum value in the rectangular one. With regard to the current sensor designs, these issues indicate the advantages of the O-type not only for the sensitivity but also for the position independence. plate in Figure 4b). For the rectangular bar; however, this difference varies from 16.6% to 67.7% depending on the position of electric wire close to or far from the center along the x-and y-directions, respectively (see the saddle horse-type bending in Figure 4b). In addition, Beff in the ring shape is about 1.5 times higher than the maximum value in the rectangular one. With regard to the current sensor designs, these issues indicate the advantages of the O-type not only for the sensitivity but also for the position independence. The results from simulation of O-types with different diameters are compared in Figure 5. It can clearly be seen that Beff decreases with increasing D, as expected (Figure 5a,c). However, it is interesting to emphasize that as the ring diameter goes beyond the part of the linear magnetic field dependence of the effective magnetic induction Beff is extended further to higher applied currents. For example, in D = 7 mm structure, Beff decreases one-half as compared with the D = 3 mm one, but its linear response range extends to current values up to 4 A (Figure 5b). This is an important design factor to determine the sensor working range. The results from simulation of O-types with different diameters are compared in Figure 5. It can clearly be seen that B eff decreases with increasing D, as expected (Figure 5a,c). However, it is interesting to emphasize that as the ring diameter goes beyond the part of the linear magnetic field dependence of the effective magnetic induction B eff is extended further to higher applied currents. For example, in D = 7 mm structure, B eff decreases one-half as compared with the D = 3 mm one, but its linear response range extends to current values up to 4 A (Figure 5b). This is an important design factor to determine the sensor working range.
Sensors 2020, 20, x 6 of 12 In a simple thought, the magnetostrictive strain and consequently the ME effect could be improved by increasing the magnetostriction/PZT volume fraction. To clarify this idea from the point of view of the magnetic flux, the simulation is performed for the SS and DS structures consisting of 2 and 4 Metglas layers, respectively. This expectation, however, does not hold here. In comparison with the SS structure, the Beff value obtained in the DS structure is down to 61% in the I-type, whereas it remains almost the same in the O-type for both structures ( Figure 6). The lowered Beff observed for the I-type may be attributed to the demagnetizing field of adjacent magnetic layers. In a simple thought, the magnetostrictive strain and consequently the ME effect could be improved by increasing the magnetostriction/PZT volume fraction. To clarify this idea from the point of view of the magnetic flux, the simulation is performed for the SS and DS structures consisting of 2 and 4 Metglas layers, respectively. This expectation, however, does not hold here. In comparison with the SS structure, the B eff value obtained in the DS structure is down to 61% in the I-type, whereas it remains almost the same in the O-type for both structures ( Figure 6). The lowered B eff observed for the I-type may be attributed to the demagnetizing field of adjacent magnetic layers.
improved by increasing the magnetostriction/PZT volume fraction. To clarify this idea from the point of view of the magnetic flux, the simulation is performed for the SS and DS structures consisting of 2 and 4 Metglas layers, respectively. This expectation, however, does not hold here. In comparison with the SS structure, the Beff value obtained in the DS structure is down to 61% in the I-type, whereas it remains almost the same in the O-type for both structures (Figure 6). The lowered Beff observed for the I-type may be attributed to the demagnetizing field of adjacent magnetic layers. .

Experimental Implementation
The dependence of the ME voltage signal on the AC magnetic-field frequency measured at a fixed DC current of 1 A is presented in Figure 7a for the investigated SS ME samples of different diameters, in whichthe resonance behavior is well observed. In addition, the results show that with increasing diameter, the resonance is shifted towards lower frequencies (fr), whereas the corresponding ME voltage signal significantly decreases. The reduction of the resonance signal seems to agree with the decrease of Beff in the Meglas laminates as already mentioned in Figure 5c (see also Figure 7b). The variation of the observed resonant frequency (fr) can be described by the radiant resonant mode [23]: 11 1 1

Experimental Implementation
The dependence of the ME voltage signal on the AC magnetic-field frequency measured at a fixed DC current of 1 A is presented in Figure 7a for the investigated SS ME samples of different diameters, in whichthe resonance behavior is well observed. In addition, the results show that with increasing diameter, the resonance is shifted towards lower frequencies (f r ), whereas the corresponding ME voltage signal significantly decreases. The reduction of the resonance signal seems to agree with the decrease of B eff in the Meglas laminates as already mentioned in Figure 5c (see also Figure 7b). The variation of the observed resonant frequency (f r ) can be described by the radiant resonant mode [23]: where ρ is the average mass density calculated from Metglas and PZT and S 11 is the equivalent elastic compliance. Both quantities are calculated from the mass density, elastic constant and volume fraction of Metglas (ρ m , s m 11 , v m ) and PZT (ρ p , s p 11 , v p ) by the following equations [24,25]: The experimental data are well fitted (see Figure 7b The experimental data are well fitted (see Figure 7b  For the DS ME O-type laminates, as illustrated in Figure 8a, the resonance frequency is about 5% lower than the SS ones of the corresponding diameters. The resonant voltage signal, however, is strongly enhanced. Indeed, going from SS to DS, the voltage response is nearly doubled (from 53.09 to 90.18 mV and 31.64 to 59.27 mV) for the samples of D = 10 and 14 mm, respectively (see in Table 1). In this case, it seems to agree with the contribution of the enhanced magnetostrictive volume fraction. As discussed in Figure 6, for the DS O-type, the effective magnetic induction Beff in the Metglas layer is For the DS ME O-type laminates, as illustrated in Figure 8a, the resonance frequency is about 5% lower than the SS ones of the corresponding diameters. The resonant voltage signal, however, Sensors 2020, 20, 2810 7 of 11 is strongly enhanced. Indeed, going from SS to DS, the voltage response is nearly doubled (from 53.09 to 90.18 mV and 31.64 to 59.27 mV) for the samples of D = 10 and 14 mm, respectively (see in Table 1). In this case, it seems to agree with the contribution of the enhanced magnetostrictive volume fraction. As discussed in Figure 6, for the DS O-type, the effective magnetic induction B eff in the Metglas layer is almost similar to that of the SS one. Here, the unique difference is that the Metglas/PZT volume fraction is twice enhanced, which leads to the observed enhancement of the resonant signal. This argument is also supported by the experimental data performed for the ME rectangular forms. For the DS ME O-type laminates, as illustrated in Figure 8a, the resonance frequency is about 5% lower than the SS ones of the corresponding diameters. The resonant voltage signal, however, is strongly enhanced. Indeed, going from SS to DS, the voltage response is nearly doubled (from 53.09 to 90.18 mV and 31.64 to 59.27 mV) for the samples of D = 10 and 14 mm, respectively (see in Table 1). In this case, it seems to agree with the contribution of the enhanced magnetostrictive volume fraction. As discussed in Figure 6, for the DS O-type, the effective magnetic induction Beff in the Metglas layer is almost similar to that of the SS one. Here, the unique difference is that the Metglas/PZT volume fraction is twice enhanced, which leads to the observed enhancement of the resonant signal. This argument is also supported by the experimental data performed for the ME rectangular forms. Practically, the frequency dependence of the ME response is presented in Figure 8b for the SS and DS I-type ME laminites with L × W = 15 mm × 1.5 mm. Clearly, there is a rather small modification  Practically, the frequency dependence of the ME response is presented in Figure 8b for the SS and DS I-type ME laminites with L × W = 15 mm × 1.5 mm. Clearly, there is a rather small modification between these two resonant lines: the resonant frequency and the signal at resonance are slightly shifted from 103 kHz to 108 kHz and from 2.45 mV to 2.24 mV for SS and DS structures, respectively (see also Table 1). For rectangular ME laminates, the resonant frequency was reported to be dependent on the sample length only (f 10 = v/2L) [16]. The stability of the observed resonant voltage can be attributed to the combination of the decrease of B eff ( Figure 6) and the increase of the magnetostrictive volume fraction in the DS sample. Thus, the simulation of the magnetic flux density is useful to comprehend the experimental results and offers helpful information to design CMC for enhanced sensitive current sensors.
The investigation of the effect of the relative position of the vortex center on the output voltage ME is also carried out. As can be seen from Figure 9, the experimental investigation confirms appropriately the simulation shown in Figure 2c. For the SS O-type (Figure 9a), the signal is perfectly independent on the vortex center position (with an error less than 1%). This error is comparable with that of the integration of six sensors array developed by A. Itzke et al. [27] and Z. Li et al. [28]. For the SS I-type sample (Figure 9b), a huge deviation by about 300% is obtained when moving the vortex center 5 mm along the sample length direction.

Current Sensor Realization
As regards the high sensitivity, sensors are realized with 6 mm diameter for the SS and DS O-types. The fabrication process is illustrated in Figure 10 for the SS one. The ME ring, after laminating, was packaged in a protective plastic cover (Figure 10a) and the coil was later wrapped around for generating the AC excited magnetic fields (Figure 10b). The sensor was mounted on a PCB for testing (Figure 10c).

Current Sensor Realization
As regards the high sensitivity, sensors are realized with 6 mm diameter for the SS and DS O-types. The fabrication process is illustrated in Figure 10 for the SS one. The ME ring, after laminating, was packaged in a protective plastic cover (Figure 10a) and the coil was later wrapped around for generating the AC excited magnetic fields (Figure 10b). The sensor was mounted on a PCB for testing (Figure 10c). In the resonant mode, the obtained V-I characteristics of the fabricated sensor are presented in Figure 11a for the SS and DS O-type ME-based sensors. Due to the limitation of the Lock-in amplifier 7265, the investigation is limited up to the output voltage of 0.375 V. The output voltage signal of DS O-type ME-based sensors responses to an extremely weak step-varying current of 10 μA is illustrated in Figure 11b. As can be seen from Figure 11a, the obtained sensor signal exhibits an almost linear behavior in the investigated current range. Sensitivities as high as 2.940 V/A and 5.426 V/A are achieved for the sensors based on the SS and DS O-types, respectively. In fact, the effect of the enhanced magnetostrictive volume fraction in improving the ME sensor sensitivity is worked out. This sensitivity is several tens of times higher than the present record of the ME ring-shape-based current sensors reported for a Terfenol/PZT laminate [29] and for a PZT/NiCoZnO-ferrite trilayer disk [11]. In particular, it is three orders higher than the value of 2.38 mV/A obtained from the ME current sensor using a Terfenol-D/PZT laminate disk inserted into the air gap of a C-shaped ferrite magnetic concentrator [30]. In addition, this sensitivity is one and two orders higher compared to the fluxgate-based sensors [31] and to the sensors based on magnetoresistance [32,33] and Hall effect [34], respectively. The achievable resolution of microampe is several orders of magnitude finer than that of commercial integrated fluxgate current sensors [35]. High sensitivity, low positional dependence error, high temperature stability at room temperature [36][37][38], simple and low-cost production make this CMC ME composite a promising candidate in practical current sensor applications. In the resonant mode, the obtained V-I characteristics of the fabricated sensor are presented in Figure 11a for the SS and DS O-type ME-based sensors. Due to the limitation of the Lock-in amplifier 7265, the investigation is limited up to the output voltage of 0.375 V. The output voltage signal of DS O-type ME-based sensors responses to an extremely weak step-varying current of 10 µA is illustrated in Figure 11b. As can be seen from Figure 11a, the obtained sensor signal exhibits an almost linear behavior in the investigated current range. Sensitivities as high as 2.940 V/A and 5.426 V/A are achieved for the sensors based on the SS and DS O-types, respectively. In fact, the effect of the enhanced magnetostrictive volume fraction in improving the ME sensor sensitivity is worked out. This sensitivity is several tens of times higher than the present record of the ME ring-shape-based current sensors reported for a Terfenol/PZT laminate [29] and for a PZT/NiCoZnO-ferrite trilayer disk [11]. In particular, it is three orders higher than the value of 2.38 mV/A obtained from the ME current sensor using a Terfenol-D/PZT laminate disk inserted into the air gap of a C-shaped ferrite magnetic concentrator [30]. In addition, this sensitivity is one and two orders higher compared to the fluxgate-based sensors [31] and to the sensors based on magnetoresistance [32,33] and Hall effect [34], respectively. The achievable resolution of microampe is several orders of magnitude finer than that of commercial integrated fluxgate current sensors [35]. High sensitivity, low positional dependence error, high temperature stability at room temperature [36][37][38], simple and low-cost production make this CMC ME composite a promising candidate in practical current sensor applications.
fluxgate-based sensors [31] and to the sensors based on magnetoresistance [32,33] and Hall effect [34], respectively. The achievable resolution of microampe is several orders of magnitude finer than that of commercial integrated fluxgate current sensors [35]. High sensitivity, low positional dependence error, high temperature stability at room temperature [36][37][38], simple and low-cost production make this CMC ME composite a promising candidate in practical current sensor applications. This signal processing is performed using the commercial Lock-in amplifier. A current sensor device, however, can be completed thanks to the integration with a home-made digital lock-in amplifier architecture already reported before [39]. The progress will be presented elsewhere. This signal processing is performed using the commercial Lock-in amplifier. A current sensor device, however, can be completed thanks to the integration with a home-made digital lock-in amplifier architecture already reported before [39]. The progress will be presented elsewhere.

Conclusions
A CMC-based current sensor with a record sensitivity of 5.426 V/A with a position-dependent error less than 1% has been designed and manufactured by using magnetic field sensors Metglas/PZT laminates in the ring shape. The innovative achievement is reached thanks to both the optimizing information from the magnetic flux simulation and the enhancement of the magnetostrictive volume fraction. In addition, manufacturing technologies help to realize the mechanical options. With respect to the OMC-based current sensors, the CMC-based sensors demonstrate advantages not only in the sensitivity, but also in the measuring accuracy. It opens a potential to commercialize a new generation of the ME-based current and/or vortex magnetic sensors.