Self-Biased Magnetoelectric Composites: An Overview and Future Perspectives

Magnetization-Graded ME-Laminates

As discussed in the previous section there are several ways to improve the magnetoelectric response of a composite. Out of these various approaches, the selection of high performance materials for improving the ME response has been the primary focus in most of the studies. The ferroelectric and ferromagnetic materials used in ME composites exhibit a symmetric hysteresis loop such as in polarization versus applied electric field (P-E) or magnetization versus applied magnetic field (M-H) measurements. A product property is then obtained in the form of polarization variation under an applied magnetic field (P-H) or conversely a magnetization variation under an applied electric field (M-E).

Recently, investigations on compositionally graded ferroelectrics have demonstrated hysteresis loop translation along the polarization axis due to the gradient polarization induced internal potential (Schubring et al. 1992; Ban, Alpay, and Mantese 2003). Figure 6 shows a schematic of the three separate cases for the creation of internal potentials in semiconductor, ferroelectric and ferromagnetic materials systems (Mantese et al. 2005), namely functionally graded materials (FGM). Such structures have given rise to a new class of transcapacitive ferroelectric devices (Transpacitors) viewed to be the dielectric equivalent of semiconductor junction devices, having potential applications in infrared detection, actuation, and energy storage. The similar concept was extended to the graded ferromagnetic systems (Mantese et al. 2005; Sudakar et al. 2007). A compositionally-graded Ni-Zn ferrite (Mantese et al. 2005) or hexagonal ferrite (Sudakar et al. 2007), with a spatial variation in saturation magnetization, had an internal magnetostatic potential, namely built-in magnetic bias along the gradient direction. Magnetization-graded structures can also be realized by subjecting a homogeneous ferromagnetic material to either temperature or stress gradients. However, these extrinsic magnetization-graded constructs differ from their compositionally graded counterparts since the internal magnetic fields of the extrinsic devices vanish once the external stress or temperature gradients are relaxed or removed. In the study in Ref. 46 magnetization graded samples of nickel zinc ferrite was synthesized by obtaining a linear variation in the zinc concentration along the length of the sample, leading to a corresponding linear variation in M. The presence of a small “built-in” magnetic field H_int of 30–44 Oe aligned along the magnetization-gradient is revealed as a shift in the magnetic inflection point of the ferromagnetic resonance signal; the shift coming from an alignment of the external field either parallel or antiparallel to the internal field. Similarly, an internal field of same magnitude was measured by low-frequency AC susceptibility measurements in compositionally graded hexagonal ferrites (Sudakar et al. 2007). Further, considering the similarity of other ferroic system, one was able to provide a quantitative theoretical analysis readily expandable to other graded ferroic system with proper modifications. Thus, investigations on functionally graded ferroics offer opportunities for discovery of novel phenomena and devices.

Figure 6:

Internal potentials of semiconductors, ferroelectrics, and ferromagnetics created by gradients in charge density, polarization, and magnetization, respectively (Mantese et al. 2005).

Considering the unique properties of the above mentioned functionally graded materials, Petrov and Srinivasan et al. proposed a model for ME interactions in a functionally graded ferroelectric-ferromagnetic bilayer structure (Petrov and Srinivasan 2008). In their study, a model focused on a bilayer of graded nickel zinc ferrite (NZFO) and lead zirconate titanate (PZT) with grading axis perpendicular to its plane under both free-standing condition and clamped condition (bilayer on SrTiO₃ substrate) was presented. The theoretical calculations predicted an enhancement in ME coupling in the graded structure as compared to the homogenous bilayer in both low frequency and resonance frequency condition. The magnitude of ME coupling coefficient was further correlated with the grading strength and direction. The theory predicted an enhancement of 50-60% in the ME coefficient due to grading as compared to homogenous bilayers. This approach suggested a promising path for manipulating the ME coupling in a composite.

However, this idea did not attract much attention until 2010, when Mandal et al. experimentally demonstrated the compositionally graded NZFO in a bilayer ME composite with PZT (Mandal et al. 2010). The grading induced bending moment counteracted with the flexural deformation due to structural asymmetry strengthening the ME coupling significantly. These experimental results were comparable to the previous theoretical calculation (Petrov and Srinivasan 2008). Further, a strong ME coupling at zero-bias field (self-biasing) and a zero ME coupling at a certain bias (zero-crossing) were observed by replacing homogenous composition with graded ferrites, as shown in Figure 7 (Mandal et al. 2010). Considering the built-in bias arising from magnetization graded structure, the self-biased α_ME was explained by assuming a torque. This torque was considered to be generated from the interaction between the out-of-plane H_int and the applied in-plane AC magnetic field (H_ac). With the increase in the in-plane DC magnetic field (H_dc), the value of torque was found to decrease, shifting the net internal magnetic field towards the direction of H_dc. and finally vanishing (zero-crossing) when it is parallel to the H_dc.

Figure 7:

ME voltage coefficient (MEVC) as a function of DC magnetic field for trilayer PZT/NZFO/PZT composites with graded or homogenous NZFO (Mandal et al. 2010).

Keeping the magnetization-graded structure as basis, but in a more efficient and cost-effective experimental approach, Mandal and Sreenivasulu et al. further investigated a magnetostriction-stepped ferromagnetic layer consisting of Ni and Metglas with negative and positive magnetostriction, respectively (Mandal et al. 2011; Sreenivasulu et al. 2011). Interestingly, they demonstrated the appearance of built-in magnetization and the resultant zero-biased ME coupling by using the ferromagnetic biphase with stepped saturation magnetization instead of a compositionally graded magnetic phase. The self-biased ME coefficient has been found to be sensitive to the gradient direction and ferromagnetic layer thickness, as shown in Figure 8. In this work, gradient direction was considered as the direction of varying magnitude of q away from the PZT-ferrite interface. For positive grading, the magnitude of q should increase away from the interface and vice-versa. The physical mechanism behind this self-biased effect was further attributed to the induced torque rising from the interacted H_int and H_ac. Interestingly, a unique MEVC hysteresis loop (Figure 8) was observed in the static transverse magnetic field measurement of ME coefficient. This behavior was further attributed to the domain rearrangement arising due to the interaction of built-in magnetization under applied transverse DC magnetic field. Theoretical calculation of the self-biased ME properties for functionally-graded ferromagnetic/ferroelectric bilayer under low frequency and bending resonance was also provided in their study (Mandal et al. 2011; Sreenivasulu et al. 2011).

Figure 8:

Theoretical (line) and experimental (line+symbol) ME voltage coefficient (MEVC) vs H for (a) PZT-Ni-NZFO and (b) PZT-NZFO-Ni samples with NZFO ferrite-to-Ni thickness ratio R=1 (Laletin et al. 2012).

Further, in order to understand the unique hysteresis and self-biased ME response in ME composites with functionally graded ferroic phases, Laletin et al. provided a systematic study on the control of the hysteresis and remanent magnetoelectric coupling in functionally stepped NZFO/Ni-PZT layered composites (Laletin et al. 2012). Differences in ME response from the homogenous ME composites in α_ME vs H was attributed to variation of q with H_dc. Significant changes including a pronounced hysteresis with a large self-biased α_ME was observed and demonstrated to be sensitive with the grading direction and ferrite-to-Ni thickness ratio. A progressive (monotonous) enhancement in maximum α_ME occurred as the ferrite-to-Ni thickness ratio was increased in grading direction, as shown in Figure 9. In similar fashion, the peak value of α_ME with positive grading was found to be higher than that of negative one. What was more interesting in this study was the observation of unusual trend/shape of the hysteresis loop depending on magnetic layer sequence and thickness ratio (Figure 9). The loop was counterclockwise under low field region when the composite has positive grading (PZT-Ni-NZFO) while clockwise at higher field range with negative grading. In both condition, the loop was found to tilt toward the H axis with larger H_bias for the peak position of α_ME. These experimental results were found to be in good agreement with theoretical calculations. The origin of this unique hysteretic behavior was attributed to the grading induced built-in field at the interface and its strain redistribution (depending on sequence and thickness of magnetic layers).

Figure 9:

PZT-Ni-NZFO graded composites, results are for samples with ferrite-to-Ni thickness ratio R in the range of 0.5–2.5. (a) R=0.5, (b) R=1, (c) R=1.5, (d) R=2.5. The arrows indicate the direction of H variation (Laletin et al. 2012).

These interesting results inspired further research on functionally graded ME composites on the magnetostrictive-stepped structure. The effect of grading was further studied with various combinations of other ferromagnetic materials. Researchers have used Ni, SmFe₂ (Smfenol), NiFe₂O₄ (NFO) and Ni_0.7Zn_0.3Fe₂O₄ (NZFO) as negative piezomagnetic coefficient (q) phase and Metglas, Ni-Fe alloy, Permendur, Terfenol-D (TD), Fe-Co alloy, FeCuNbSiB (FCNSB) alloy as positive q phase. The main characteristics of the developed functional-ferromagnetic-graded ME composites are shown in Table 2 in order of composite configuration. In addition to the asymmetric piezoelectric/graded-ferromagnetic (P-M₁-M₂) laminates, piezoelectric layer laminated between two graded-ferromagnetic layers (M₂-M₁-P-M₁-M₂) in a symmetric configuration has also been studied. For comparison, homogenous ME composites with piezoelectric/ferromagnetic (P-M) and ferromagnetic/piezoelectric/ferromagnetic (M-P-M) configurations were also provided. Other structures like semicircular composite (Hong et al. 2013), piezoelectric cantilever with graded-ferromagnetic tip mass have also been reported (Zhang et al. 2013).

From the results provided in Table 2, several interesting factors can be noticed: (a) The ferromagnetic-graded laminates resulted in a giant ME effect under zero-magnetic bias and an enhancement in ME coefficient under a magnetic bias field; (b) The self-biased ME coupling arises due to transverse magnetization that originates from grading in magnetization. This mechanism is effective in both asymmetric and symmetric functionally-graded ME composites; (c) Thickness ratio between magnetization-graded ferromagnetic phases plays an important role towards tuning the magnitude of both self-biased, peak ME coupling coefficient, and the corresponding zero-crossing field (H_c) and optimum bias field (H_opt); (d) For positive grading (g) of q (P: magnitude of q increases away from the PZT-ferrite interface), the peak value of α_ME shows a factor of two higher than that of negative grading (N) and homogeneous ME laminates. (e) A significant enhancement of self-biased ME coupling coefficient was attained in symmetric system when operating at the mechanical resonance than that of asymmetric system operating at low frequencies for functionally-graded ME composites. Thus, studies on these compositionally and functionally-graded ME laminates resulted in understanding of the self-biased magnetoelectric coupling and their related electrical response as a function of magnetic field.

Electric-Field-Induced Bending Vibration Mode

According to the above discussion, it can be noticed that the self-biased ME response could be obtained with the presence of the flexural deformation in a ferromagnetic graded/stepped structure. However, this method of generating self-bias depends upon the composition grading which requires a special synthesis process and this creates additional steps in developing functional devices. Moreover, one important question needs to be addressed: whether the self-biased ME effect will be generated or not in ferromagnetic homogenous system with net zero magnetization moment?

In addressing this issue, Yang et al. first proposed an alternative methodology for inducing external bending strain via changing electrical connection to invoke self-biased ME response, as shown in Figure 10 (Yang et al. 2010). In this work, a 2–2 type composite was fabricated by laminating Ni plate in the center of two 3–0 type particulate composite plates (Figure 10(d)). This 3–0 type composites consisted of 0.948Na_0.5K_0.5NbO₃–0.052LiSbO₃ (NKNLS) matrix and Ni_0.8Zn_0.2Fe₂O₄ (NZF) as dispersant. The differences in the magnitude of susceptibility and coercivity between Ni and NZF particles resulted in a built-in bias field (H_int) along the interface. However, it was further noted that the three-phase laminate did not have effective net magnetic gradient due to the balanced symmetry NZF-Ni-NZF (zero net built-in bias) structure. Furthermore, by comparing the laminates under different electrical connection, laminates with induced radial vibration showed zero remnant α_ME (α_ER), while laminates with induced bending vibration exhibited hysteresis in α_ME as a function of DC magnetic field with non-zero α_ER. The induced bending mode was considered to be originating from the electrical connection with 180^o voltage phase difference between top and bottom of the poled 3–0 particulate composites. This asymmetry, including bending strain, was found to increase the magnetic interaction variation alternatively along the two interphases. This further resulted in an effective magnetic gradient in the dynamic process. These results demonstrated that the self-biased effect can be realized in a symmetric structure with zero net magnetic gradients by invoking the bending strain through electrical connections.

Figure 10:

ME voltage coefficient of ME composites in various configuration, (a) NKNLS-NZF/Ni bilayer, (b) NKNLS/Ni bilayer, (c) NKNLS-NZF/Ni/NKNLS-NZF trilayer with series electrical connection, (d) NKNLS-NZF/Ni/NKNLS-NZF trilayer with parallel electrical connection, and (e) NKNLS/Ni/NKNLS trilayer with parallel electrical connection (Yang et al. 2010).

Since the different ferromagnetic phases have been considered to play an important role in magnetic interaction, the influence of the NZF particles distribution and interaction toward self-biased behavior was further presented (Yang et al. 2011). This was expected since the magnetic interaction between NZF and Ni could be tuned by modifying the anisotropic response of NZF particles with different distribution (θ_NZF), size (R_NZF) and shape. However, a proper model that associates with all these variables to a ME coupling is yet to be formulated, so that ΔaER=f(Hbias,Δxcomposition,θNZF,RNZF) could be predicted and used to control the dependence and magnitude of self-biased magnetoelectric coefficient.

The influence of operation mode in the three-phase lead-free laminates has been investigated, as shown in Figure 11 (Yang et al. 2011). Similar hysteretic α_ME behavior was demonstrated between direct-ME (Figure 11(a)) and converse-ME (Figure 11(b)) coupling of the composites. Self-biased effect was further explained by the shift of magnetostriction curve of the two-phase ferromagnetic layer under external magnetic bias, as shown in Figure 11(d). The frequency dependence of CME effect was demonstrated to be identical to that of DME effect in both magnetic bias and zero-biased conditions. These results indicated that magnetic induction switching is possible by applying only AC electric field. This is technically important toward developing core-free magnetic flux density and electrically controlled memory devices. Therefore, the self-biased ME effect could be realized even in graded-ferromagnetic system having net zero magnetization under external bending strain induced built-in bias with specific electrical connections. The symmetric structure with simple and easy fabrication process along with the easy manipulation of the self-biased effect in this three-phase laminates provides attractive advantage in possible ME applications.

Figure 11:

(a) Direct ME coefficient α_DME and (b) Converse ME coefficient α_CME as a functional of H_bias, (c) Integral value of α_DME and α_CME with respect to the H_bias, and (d) magnetostriction variation of Ni, KNNLS-NZF, and bending mode KNNLS-NZF/Ni/KNNLS-NZF as a function of H_bias (Yang et al. 2011).

In summary, functionally-graded magnetoelectric composites can be realized in various configurations that can be categorized in asymmetric or symmetric configuration, as shown in Figure 12. Taking advantage of the magnetization-graded-induced built-in bias, these functionally graded ME laminates could be used to produce unique phenomena including self-biased magnetoelectric effect, magnetoelectric hysteresis loop and enhanced peak ME coupling coefficient. There are eight typical functionally graded structures: (1) compositionally graded ferromagnetic layer with built-in magnetic potential was first synthesized and analyzed. Asymmetric/symmetric ME laminates based on compositionally-graded-ferromagnetic layer illustrated a new path toward realizing enhanced ME coupling coefficient; (2) Subsequently, for ease of fabrication, two ferromagnetic metal/alloy/ceramic thin plates with different piezomagnetic coefficient were laminated together with different sequence to form the graded magnetization (or built-in bias), namely stepped-ferromagnetic layer. ME laminates based on this concept were well studied with the effect of materials selection, thickness ratio, grading sequence and so on, (3) Discrete graded ME laminates with opposite magnetostrictive layer on either side of piezoelectric and piezoelectric cantilever with graded ferromagnetic tip mass; (4) Three phase ME laminates with 0–3 particulate composites on a homogenous ferromagnetic layer. Even with a net zero magnetization under a P-M-P configuration, the self-biased ME effect can be evoked by the electrical connection induced bending moment. All of these configurations were made possible due to the simple epoxy bonding approach, and this simple approach also opens up the possibility to fabricate more complex composite configurations and/or poling conditions resulting in different operation mode (such as L-T, T-L, L-L or T-T (Zhai et al. 2008)).

Figure 12:

Schematic illustration of various functionally graded magnetoelectric composites configuration: (a) asymmetric structure; (b) symmetric structure.

(AFM-FM)-FE Exchange Bias Mediated ME Nanostructure

It was not until 2012, Lage and Meyners et al. developed the self-biased ME nanostructured composites based on intrinsic magnetostriction arising from exchange bias coupling (Lage et al. 2012). Figure 15(a) shows the schematic configuration of the EB mediated ME composite, where the multilayers with the sequence of NM-AFM-FM Ta/Cu-Mn₇₀Ir₃₀-(Fe₅₀Co₅₀ or Fe_70.2Co_7.8Si₁₂B₁₀)] serving as the magnetostrictive component, while the AlN was selected as piezoelectric phase. Similar to EB coupling discussed above, the magnetically hard AFM spin plays an important role in exerting a microscopic toque on the FM spin, leading to a shift of H_EB (Berkowitz and Takano 1999) and (Nogués and Schuller 1999). The NM Ta/Cu bilayer was used as a buffer layer for texturing AFM (Mn₇₀Ir₃₀), which was mandatory for reliable EB. To evoke the H_EB, a field cooling process for the multilayered system above the Néel temperature of the AFM material is necessary. Normally, the magnitude of the shift is attributed to the thickness, interface microstructure and roughness of the AFM/FM layer (Berkowitz and Takano 1999; Nogués and Schuller 1999). In the AFM-FM bilayer system, due to the pining effect anisotropy, exchanging bias has always been observed along the pinning longitudinal direction of the thin film. On the contrary, the anisotropic field is approximately reciprocally proportional to the magnetostriction leading to a maximum magnetostriction under a transverse magnetic field. Therefore, in order to adjust the shift of magnetostriction curve for a maximum q and the resultant self-biased ME voltage coefficient, an inclination angle (φ) was induced with respect to the longitudinal direction of the film, as shown in Figure 15(c)–(e). By optimizing the thickness and inclination angle of the system, this EB mediated self-biased ME nanostructures demonstrated a giant ME coefficient of 96.7 V cm⁻¹ Oe⁻¹ for φ=70^o at fr=1.19 kHz at zero-bias field, as shown in Figure 15(b). This concept has now further lead to an maximum coefficient of 430 V cm⁻¹ Oe⁻¹ by a thickness variation of the ferromagnetic layer (Lage et al. 2014).

Figure 15:

(a) TEM image of the Fe₅₀Co₅₀ multilayer system on a AlN substrate and a magnified view (inset), (b) magnetoelectric voltage coefficient for the Fe_70.2Co_7.8Si₁₂B₁₀-based multilayer system with the pinning direction induced at φ= 70^o, (c) normalized magnetization curves, (d) corresponding magnetostriction curves and (e) piezomagnetic coefficient of Fe₅₀Co₅₀ multilayer stacks on cantilever samples for selected values of the inclination angle φ (Lage et al. 2012).

Although the first EB mediated self-biased ME composites were reported recently, the development of AFM-FM exchange bias mediated self-biased ME sensor has been rather slow (Lage et al. 2012,2013; Jahns et al. 2013). The lack of immediate progress could be due to the difficulty in synthesizing such system with complex multilayer stacked design, need for field cooling and control of ME coupling by film thickness and EB inclination angle. However, it has been believed that the implementation of such EB mediated ME nanostructure with self-biased effect could be promising toward MEMS-scale on-chip device fabrication (e.g. magnetic field sensor array). What’s more important, this work created a new pathway for developing magnetoelectric composites by incorporating the exchange bias coupling.

(Soft-Hard Biphase FM)-FE Exchange Bias Mediated ME Bulk Laminate

Continuing the work on EB mediated self-biased ME composite, it has been noted that although the film thickness, field cooling and incident angle control of the (AFM-FM)-FE multilayer configuration is not the main obstacle to study the EB coupled self-biased coupling, synthesizing the complex multilayer nanostructure is rather challenging and expensive toward practical application. To make it easier and cost effective, bulk ME laminates based on the soft-hard biphase FM exchange bias coupling was demonstrated in 2–2 type multi-push-pull configuration consisting of annealed Metglas, Metglas and PZT. (Li et al. 2013) It is well known that amorphous Metglas foil with a homogenous “soft” ferromagnetic material, usually shows a symmetrical slim M-H hysteresis loops with a biquadratic λ behavior with respect to H_bias at zero-bias point. However, under high temperature annealing, transition metal elements (Fe, Co) of the alloy tends to form crystallized hcp-Co, a-Fe and iron oxide phases, which possess “harder” magnetic properties as compared to that of amorphous Metglas (Rivas et al. 2005; He et al. 2009). These partially crystallized particles lead to unidirectional magnetization anisotropy (after premagnetizing) in adjacent amorphous Metglas layers. This reflects in the shift of M-H loop (Giri, Patra, and Majumdar 2011; Gonzalez et al. 2000; Gubbiotti et al. 2002; Rivas et al. 2005). Since the magnetostriction originated from magnetization variation (magnetic domain rotation and domain wall migration), the exchange bias resulted in a same magnitude of shift in the position of λ= 0 at H_EB with non-zero q at zero-bias. Therefore, a giant self-bias ME coefficient was realized with the magnitude of 12 V cm⁻¹ Oe⁻¹ as shown in Figure 16, which could be further enhanced to 380 V cm⁻¹ Oe⁻¹ at the EMR frequency of 33.7 kHz (Li et al. 2013).

Figure 16:

Magnetoelectric voltage coefficient of Metglas/PZT/Metglas laminates measured at H_ac = 0.1 Oe at a frequency of f= 1 kHz (Li et al. 2013).

However, except for the high self-biased response and simple EB coupling mechanism of this laminate composites, the magnitude of maximum α_ME was lower than that of conventional push-pull mode ME laminates with same dimension (Li et al. 2012). This difference in α_ME was ascribed to the precipitation of magnetically hard particles. These particles not only play an important role in EB coupling, but also dramatically affect the saturate magnetostriction of Metglas. The magnitude of a_H0 can be manipulated by controlling the thickness of annealed Metglas, however it is rather hard to operate due to the contrary behaviors of H_EB and α_ME, where the increase of H_EB will result in a decrease of α_ME.

To summarize this section, a schematic diagram of EB mediated ME composite with various configuration is shown in Figure 17. Although the investigation of exchange bias has been ongoing since its discovery in 1956 (Meiklejohn and Bean 1957), the utilization of exchange bias coupling in magnetoelectric/multiferroic system attracted interest of researchers a decade ago. Among these prior research of EB mediated ME coupling; most of efforts have been focused on electrical control of magnetism in FM films (Martin et al. 2008; Vaz et al. 2010; Ma et al. 2011). The investigation of EB induced self-biased ME effect has just started with two preliminary research in either a (AFM-FM)-FE thin film nanostructure(Lage et al. 2012) or a (Soft-hard biphase FM)-FE bulk laminate(Li et al. 2013), as shown in Figure 17(a) and (b). Despite these efforts, the fundamental understanding of the impact of EB mediated self-biased response and its technological aspects are not well established. In principle, the concept of exchange bias mediated magnetoelectric composites could also be expanded to other EB coupling mechanism including: (1) multiferroic with (FE-AFM)-FE nanostructure Figure 17(c)], (2) soft-hard biphase FM-FE core-shelled bulk structure Figure 17(d)], and (3) RKKY-liked EB coupling such as (AFM-NM-FM)-FE or (SG-FM)-FE nanostructures. In that case, the multicomponent magnetic layers with EB coupling could be used to establish a non-zero piezomagnetic coefficient at zero-bias. This would further lead to a giant self-biased ME coupling. In particular, exchange bias with multiferroic (e.g. BiFeO₃ with FE and AFM order) and soft-hard biphase FM multilayer ribbon seems to be most promising candidate, as shown in Figure 17(c) and (d), for aforementioned purpose due to their ease of synthesis and capable of EB coupling at room temperature.

Figure 17:

Schematic diagram of four possible EB mediated ME composite configurations. (a) (AFM-FM)-FE; (b) (soft/hard FM)-FE; (c) FM-multiferroic (d) hard-soft-FE.

Co-Fired Ceramic Composites

Since the ME effect originates through elastic coupling at the interface, it is important to consider the influence of synthesis method toward optimizing the interface bonding. The direct bonding that completely excludes the utilization of epoxy layer with low mechanical strength is favorable. In bulk system, co-firing techniques at high temperature not only enhances the mechanical coupling between the piezoelectric and magnetostrictive constituent (Srinivasan et al. 2001; Yan, Zhou, and Priya 2013; Yan, Zhou, and Priya 2014a), but also dramatically reduces the cost due to utilization of conventional processes used for multilayer capacitors (Israel, Mathur, and Scott 2008). Different materials combinations, mole ratios, phase connectivity, physical geometries, compacting procedures, sintering procedures and microstructures were therefore examined (Fiebig 2005; Priya et al. 2007; Nan et al. 2008; Zhai et al. 2008; Vaz et al. 2010; Ma et al. 2011). However, in spite of all these efforts, the development of co-fired ME composite has been pretty slow. Several obstacles for the development of co-fired ME composites were identified:

1. Co-sintering different phases together is extremely challenging through high temperature thermal cycling because of the large difference in shrinkage rates and thermal expansion mismatch among different phases.

2. The opposing behavior between high concentration of magnetostrictive particles and low resistivity of sintered particulate ME composites, results in either an ineffective magnetic induced interaction or bad poling condition.

3. Atomic interfacial inter-diffusion and/or chemical reactions between the constituents and/or their starting materials during the high temperature co-sintering process.

4. Residual strain or stress originated due to mechanical defects, interface diffusion, lattice mismatch and thermal expansion mismatch between different constituents, leading to either a limited mechanical coupling or unexpected magnetic/piezoelectric property anisotropy.

Figure 20:

Development of co-fired magnetoelectric composites. It shows ME voltage coefficient (α_ME) for different types of sintered ME composites (Yan, Zhou, and Priya 2014b).

The co-fired bulk ME ceramic composites exhibited promising larger ME effect. However, the self-biased ME effect was observed in high-temperature co-fired ceramic composites. This effect has been rarely reported and explained, mainly due to their inherent preparation challenges and acquired built-in stress during co-firing process. Islam et al. found that 0.8PZT-0.2NZF particulate composite exhibited a high response of 0.45 V cm⁻¹ Oe⁻¹ with a non-zero α_ME of 0.09 V cm⁻¹ Oe⁻¹ at the low frequency of 1 kHz. The magnetic particles were well dispersed in the matrix of piezoelectric materials and their effective contact interface can be further controlled by the concentration of induced magnetic particles, leading to a tunable feature. (Islam et al. 2006) With the use of nano-grained NiFe_1.98O₄ (NFO) in the matrix of BaTiO₃ (BTO) powders, Sreenivasulu et al. found a large maximum α_ME of 0.252 V cm⁻¹ Oe⁻¹ in BTO-NFO particulate composite, which was about five times larger than their respective microcomposites (Sreenivasulu et al. 2009). More interestingly, different from conventional microcomposites, all the corresponding nanocomposites illustrate an obvious hysteretic α_ME vs H behavior, demonstrating a maximum α_H0 of 0.15 V cm⁻¹ Oe⁻¹. The manipulation of ME and self-biased ME response can be attributed to the difference in lattice strain, interface contacts and their effect on the corresponding magnetic properties.

Alternatively, Srinivasan et al. observed a giant enhancement (0.46 V cm⁻¹ Oe⁻¹) and a noticeable non-zero α_ME (0.1 V cm⁻¹ Oe⁻¹) at zero-bias field in a co-fired PZT/NFO laminates, as shown in Figure 21(a) (Srinivasan et al. 2001). For the first time, they considered the influence of growth-induced stress and its effect on magnetic anisotropy and the interfacial coupling. As expected, differential thermal expansion (2 ppm for PZT vs 10 ppm for most ferrites) and thermal conductivity could result in built-in strain between contacting constituents during the high temperature process. This strain may further couple with the magnetostrictive strain resulting a magnetic anisotropy and/or enhanced ME coupling. Continuing this research, they observed a giant hysteresis and remanence in α_ME vs H in the co-fired LSMO/PZT bilayer system (Figure 21(b)) (Srinivasan et al. 2002). With increasing the numbers of co-fired layers, a degradation of α_ME was observed and attributed to the element diffusion through enlarged interface area and growth-induced strain at the interface. Similar behavior was also observed in other co-fired 2–2 laminated systems such as BTO-NCZF and PZT-NCZF multilayers (Islam and Priya 2006; Yan, Zhou, and Priya 2013). Interface homogeneities, microstructure roughness, intrinsic lattice strain, inter-diffusion and chemical reactions between constituents has been hindering their improvement toward higher coupling factor. It was not until recently Yan et al. cofired a NCZF-PMNPT-NCZF trilayer composite utilizing Ag electrode as buffer layer between different constituents (Yan, Zhou, and Priya 2013) With the effective Ag barrier, chemical reaction and/or element migration of the constituents is avoided by macroscopic separation of the magnetostrictive and piezoelectric phases. They obtained a giant ME voltage coefficient of 0.83 V cm⁻¹ Oe⁻¹ followed with a self-biased a_H0>0.5 V cm⁻¹ Oe⁻¹ (Figure 21(c)). By using the textured piezoelectric layer to form the engineered domain state, they were able to further enhanced the self-biased ME voltage coefficient up to 1.21 V cm⁻¹ Oe⁻¹, which exceeds the highest value gained from any co-fired ME composites by a factor of 10!

Figure 21:

ME voltage coefficient of various co-fired ME composites (a) PZT-NFO bilayer structure (Srinivasan et al. 2001), (b) LSMO-PZT bilayer structure (Srinivasan et al. 2002), (c) NCZF/T-PMN-PT/NCZF (C-N/T/N), NCZF/R-PMN-PT/NCZF (C-N/R/N), and epoxy bonded Metglas/R-PMN-PT/Metglas (B-M/R/M) trilayer structures. R and T stands for random and textured ceramics (Yan, Zhou, and Priya 2013).

Although it has been discussed that the magnetostriction hysteresis of the ferromagnetic layer in low field range plays an important role toward self-biased ME effect (Yan, Zhou, and Priya 2013), we can speculate one more possible reason for a unique and favorable interface bonding in which the growth induced built-in stress cannot be neglected. For co-firing laminates without barrier layer, except for thermal expansion and conductivity mismatch between constituents, the rough interface contact and inter-diffusion may also bring extra stress during co-sintering process. For co-firing laminates using Ag as an effective barrier layer, the silver itself has even much larger thermal expansion coefficient (–18 ppm) than that of piezoelectric (– 2 ppm) and ferrites (–10 ppm) phase, and its thermal conductivity is much higher than that of piezoelectric and ferrite. Difference in thermal expansion and thermal conductivity could result in built-in interface strain which is comparable to magnetostrictive strain. However, none of these hypotheses have been demonstrated experimentally. As an extension to Yan’s work (Yan, Zhou, and Priya 2013), we co-fired the NCZF-PMNPT-NCZF composite with and without the Ag electrode. As shown in Figure 22, the hysteresis in the ME response was dramatically reduced without Ag inner electrode. This result clearly demonstrated the relationship between the hysteretic behavior and internal stress arising due to the thermal mismatch between metallic and ceramic layers.

Figure 22:

Magnetoelectric voltage coefficient as a function of DC magnetic field for co-fired ME laminates with and without Ag inner electrode (IE).

In summary, the development of the co-fired self-biased magnetoelectric composites can be categorized into three groups, as shown in Figure 23. The self-biased ME response of the co-fired composites is determined by two major aspects: (1) low field magnetostrictive hysteresis; (2) built-in stress arising from thermal mismatch, lattice mismatch, chemical reaction, inter-diffusion, and so on. This phenomenon can be further controlled by several impact factors including: (1) selected constituents’ composition, (2) magnetic particle size and distribution, (3) sintering process, (4) buffer layer between constituents and so on.

Figure 23:

Development of co-fired self-biased ME composites.

Thin Film Residual Stress

The thin film deposition is another widely accepted direct bonding method for ME composites with unique advantages over co-fired bulk composite. Thin film deposited heterostructures, with less possibility of inter-diffusion during low temperature (600^°C–800^°C) growth process, provide strong bonding at coherent interface. This method further provides opportunity for manipulating composition and connectivity of thin film composites at nanoscale, which is advantageous for their implementation in on-chip scalable MEMS functional devices. Nanostructured thin film ME composites has been investigated in various phase connectivity (0–3 type particular films, 2–2 type layered heterostructures, 1–3 type vertical heterostructures) using either physical vapor deposition (PVD) methods (pulsed laser deposition, sputtering, molecular beam epitaxial) or chemical vapor deposition (CVD) methods (sol-gel spin coating, metal-organic chemical vapor deposition) (Ma et al. 2011; Ramesh and Spaldin 2007; Wang et al. 2010; Martin et al. 2008, Jahns et al. 2013). By optimizing the materials selection and deposition parameters, ME composite thin films with coherent interface were developed by precise control of the lattice mismatching and thickness of constituent components.

The coupling interaction, between piezoelectric and magnetostrictive phases, in the nanostructured films has been attributed to the elastic coupling as in bulk composites. However, in thin films, the mechanical constrain arising from the substrate (Nan et al. 2005) and built-in stress (Ibach 1997), could significantly affect the ME interactions. Furthermore, prior studies of stress effect indicated that the magnetoelastic coupling of strained ferromagnetic films deviated sharply from the respective bulk behavior due to strain (Sander et al. 2003). These factors result in remarkable variations of spontaneous polarization and magnetization in the ME films, thereby a dramatically different magnetoelectric behavior than that of bulk system (Table 4).

The non-zero α_ME at zero bias has been commonly found in thin film ME nanostructures. In some cases, at zero-bias the film (CFO-PZT particulate) exhibited an initial high α_ME value of 0.22 V cm⁻¹ Oe⁻¹ at H_ac = 10 Oe at1 kHz (Figure 24(a)), which was much larger than that of biased condition, indicating an easy-magnetization characteristic of the film (Wan et al. 2005). However, considering the magnetically “hard” bulk CFO material with large coercivity beyond –2 kOe, the ease of domain rotation was attributed to the residual stress arising along the film-on-substrate interface. Since the residual stress from the film-on-substrate structure has been considered sensitive to the thickness, subsequent study performed on the CFO-PZT system with higher thickness – 1 µm, as shown in Figure 24(b) (Wan et al. 2006). The variation in the magnitude of stress not only resulted in the sharp reduction of the self-biased α_ME to 0.005 V cm⁻¹ Oe⁻¹, but also shifted the optimum H_bias to a higher value of 4.5 kOe. Moreover, similar to the bulk samples, the magnetic particle size/concentration in the ferroelectric matrix was found to significantly affect the self-biased ME response of the composites films (Zeng et al. 2004; McDannald et al. 2013). Figure 24(c) illustrates a series of ME voltage coefficient as a function of magnetostrictive phase (CFO) concentration for 0–3 type PZT-CFO nanocomposite films (McDannald et al. 2013). This tunable self-biased behavior was explained by assuming a finite remnant magnetization of the magnetic nanoparticle upon clustering (McDannald et al. 2013; Tahmasebi et al. 2011). Alternatively, 2–2 type layered heterostructures (Figure 24(d)) exhibited significant larger self-biased α_ME than that of 0–3 type particulate film and single phase multiferroic films (Tiercelin et al. 2008; Tong et al. 2014).

Figure 24:

ME voltage coefficient as a function of DC magnetic field for (a) PZT-CFO 0–3 type nanocomposite films with thickness of –400 nm (Wan et al. 2005), (b) PZT-CFO 0–3 type nanocomposite films with thickness of –1 µm (Wan et al. 2006), (c) PZT-CFO 0–3 type nanocomposites films with various magnetic concentration. PC1, PC2, PC3 and PC4 are stands for films with, 0.065%, 0.10%, 0.14% and 0.46% molar concentration of CFO, respectively (McDannald et al. 2013); (d) 2–2 type AlN/[FeCoSiB + Terfenol-D] composite films, inset is the ME coefficient of AlN/FeCoSiB composite film (Tiercelin et al. 2008; Tong et al. 2014).

Nonlinear Magnetoelectric Effect Characterization

Demonstration of the nonlinear magnetoelectric effect controlled by the amplitude and frequency of applied AC magnetic field was reported in a ceramic NZFO/PZT laminated structure, where frequency doubling and generation of harmonics were explored at very low frequencies (1 mHz to 1 Hz) and high field amplitudes (200 Oe–1000 Oe) (Kamentsev, Fetisov, and Srinivasana 2006). Inspired by this work, Ma et al proposed a frequency multiplier based on an epoxy bonded FeBSiC/PZT laminate and demonstrated its capability of doubling frequency in a broad range (20 Hz to 2 kHz) without additional adjustment (Ma et al. 2011b). Thereafter, Zhang et al. expanded the study of the frequency multiplying behavior using fast Fourier transform (FFT) frequency spectral patterns of the ME voltage in a Metglas/PZT unimorph structure (Zhang et al. 2012). Both even and odd harmonic signals were found with applied H_dc, whereas only even harmonic signals were observed in the absence of H_dc. This behavior was attributed to the combination of a mechanical resonance phenomenon and the nonlinear character of the magnetostriction. Furthermore, Wang et al. systematically investigated the ME voltage (V_ME) for various amplitudes of H_ac up to 9 Oe over a frequency range of 0.1–40 kHz with zero-bias DC magnetic field (Wang et al. 2013). The anomalous responses of V_ME were suggested to be associated with the eddy-current loss in the magnetostrictive layers. Theoretical calculation conducted for the nonlinear magnetoelectric coupling shows its potential for applications such as tunable magnetic field sensors and frequency multipliers (Fetisov et al. 2013).

Nonlinear behavior of the magnetoelectric coupling observed under the varying amplitude or frequency of applied magnetic field arises mainly due to the influence of the nonlinearities in magnetic and magnetostrictive phase. Four aspects of this nonlinear ME effects has been rationalized as:

1. Frequency doubling: The frequency doubling was characterized as an output V_ME with a frequency of 2f was generated from the sample by applying a bipolar H_ac with frequency f in the absence of H_dc (0 Oe), as shown in Figure 25 (Ma et al. 2011; Kamentsev, Fetisov, and Srinivasana 2006). This effect was found to rely on the fact that the magnetostriction was independent of the sign of applied magnetic field, but the amplitude (Wang et al. 2013). Therefore, the generation of an unipolar strain under bipolar magnetic field gave rise to the double frequency 2f of the generated signal V_ME. Additionally, this double frequency behavior could be used under a broad frequency and amplitude range, and could be further switched by a low DC magnetic field (Kamentsev, Fetisov, and Srinivasana 2006; Ma et al. 2011; Zhang et al. 2012).

2. High-order harmonics: By investigating the FFT frequency spectral pattern of V_ME, it was found that higher-order harmonic signals were present_.(Kamentsev, Fetisov, and Srinivasana 2006). The number of harmonics seen in the spectra were found to decrease with an increase in the applied f_ac (Zhang et al. 2012), whereas the relative amplitude of the harmonic peaks increased at high magnitude of H_ac (Wang et al. 2013). More interestingly, both odd and even harmonics were found with applied H_dc, while only even harmonics for zero-biased condition were observed (Zhang et al. 2012). On tuning the input H_ac with frequency of fr/n, the nonlinear ME coupling was dramatically enhanced (Fetisov et al. 2013). Thus, this phenomenon offers an effective way for achieving a high ME coefficient with lower input frequency, which breaks the geometrical limitation of sample resonance frequency.

3. DC Magnetic field effect: Depending on the amplitude of applied H_ac, the H_dc was found to play an important role toward switching the frequency multiplier behavior of nonlinear ME coupling, as shown in Figure 26(a) and (b) (Ma et al. 2011; Zhang et al. 2012). When H_dc=0 Oe, the ME response V_ME was found to double the frequency of applied H_ac due to magnetostriction nonlinearity as discussed before. However, on applying a H_dc with amplitude larger than H_ac, this double frequency behavior was found to disappear. This DC field effect was attributed to the extrinsic relations of the applied magnetic field and V_ME (Ma et al. 2011):

   [6]VME∝H2=HdcHacsin2πft+Hac2cos4πft

where A is a constant independent of applied magnetic field and depends only on the compliance of the constituents in the composite, the p=∂2λ/∂H2 is the second derivative of magnetostriction over the field. Hence, the nonlinear ME coefficient [a_NLME=V_NLME/(t_pH_ac²)] was found to follow p, (Figure 26(c)) and reached a maximum near zero bias field. It further vanished at H_bias illustrating another peak value and then gradually reduced to zero at higher field.

Figure 25:

Waveform of ME voltage output without (a) and with (b) DC magnetic field. The thin red lines correspond to the input signal while the thick dark dot curves correspond to the output signals (Ma et al. 2011).

Figure 26:

Dependence of the ME voltage u generated by the FeBSiC-PZT bimorph structure as a function of the frequency f of ac magnetic field h. (a) u₁ is the voltage under linear ME excitation regime with the DC bias H₀ = 18 Oe, (b) u₂ is the voltage under nonlinear excitation regime with the bias field H₀ = 0 Oe, (c) the linear ME voltage u₁ and nonlinear ME voltage u₂ as a function of applied DC bias field H₀ (Zhang et al. 2012).

1. AC Magnetic field effect: Both amplitude and frequency of H_ac was found to play an important role toward nonlinear ME interactions through a combination of various phenomena including eddy-current loss and nonlinearity of the magnetostrictive phase. In the absence of H_dc, the magnetostriction can be expressed as (Wang et al. 2013):

   [8]λHac=A0+A1cosωt+A2cos2ωt+A3cos3ωt+A4cos4ωt+A5cos5ωt

whereA0=a0+12a2Hac2+38a4Hac2, A1=a1Hac + 34a3Hac3+58a5Hac5,A2​=​12a2Hac2​+12a4Hac4,A3​=​14a3Hac3​+​516a5Hac5,and A5=516a5Hac5 and A₅ = 516a₅H_ac⁵, where a_i are the ith Fourier coefficient. Considering equation 5, the variation of H_ac gives rise to the change in the relative amplitude of the harmonic signals as discussed before. The eddy-current induced losses in soft magnetic materials can be given as (Kendall and Piercy 1993; Wang et al. 2013):

where s and ρ are the cross-sectional area and resistivity of the magnetic material, μzero is the dynamic permeability extrapolated to zero frequency, and H_pk is the peak value of the applied bipolar magnetic field. The eddy-current induced energy loss becomes larger, leading to a reduced dynamic magnetostriction and therefore a decrease in V_ME with increasing f, as shown in Figure 27 (Wang et al. 2013).

Figure 27:

(a) ME voltage variation as a function of frequency under various amplitudes of H_ac, inset shows an enlarged view near the resonance frequency, (b) ME voltage output as a function of H_ac at resonance frequency of 1, 10, 20kHz and the EMR condition (Wang et al. 2013).

According to the above discussion, it can be concluded that the self-biased response can be also realized by relying on the magnetostrictive nonlinearity. Therefore, in the absence of H_dc, a giant nonlinear ME voltage coupling coefficient could be obtained in ME laminates, which could be further controlled using the amplitude and frequency of applied AC magnetic field. What’s more important, the unique frequency multiplying behavior provides great potential of using such non-linear ME effect towards applications including high sensitivity sensors and frequency multiplier devices.

Figure 28:

(a) Schematic illustration of the cross-modulation based ME composite, (b) measured modulation spectrum taken at f_div = 1 kHz, f_inc = 1 Hz from PZT-Metglas laminate with different numbers N of Metglas layers (Shen et al. 2011).

Cross-Modulation Techniques

Furthermore, by utilizing the nonlinear magnetoelectric coupling, cross-modulation (or frequency conversion) technique was proposed (Zhuang et al. 2011; Shen et al. 2011). In particular, in order to detect an incident AC field H_incsin(2πf_inct) with low frequency f_inc (0.1 Hz–1 Hz), a drive field H_divsin(2πf_divt) with higher frequency f_div (1 kHz or higher) was applied, as shown in the schematic (Figure 28(a)). In the presence of two AC magnetic field, the nonlinear ME interaction resulted in generation of the cross-modulated voltage with frequency of (f_div±f_inc), as shown in Figure 28(b). Therefore, the low frequency signals were modulated to a higher frequency in which lower noise floor were present. The effective magnetic field and generated V_ME could be expressed as (Zhuang et al. 2011):

without applying DC bias, the induced nonlinear ME output could be measured by considering the 2^nd order cross-term, given as (Shen et al. 2013):

where the 2nd order coefficient could be expressed as the nonlinear ME coefficient (a_NLME) (Shen et al. 2011), (Shen et al. 2013):

Shen et al. investigated the cross-modulation techniques with Metglas/piezoelectric laminates and found that an optimum α_NLME could be obtained near H_dc = 0 Oe for Metglas/PMN-PT (Shen et al. 2011). The lack of requirement for the DC bias makes the modulation approach promising. The nonlinear ME coefficient was found to be highly dependent on the magnetic flux concentration. A giant α_NLME=7.5 V cm⁻¹ Oe⁻² at H_dc=0 Oe was obtained by optimizing the Metglas configuration (Shen et al. 2013). The behavior of α_NLME follows well with the second derivative of the magnetostriction as a function of DC bias, as shown in Figure 29. The results demonstrated high sensitivity of 200 pT at 10 mHz and 20 pT at 1 Hz by effectively reducing the vibration noise through the frequency modulation (Liu et al. 2013). Theoretical investigation regarding the nonlinear ME interaction and its applications in frequency modulation have been conducted and compared with the experimental data (Burdin et al. 2014). Different from linear ME interaction, the nonlinear magnetostriction at the cross-modulation frequency f_div±f_inc was given as λ=3λsχ22Ms2HdivHinc, where thinner magnetostrictive materials with higher magnitude of χ were desired (Gillette et al. 2011; Li et al. 2013). Hence, the magnitude of α_NLME was further improved to 100 V cm⁻¹ Oe⁻² at H_dc=0 Oe at f_r in Metglas/PMN-PT based laminates with thin Metglas (Shen et al. 2014).

Figure 29:

(a) Magnetostriction and piezoelectric coefficient of 8 cm-long Metglas as a function of H_dc, (b) The corresponding ME coefficient curve which is shown to be highly dependent on the piezomagnetic coefficient, (c) Derivative strength of piezomagnetic coefficient as a function of H_dc, (d). The corresponding nonlinear ME coefficient curve which is shown to be highly dependent on the derivative of piezomagnetic coefficient (Shen et al. 2013).

In summary, the self-biased magnetoelectric response can also be observed in conventional laminated composites due to the nonlinear magnetoelectric interaction effect. The ME nonlinearity of the composites could be determined by several major factors including: (1) the absence of DC magnetic bias H_dc=0 Oe; (2) proportionality to the second derivative of the magnetostriction p=∂2λ/∂H2; (3) sensitivity to the amplitude and frequency of the applied AC magnetic field; (4) dependence on the magnetic susceptibility and flux density of the magnetic layer in the composites.