A differential magnetoelectric heterostructure: Internal noise reduction and external noise cancellation

Multiferroics represent an appealing class of multifunctional materials that simultaneously exhibit several ferroic orders, such as ferroelectricity and (anti-) ferromagnetism.^1,2 The coexistence of these order parameters brings about novel physical phenomena and offers possibilities for new device functions.² Of particular interest is the existence of a cross-coupling between the magnetic and electric orders, termed the magnetoelectric (ME) effect.^2–4 This coupling enables the control of the ferroelectric polarization by a magnetic field, and conversely the manipulation of the magnetization by an electric field.⁵ This phenomenon offers promising applications: magnetic field sensors that could replace low-temperature superconducting quantum interference devices (SQUID), and electric-write magnetic-read memory devices that combine the best of ferroelectric and magnetic random-access memories.⁶ Even though over ten different compound families have been widely investigated as multiferroic ME materials such as the well-known BiFeO₃ and rare earth magnanates,^7–9 a single-phase material has not yet been reported that demonstrates a technology capability as a viable memory device.^5,10 For the sensor applications, the difficulties of coupling electric and magnetic orderings in a single phase have been circumvented by forming multi-phase multiferroic composites of piezoelectric and magnetostrictive components that can be electromagnetically coupled by stress mediation.¹⁰ In such composites, the ME effect is known as a product tensor property, as first proposed by van Suchtelen in 1972.¹¹ Product tensors are the result of the magnetostrictive effect (magneto-mechanical effect) in a ferromagnetic phase and the piezoelectric effect (mechano-electrical effect) in a ferroelectric on each other.⁵ In the past few years, multi-phase ME composites have received tremendous attention.¹² Various composites with different phase connection distribution (e.g., 0–3 type particle, 2–2 type laminate, and 2–1 or 3–1 type fiber composites) and with different material components have been reported.^5,7,13–16 A significant breakthrough was the report of the multi-push-pull mode, which comprised magnetostrictive Metglas alloys and piezoelectric Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT) single crystal fibers with interdigitated-electrodes.¹⁷ A giant ME coefficient α_E of 52 V/cm Oe and an extremely low equivalent magnetic noise of 5.1 pT/√Hz at 1 Hz were found in Metglas/PMN-PT sensors at low frequencies.^12,17

Magnetic sensors have assisted humans in analyzing and controlling a wide range of functions for many decades. Presently, the commercial market is dominated by widely used instruments, such as search coils, flux-gate magnetometers, SQUID, optical pumping, Hall-effect, magneto-resistance, and giant magneto-impedance effect based magnetometers.¹² Recently, magnetic sensor technology has experienced a number of exciting advantages, including engineering methods of sensor arrays^18,19 and magnetic flux concentration,^20,21 and new families of chip scale atomic,²² magnetic tunnel junctions,²³ giant magneto-resistance,²⁴ and ME magnetometers. Compared with the other magnetometers, the ME sensor has notable advantages of low cost, small size, high sensitivity, low power consumption, and room temperature operation, or at least trade-off spaces between them. However, with regards to applications of ME sensors in real-world environments, due to the piezoelectric component in ME composites, difficulties of magnetic field sensitivity enhancements are aggravated by contamination of the ME signals by external vibration noise sources,¹² which is the disadvantage and challenge of the ME detection with respect to the other magnetometers.

The approach to a solution has focused on several strategies, e.g., (i) enhancement of the ME coefficient or gain; (ii) reduction of the noise power spectrum density including internal noises such as tan δ, DC resistance, and electrical circuit noise sources; and (iii) the cancellation of external noise sources such as vibration and thermal noises.¹⁷ The enhancement of the signal-to-noise ratio (SNR) is, perhaps, the most important developmental work for practical use of ME magnetic sensors, which requires both a maximum ME gain and rejection of noise.^12,25

In this paper, we present the realization of a significant equivalent magnetic noise reduction by simultaneously reducing the internal noise by sensor stacking in Metglas/piezofiber bimorph heterostructures and the cancelling of external noise by a mechanical-gradiometeric differential method. The proposed laminate structure had a unique piezoelectric core composite with two output terminals. This core consisted of five Pb(Zr,Ti)O₃ (PZT) fibers with ends symmetrically interrogated by two pairs of Kapton interdigitated (ID) electrodes (Kapton^®), and two N-layer longitudinally magnetized Metglas foils symmetrically crosswise stacked and bonded on top and bottom of a Kapton^® layer using epoxy resin to form a dual-terminal hybrid differentiated bending mode heterostructure, as shown in Figures 1(a) and 1(c). The working principle of this laminate design is based on the symmetric signal/asymmetric noise or asymmetric signal/symmetric noise method,^26,27 in response to an incident magnetic field and external noise sources (such as vibrational and thermal noises), as shown in Figure 1(b). The Metglas layers contract or elongate along the longitudinal directions under application of a magnetic field, resulting in flexural motions of the core composite, as illustrated in Figure 1(c). In turn, asymmetric ME signals V_ME,1 and V_ME,2 from the two terminals are generated as the polarizations P₁ and P₂ are reverse to each other [see Figure 1(a)]. The symmetric noise signals V_Noise,1 and V_Noise,2 also have contributions from the external noise sources: for example, uniform flexural motions of the core composite are induced by an applied external vibration (see Figure 1(d)). A serial combination of these two terminals results in a reduction of the internal noise signals (via noise charge density reduction) and an attenuation of the external noise signals based on the asymmetric signal/symmetric noise technique. Conversely, when P₁ and P₂ are equal, a parallel combination of the two terminals can also yield a reduction of the internal noise signals (via ME signal enhancement using a charge mode) and an attenuation of the external noise signals based on a symmetric signal/asymmetric noise technique. It is important to note that the here-proposed mechanical-gradiometeric differential heterostructure was based on a unique piezoelectric core with only different poling directions. This offers the potential to achieve higher external noise attenuations with respect to previously reported multiple piezoelectric core based differential ones,^26,27 since the external noises from the two differential terminals within one piezoelectric core probably have a nearly identical phase when suffered from a unique external noise source. Photographs of a dual-terminal Kapton^®/PZT-fiber core composite and a hybrid differentiated Metglas/Kapton^®/PZT-fiber sensor are shown in Figures 1(e) and 1(f), respectively.

After the hybrid differentiated heterostructure was fabricated, the capacitance C and the dielectric loss tan δ for terminal 1, terminal 2, and a series combination of both of the two terminals were measured (410 pF, 418 pF, and 230 pF; 0.012, 0.012, and 0.012), and the DC resistance R_dc for the various terminals was determined to be 62 GΩ, 60 GΩ, and 120 GΩ. These results indicate that the dominant internal noise can be reduced if terminals 1 and 2 are connected in series.^17,28

The voltage induced on terminal 1, terminal 2, and the series connection of these two terminals was measured using a lock-in amplifier as a function of DC magnetic bias (H_dc) and in response to a Helmholtz coil driven by an AC magnetic field of H_ac = 0.1 Oe at a frequency of f = 1 kHz. These measurements were performed on ME laminates with a hybrid differentiated Metglas/piezofiber heterostructure for various layers of Metglas, as shown in Figures 2(a)–2(c). Both dc and ac magnetic fields were applied along the length direction of the heterostructure. From these figures, it can be seen that the values of α_V for the laminate with different N were nearly zero for H_dc = 0; dramatically increased as H_dc was increased; reached a maximum at a particular H_dc; and subsequently decreased as H_dc was further increased. These trends of α_V vs H_dc reflect the fact that the ME coefficient is directly proportional to the piezomagnetic coefficient of the Metglas/piezofiber heterostructure.¹⁷ Figure 2(d) shows a summary of the data shown in Figures 2(a)–2(c) and shows the variation of the maximum values of α_V with N for corresponding terminals of the hybrid differentiated heterostructure. The ME charge coefficient α_Q is also presented in this figure: note that α_V was a derivative measurement determined from α_Q and the capacitance of the corresponding terminals. The values of α_V and α_Q did not significantly decrease after reaching a maximum with increasing N, as previously reported for sandwiched laminates.²⁹ An abnormal thickness fraction-dependent ME coefficient for bending mode ME laminates has been discussed elsewhere.³⁰ It can be seen that the ME coefficients were maximum for N = 5 for the various terminals, and that the value of α_V for terminals 1 and 2 in series connection was enhanced to 4.9 V Oe⁻¹ from 2.6 and 2.7 V Oe⁻¹ for the individual terminals. These results show the sum of the individual signals was ∼1.9 times higher than that of the individual signals. However, the values of α_Q were almost independent of connections.³¹ In Figure 2(c), we can see that the maximum values of α_Q were 1100, 1130, and 1120 pC Oe⁻¹ for individual terminals 1, 2, and both in a series connection for N = 5. It can been seen that the individual terminals exhibit similar ME and dielectric properties to that of regular, non-hybrid heterostructures.^32,33

To examine the working principle of the hybrid differentiated heterostructure, the time-domain waveform of the ME output voltage of terminals 1 and 2 in response to an incident H_ac = 0.1 Oe at f = 1 kHz is presented in Figure 2(e). It can be seen that the ME output signals from terminals 1 and 2 are nearly in-phase (i.e., symmetrical signals), resulting in an approximate doubling of the output signal upon summation under terminals 1 and 2 in a series connection (see Figure 2(d)). This also shows that the incident magnetic field results in a flexural deformation of the hybrid differentiated heterostructure, as shown in Figure 1(d).

Figure 3(a) shows the noise power spectral density (PSD) of a sensor unit based on terminal 1, terminal 2, and terminals 1 and 2 in a series connection in the absence of incident vibration sources and over a frequency range of 0.125 Hz < f < 100 Hz. The results reveal that the noise PSD of the sensor unit based on the terminals 1 and 2 in series connection was significantly lower than that based on individual terminals for f < 10 Hz, whereas the noise PSD of the various connections were nearly equal for f > 10 Hz. The equivalent magnetic noise spectra given in Figure 3(b) were obtained through a conversion of the corresponding noise PSD (see Figure 3(a)), gain factor of the charge amplifier (5.18 V/pC), and the ME charge coefficient^17,28 Equivalent $magnetic noise (T/Hz)=Noise PSD (V/Hz)5.18(V/pC)×αQ(pC/Oe)×104.$

This provides a mechanism to reduce the internal noise, since the sum signals from terminal 1 and 2 in series connection is notably reduced relative to the individual ones (see Figure 3(a)), while α_Q remains at a constant value (see Figure 2(d)). At f = 1 Hz, the equivalent magnetic noise for terminals 1 and 2 in a series connection was 15.3 pT Hz^−1/2, which was reduced by a factor of ∼1.4 relative to that of the individual terminals: note that this noise floor reduction is equivalent to that offered by sensor arrays in a serial mode.^31,32 The results clearly indicate that each of the individual terminals have similar equivalent magnetic noises compared to that of regular non-hybrid sensors, while the two terminals in series connection exhibit a × 1.4 lower value in the low frequency region (e.g., f = 1 Hz). In order to quantitatively understand the noise floor reduction of our hybrid differential heterostructure, a noise reduction factor was defined by the noise floor of the individual terminals relative to the terminals connected in series. Figure 3(c) presents the noise reduction factor of the hybrid differentiated heterostructure. In the frequency range A (0.3 Hz < f < 2 Hz), the noise reduction factor was about 1.4 because the noise floor in this range was dominated by the internal noise sources (i.e., tan δ and DC resistance),¹⁷ which can be elucidated from their 1/f characteristics. In the frequency range B (2 Hz < f < 6 Hz), the noise floor was dominated by the lab-generated incident vibration noise sources, since the noise floor decreased in proportional 1/f, except the broad peaks. Thus, a higher noise reduction factor was obtained in this range and exhibited a value of 4.5 at f = 3.5 Hz. Incident vibration noise cancellation of the hybrid differentiated sensor will be discussed in more detail in the following paragraphs. In the frequency range C (6 Hz < f < 100 Hz), the noise PSD was dominated by the lab-generated stochastic noise sources (i.e., the noise floor in this high-frequency range was even higher than that at low-frequency ones), and the noise reduction factor changed significantly and exhibited a value even less than 1 at some typical frequencies. These results indicate that the phase of vibration in the high frequency region C of terminals 1 and 2 varied erratically.

Next, the external vibration cancellation of the hybrid differentiated heterostructure was investigated. In these measurements, the heterostructure was symmetrically affixed on a shaker, as illustrated in Figure 4(a). The response of each individual terminal to 30 Hz, 50 Hz, and 100 Hz incident vibration sources, as well as the summation of the constituent signals, is presented in Figures 4(b)–4(d), respectively. Upon exposing the hybrid differentiated heterostructure to an incident vibration source, the amplitude of the combined vibration-induced signals (i.e., terminals #1 and #2 in series connection) were significantly attenuated relative to either of the two constituent signals (i.e., terminals #1 or #2). We found that the two individual vibration-induced signals were quite close to being reversed in-phase, as well as at the higher-order harmonics at 30 Hz. This supports our hypothesis that the incident vibration sources tend to excite the hybrid differentiated heterostructure in a uniform bending deformation (see Figure 1(d)), enabling cancellation of vibrational signals when terminals 1 and 2 are connected in series. From these figures, it can also be seen that the hybrid differentiated heterostructure exhibits a significant cancellation of the vibration noise at a wide frequency range from tens to hundreds of Hertz.

Finally, to more accurately analyze the external noise cancellation of the hybrid sensor, the noise PSD of individual terminals and their serial combination was measured under an external vibration at 10 Hz, via a shaker laid on top of the chamber. Figures 5(a) and 5(b) show the corresponding noise PSD and equivalent magnetic noise over the range of DC to 50 Hz. At the vibration drive frequency of 10 Hz and the higher-order harmonics (20, 30, 40, and 50 Hz), the amplitudes of both the noise PSD and equivalent magnetic noise for the serial combination were much lower than that of either individual terminal. Figure 5(c) shows the noise reduction factor as a function of frequency. A noise reduction factor of 11.1 at 10 Hz was observed, which varied from 9.0 to 9.9 at the second-, third-, fourth-, and fifth harmonics. These results indicate the current design of our hybrid differentiated heterostructure has a capability to reject the external vibration noise by a 10-fold attenuation factor.

In summary, we present a differential structural design for a Metglas/PZT-based ME laminate composite that has excellent ability for external vibrational noise cancellation and internal noise reduction. It works in a differential bending mode, which can generate symmetric signals and asymmetric noises. This structural design offers potential applications as a magnetic sensor in real environments, due to its capability to reduce internal and external noise sources.

This work was sponsored by the Office of Naval Research.