Magnetoelectric materials and devices

Multiferroic materials, which have two or more ferroic orders, such as ferroelectricity, ferromagnetism, and ferroelasticity, have received intense research interests due to both theoretical physics and potential multifunctional applications. Among them, a strong coupling between ferroelectricity and ferromagnetism is highly desired. Magnetoelectric (ME) effect is the coupling between polarization (P) and magnetization (M), i.e., the control of P by applying a magnetic field (direct ME effect) or the manipulation of M through an electric field (converse ME effect). There are two ME coupling coefficients that are used to describe the strength of ME coupling: (i) direct ME coupling coefficient α_Direct = (∂P/∂H)_T,E for isothermal processes or α_Direct = (∂P/∂H)_S,E for adiabatic processes and (ii) converse ME coupling coefficient α_Converse = μ₀(∂M/∂E)_T,H for isothermal processes or α_Converse = μ₀(∂M/∂E)_S,H for adiabatic processes. By applying the first and second laws of thermodynamics to ME materials (both single-phase and composites) for lossless and reversible processes, the direct and converse ME coefficients are equal for both isothermal and adiabatic conditions.¹ This equality of the direct and converse ME coupling coefficients has been commonly known for decades² and experimentally confirmed in a ME sandwich structure with a single crystal PZN-PT slab between two polycrystalline Galfenol (FeGa) layers.³ Owing to the realization of the strong ME effect in ME composites, research works on this area are increasing year by year since the 21st century. As shown in Fig. 1, the year number of published papers on magnetoelectric is recorded from Google Scholar. It is clear that the number of papers increases dramatically since the revival of ME effect, which indicates that researchers are becoming more and more interested in this topic. Strong ME coupling, which is critical for various ME devices, has been demonstrated in these multifunctional materials.^1,4–14 The coexistence of magnetization and polarization in these ME materials provides additional degrees of freedom in the development of novel devices such as sensors,^15–20 filters,^21–24 inductors,^25–30 antennas,^31–38 energy harvesters,^39,40 storage devices,^41–44 etc.^45–48 

The birth of ME effect was marked by two independent events: (i) the magnetization or polarization of a moving dielectric in an electric field⁴⁹ or a magnetic field;⁵⁰ (ii) Curie proposed the possibility of the intrinsic ME effect in 1894.⁵¹ More than 60 years later, it was proved on the basis of crystal symmetry by Landau et al.⁵² Since the experimental demonstration of ME effect in single-phase material Cr₂O₃,^53–55 many efforts have been made to explore the possibility of achieving strong ME coupling in single-phase materials. Several families of the single-phase compounds were found with ME behavior: Bi compounds,^6,56–59 rare earth (RE) manganites,^60–62 Pb family perovskite oxides,^63–66 REMn₂O₅ family,^67–69 fluoride family,^70,71 etc. However, they are reported in small numbers due to the contradiction between the formation of magnetic moments with partially filled d-orbitals and the requirements of empty d-orbitals in ferroelectric (FE) oxides.^72,73 In addition, these single-phase multiferroic materials are also suffering from the weak ME coupling effects and the low Curie temperature.⁷⁴ The common characteristics of ME effect in different single-phase multiferroic materials are summarized in several review papers.^5,73,75–77

The magnetodielectric (MD) effect in (ferro)magnetic dielectrics has been investigated extensively to control the dielectric properties with a magnetic field for applications such as field-tunable capacitive resonators.^78,79 A detailed magnetic field dependence of the dielectric constant (ε) and electric polarization in DyMn₂O₅ single crystal was investigated by Hur et al.⁶⁸ Due to the high sensitivity of the incommensurate state to external perturbation, an unprecedented large change in the dielectric constant with a magnetic field was discovered for more than 100% in a wide temperature range below 20 K. This “colossal magnetodielectric” (CMD) effect near a unique commensurate–incommensurate magnetic transition clearly shows an exciting interaction between spin and lattice degrees of freedom. An extraordinary change in the dielectric constant with the increasing temperature (T) under different magnetic fields (H) was discovered. The zero-field curve exhibits clear dielectric anomalies occurring at magnetic transition states, which suggests a significant spin/lattice coupling. A maximum change for ε of ∼109% at 3 K with H of 7 T was achieved. When H is applied along the b axis, the magnetic easy axis, the MD effect is large as well, but not as significant as that for the a axis. The change in Δε/ε₀ as a function of H at 3 and 20 K for magnetic field cooling (FC) and zero-magnetic field cooling (ZFC) was also measured. Compared to the largest change of 109% for FC at 3 K, the change for ZFC is slightly less, ∼90%. The maximum value at 20 K is reduced to ∼40%. In the measurements of the change in the electric polarization (P) with increasing H at 3 K, a hysteresis loop and an abrupt change at ∼1.8 T were observed, which are closely correlated with the magnetization loop and Δε/ε₀ curve at 3 K. Kimura et al. reported the discovery of ME effect in perovskite manganite TbMnO₃ and realized the magnetic control ferroelectric polarization.⁶¹ Via the magnetoelastically induced lattice modulation, the magnetic structure was modulated with the emergence of spontaneous polarization. The schematic of the crystal structure of TbMnO₃, which is the orthorhombically distorted perovskite structure, at room temperature and spatial variation along the b axis of Mn magnetic moment is shown in Fig. 2(a). The magnetic field dependence of the change in electric polarization along the a axis at various temperatures is displayed in Fig. 2(b). A remarkable change in the polarization (∼6 × 10⁻⁴ C m⁻²) is caused by the magnetic field-induced polarization with the nature of first-order phase transition. Figure 2(c) shows the phase diagram of TbMnO₃ with magnetic phase boundaries denoted by triangles for the magnetic field applied along the b axis.

In this section, we first introduce the basic idea about ME composites and their common structures. Then, a brief history of the development of bulk ME composites is given. After that, the pros and cons of bulk ME composites based on different materials are discussed. Finally, a specific example of a ME laminate composite with PZT and Terfenol-D disks is presented for further understanding. In order to compensate for the deficiencies of the single-phase materials, a giant ME coupling at room temperature was realized by tailoring the properties of artificial multiferroic composites, which are consisted of ferroelectric (FE) and ferromagnetic (FM) compounds.^80–82 The purpose of this method is to generate cross coupling between the parent compounds via elastic interaction. This novel structure owns both properties of their parent materials, which is known as a product-property of the composite.^83,84 These multiferroic composites were found to have a large ME coefficient that is one to two orders higher than that of the single-phase materials. The practical applications of the ME effect become true as a result of the appearance of the ME composites with a much larger ME coefficient above room temperature. There are different structures for multiferroic composites that create strong ME coupling for multifunctional applications:⁸ (i) 0–3-type mixed phase of particulate nano-composites, (ii) 1–3-type vertically mediated architecture with three-dimensional ferromagnetic nano-pillars embedded in a ferroelectric phase, and (iii) 2–2-type classic ME multilayers that are widely used for devices due to the advances in thin-film growth techniques. By properly choosing the properties such as connectivity, microstructure, volume fraction, of individual phases, the composite structures open up new paths for tailoring the ME coupling. This technique was initially investigated in the 0–3-type ceramic composites^84–86 and later in the 2–2-type laminated multilayers.^87–90 More recently, Dong et al. proposed ME composites structures with 2–1 and 1–1 connectivity, which exhibited an enhanced ME coupling coefficient.^91,92 They reported a high off-resonance ME coupling coefficient of 22 V cm⁻¹ Oe⁻¹ in a 2–1 connectivity composite consisting of an amorphous Metglas alloy and multiple piezoelectric fibers.⁹¹ An enhanced resonant ME coupling coefficient of ≈7000 V cm⁻¹ Oe⁻¹ was later found in a 1–1 connectivity L–T (longitudinally magnetized and transversely poled) ME composite consisting of a PMN-PT single-crystal fiber and laser-treated amorphous Metglas alloy.⁹² 

The first work on the ME composites was reported at Philips laboratory about sintered BaTiO₃ (BTO)/CoFe₂O₄ (CFO), which were fabricated by unidirectional solidification.^84–86 The ME coefficient of BTO/CFO is much larger than that of single-phase multiferroic materials such as Cr₂O₃, which is 130 mV cm⁻¹ Oe⁻¹. These research studies did not attract too much attention at first, but they did motivate a significant theoretical effort on ME ceramic composites before 2000. In the early 2000s, the experiments on the ME effect of the giant magnetostrictive material Tb_1−xDy_xFe₂ (Terfenol-D) became a milestone in the development of bulk ME composites. After that, various ME bulk composites consisting of the ferroelectric phase, such as BTO, Pb(Zr, Ti)O₃ (PZT), Pb(Mg, Nb)O₃–PbTiO₃ (PMN-PT), and polyvinylidene fluoride (PVDF) and the ferromagnetic phase, such as CFO, Terfenol-D, and LaMnO₃ (LMO), have been investigated over the last few years.

In the last decade, various bulk ME composites such as ceramic composites, magnetic alloy-based composites, and polymer-based composites have been extensively investigated. To achieve bulk ceramic composites, co-sintering at high temperatures is generally used to get different combinations of ferroelectric oxides and magnetic oxides. The low ME coupling so far observed in ceramic composites is mainly due to the preparation problems such as inter-diffusion, reaction, and thermal expansion mismatch between two ME phases at high temperature. One of the main problems for the particulate ceramic composites is their leakage problem that results from the conductive ferrites. The core–shell structured particles with a high concentration of the ferrite-core well into the piezoelectric-shell, which can prevent the ferrite-core from direct contact during the sintering process, are an effective method to avoid this problem.^93,94 However, it is very difficult to prepare good core–shell structured particles with ferrite-core and piezoelectric-shell. More work was also done on other fabrication techniques to improve the properties of particulate ceramic composites.^95,96 High ME effect can be achieved in the 2–2-type laminate composite ceramics due to the elimination of the leakage problem. However, the ME signal strength induced from the piezoelectric layer is reduced because the ferrite layers are not conductive enough to serve as electrodes. To solve this problem, internal electrodes between piezoelectric and magnetostrictive layers are introduced to reduce the loss. Among bulk ME composites, magnetic alloy-based composites such as the laminate structures of Terfenol-D and different piezoelectric layers have shown the strongest ME effect. With further optimization for such magnetic alloy-based composites, a larger ME voltage coefficient can be obtained up to ∼57 V cm⁻¹ Oe⁻¹.⁹⁷ Furthermore, by optimizing structural designs for considering the mechanical behavior, a larger ME response was shown in some novel structures of the bulk ME composites such as an ultrasonic horn with more mechanical energy converted into electric energy.⁹⁸ However, due to the high saturation field and low permeability, Terfenol-D-based composites are not appropriate for low field applications. Instead, soft magnetic alloys, such as Metglas⁹⁹ and Permendur,¹⁸ are preferred. The polymer binders, which are used to bond the piezoelectric layer and magnetic alloys together, can drastically influence the ME response of the magnetic alloy-based composites. In order to eliminate the adhesive fatigue and aging effect of the interfacial binders, magnetic alloys can be directly deposited on top of the piezoelectric materials via various deposition techniques such as magnetron sputtering.^100,101 Due to the direct and tight bonding effect between the piezoelectric and magnetic phases, where the interfacial binders are not desired anymore in such composites, the ME response can be greatly enhanced. Polymer-based composites are also a great choice for realizing large ME coupling because they are easily fabricated with improved mechanical properties. Good stability during the fatigue measurement and the aging test has been demonstrated in a polymer-based composite with a PZT rod embedded in the Terfenol-D/epoxy matrix.¹⁰² Compared to the ceramic and magnetic alloy-based ME composites, the 0–3-type particulate polymer-based composites with magnetic particles embedded in the piezoelectric polymer phase attract wide interest due to the easy fabrication process.

Based on the product property, a ME material that was composed of piezoelectric oxide BaTiO₃ and magnetostrictive ferrites such as CoFe₂O₄ was developed by Philips in 1972.¹⁰³ By stacking and bonding PZT and Terfenol-D disks, Ryu et al. investigated a ME laminate composite with no chemical reaction involved in the fabrication process.¹⁰⁴ The schematic structure and photograph of the device are shown in Figs. 3(a) and 3(b). Figure 3(c) displays the measured ME voltage coefficients of PZT and Terfenol-D laminate composites as a function of the DC magnetic bias field. It was found that ME coefficient increases with the decreasing thickness of the PZT layer, which can be explained by the increasing compressive stress in the thinner PZT layer. A maximum value for the ME coefficient at 1 kHz of 4.68 V/cm Oe at room temperature was obtained. The theoretical ME coefficient equation for the laminate composite can be derived as follows: $dEdH=VoutHac×tp=2×g31×σ31pEHac(V/cmOe)$⁠, where g₃₁ is the piezoelectric voltage constant and $σ31pE$ is the compressive stress in the PZT layer. Therefore, a larger ME voltage coefficient can be acquired when the compressive stress in the PZT layer is higher. The theoretical calculation for the output voltage (dV/dH) and the ME coefficient (dE/dH) as a function of the thickness ratio (t_t/t_p) between Terfenol-D and PZT is presented in Fig. 3(d). The output voltage decreases, and the ME voltage coefficient increases with the increasing thickness ratio. Both values saturate when the thickness ratio is larger than 10.

Owing to the popularity of thin-film growth techniques that provide a way of depositing high-quality thin films and modify their properties by strain engineering, single-phase multiferroic thin films have been produced by utilizing different growth methods such as physical vapor deposition (PVD),^105,106 chemical vapor deposition (CVD),^107,108 atomic layer deposition (ALD),^109,110 and sol-gel, etc.¹¹¹ Research studies on thin-film ME materials have revealed a bunch of fascinating phenomena, and they have opened the door to design future miniaturized integrated devices such as high-density information storage and microelectromechanical systems (MEMS) devices. The majority of the published papers on single-phase thin films are devoted to hexagonal manganites such as Bi-based perovskites^112–115 and solid solutions of Pb-based perovskites.^116,117 Although the artificial FE/FM layer composites have been applied to many excellent devices such as tunable inductors, ME antennas, and high sensitivity magnetic sensors, they are not promising for two kinds of devices: multiferroic ME random access memories (MERAMs) and voltage-controlled magnetic tunnel junctions (MTJs). These applications require single-phase epitaxial multiferroic thin films, while ME composites are limited by the speed of acoustic waves and the tunneling current reduction. YMnO₃ belongs to the REMnO₃ oxide family, which is one of the typical manganite studies in thin-film materials. As reported,^118–120 YMnO₃ is a low-temperature multiferroic and room-temperature ferroelectric oxide, which can be explained by electrostatic and size effects. By utilizing rf magnetron sputtering, Fujimura et al. suggested YMnO₃ thin films as a new candidate for nonvolatile memory applications because of the absence of volatile components.¹²¹ Moreover, they are suitable candidates for future ferroelectric-gated field-effect transistors because they display a large electric polarization that is highly correlated with spin below 35 K.¹²² BiFeO₃ (BFO) has been widely studied in decades due to its interesting multiferroic and potential magnetoelectric properties: they have all ferroic orders at room temperature.^113,123,124 However, the cross coupling in single-phase BFO is very weak, and their mechanism is poorly understood. The interest in BFO thin films continues to grow due to their enhanced properties such as electric polarization and thickness-dependent magnetism compared to bulk BFO single crystal. The main disadvantages for devices based on BFO thin films are their leakage current, fatigue, and thermal decomposition near the coercive field. A new way for realizing room-temperature single-phase ME thin films was developed by Kumar et al.¹²⁵ The single-phase polycrystalline thin films are lead-based solid solution perovskites and synthesized by chemical solution deposition.

Kumar et al. reported a new synthesis process by using both chemical solution deposition and pulsed laser deposition (PLD) for realizing a novel single-phase perovskite ME thin film.¹²⁵ This novel single-phase thin film was composed of (PbFe_0.67W_0.33O₃)_0.2(PbZr_0.53Ti_0.47O₃)_0.8 (0.2PFW/0.8PZT) and was observed to have properties such as high dielectric constant, low dielectric loss. Through the strain effect via electrostriction and magnetostriction, a strong ME coupling was revealed from the ferroelectric hysteresis flop when an external magnetic field was applied. The switching of the polarization happens due to the lengthening of the relaxation time that strongly couples the polarization and spin, rather than because of the magnetically induced phase transition. Figure 4(a) shows the three-state logic switching of 0.2PFW/0.8PZT at room temperature. The switching from +P_r to −P_r is measured at 48 kV cm⁻¹, and magnetization is switched from +P_r to 0 at 0.5 T. The polarization curve at 0.5 T, which is a leaky linear dielectric, is displayed on an expanded scale in Fig. 4(a). The real and imaginary parts of the dielectric constant as a function of frequency at various magnetic fields are graphed in Fig. 4(b). The change in dielectric susceptibility, which requires strong coupling between spin fluctuations and polarization fluctuations, is due to the field dependence of the relaxation time. As the magnetic field increases, the correlation length of spin clusters increases, and hence, the fluctuation time decreases. Figure 4(c) shows the stretched exponential parameters that are utilized to obtain the relaxation time, which can also be calculated from the characteristic dielectric spectra in Fig. 4(b).

The design of single-phase thin films with a large ME coefficient has been a fundamental challenge for many years. Zhao et al. recently found a robust room-temperature ME thin film with strong ME coupling and a high Curie temperature of ∼1000 K.¹²⁶ The (001)-orientated Bi₅Ti₃FeO₁₅ thin films are grown by PLD. The short-range magnetic ordering at ∼620 K is due to the existence of Fe-rich nanodomains, which are characterized by the state-of-the-art aberration-corrected high-angle annular dark-field scanning TEM (HAADF STEM) and shown in Fig. 5(a). It can be clearly recognized in this image that Bi atoms (Bi₃Ti₄O₁₃)²⁻ are sandwiched by two stacked Bi layers (Bi₂O₂)²⁺, and individual columns of Ti/Fe atoms are in between these three layers along the [110] direction of the crystal. An atomic shift of the Ti/Fe columns from the central position can also be confirmed from the detailed analysis of the image, which is viewed as direct evidence of the ion-displacement driven ferroelectricity. Figure 5(b) shows the schematic diagram of the Aurivillius structure of BTFO. The ZFC-FC curves under different magnetic fields were measured to examine the magnetic properties of the BTFO film and are presented in Fig. 5(c). A weak ferromagnetic transition at ∼620 K is evidenced by the ZFC-FC curves above room temperature, as shown in the inset of Fig. 5(c). As indicated in Fig. 5(c), an enhancement of the magnetization on both ZFC and FC curves was observed for all magnetic fields. All these curves were accompanied by bifurcations, and the temperature for this feature decreases with the increasing field. These behaviors indicate a spin-glass-like phenomenon, which arises from the spin frustration caused by the strain effect at the film/substrate interface or from the competition between the antiferromagnetic and ferromagnetic transitions in the thin film.^127,128 In order to verify the ME coupling that is due to short-ranged magnetic ordering, the dielectric constant, electric polarization, and ME coupling coefficient were measured as a function of the magnetic field and are displayed in Figs. 5(d)–5(f). The typical frequency dependence of the dielectric constant and loss under zero field is shown in the inset of Fig. 5(d). As shown in Fig. 5(d), the magnetic field dependence of the dielectric constant at 10 kHz was also measured at room temperature. A continuous increase in electric polarization values as the magnetic field increases was observed at temperatures of 10, 50, 100, and 300 K, as shown in Fig. 5(e). The increase in the electric polarization under an increasing magnetic field, especially at low temperatures, indicates the coupling between two ferroic orders. As presented in Fig. 5(f), a maximum value of ∼400 mV/(Oe cm) for the room temperature ME coefficient at zero magnetic fields was achieved. This is due to the spin canting of magnetic-ion-based nanodomains via the Dzyaloshinskii–Moriya interaction and was directly measured from the magnetic-field-induced electric voltage. The inset shows the M–H loop with a saturated magnetic moment of ∼8 emu/cm³ at room temperature, which evidences the weak ferromagnetism in the thin film.

The development of both theoretical modeling approaches and experimental fabrication techniques has assisted in the discovery of new ME thin-film composites with much larger coupling coefficients. During the last decade, many efforts have been put into the investigation of ME thin-film heterostructures consisting of piezoelectric and magnetostrictive orders with strong ME coupling. Advanced equipment and techniques make it feasible to fabricate and characterize high-quality ME thin-film heterostructures with a smooth interface between FE and FM layers for realizing practical devices based on ME effect. In comparison with bulk materials, thin-film ME composites have some distinct advantages such as low interface losses and complementary metal–oxide–semiconductor (CMOS)-compatible fabrication process. Piezoelectric thin films also require much lower voltage to achieve the same level magnitude of electric fields. In addition, the atomic-level combination, precise control of the lattice matching, and epitaxial film growth for ME phases can be achieved. 2–2-type structures are the most investigated configuration in thin-film ME composites as they have a reduced leakage current and are easy to be synthesized. There are several factors that affect the cross coupling in thin-film ME heterostructures: properties of FE and FM materials, substrate, volume fraction, configuration geometry, etc. The selection of appropriate piezoelectric and magnetostrictive thin films is particularly significant in getting a composite with large ME coupling for practical devices. Some typical piezoelectric and magnetostrictive thin films used as constituents of ME composites are listed here: ZnO,¹²⁹ AlN,¹³⁰ AlScN,¹³¹ Metglas,^132,133 FeGaB,¹³⁴ FeGaC,¹³⁵ and CoFeC.¹³⁶ Among all piezoelectric materials used for thin-film ME composites, AlN seems to be the most favorable choice with respect to film ME devices due to the compatibility with MEMS processes, although the piezoelectric response is poor. AlN is preferable for MEMS resonators at high operation frequency because of its high acoustic velocity and excellent stability at high temperatures. However, it has a low electromechanical coupling coefficient (K²) of less than 1%. Recently, AlScN thin films with scandium (Sc) doped were used to fabricate MEMS devices and demonstrated a significantly enhanced K² value up to 3.8%–4.5%. As for the thin-film piezomagnetic phase, the largest piezomagnetic coefficients have been found in amorphous FeGaB and FeGaC films. They have a record high piezomagnetic coefficient of 9.71 ppm/Oe and a high saturation magnetostriction constant of 81.2 ppm, which are critical for achieving strong ME coupling in thin-film ME composites.

In the last few decades, ferromagnet-metalloid alloy films have been broadly used in multifunctional ME devices due to their excellent properties, such as soft magnetism, large magnetostriction constant, and industrial-scale fabrication process. Wang et al. reported on the magnetostrictive behavior and microwave properties of a series of (Fe_0.5Co_0.5)_xC_1−x films on silicon substrates.¹³⁶ A high saturated magnetostriction constant of 75 ppm, a high piezomagnetic coefficient of 10.3 ppm/Oe, and a low coercivity of less than 2 Oe were obtained in the CoFeC thin films. Their excellent properties arise from the coexistence of nanocrystalline and amorphous phases. As shown in Figs. 6(a)–6(f), the high-resolution transmission electron microscope (HRTEM) was used in different CoFeC samples to investigate the change in their nanostructures with carbon doping. Bright field scanning transmission electron microscopy (STEM) and the corresponding energy-dispersive x-ray spectroscopy results for Fe, Co, and Ta elements are presented in Figs. 6(a) and 6(b), which indicate that these atoms are distributed homogeneously. As presented in Figs. 6(d)–6(f), the FFT images change from a diffraction matrix to a plurality of diffraction rings with a few dots and then to a weak diffraction as the carbon content increases from 0% to 4.4% and then to 13.2%. These results confirm that the structure of CoFeC films transforms from the ordered lattice to the intermediate nanostructure and then to the disordered amorphous state. Liang et al. did a systematic investigation on the various properties of FeGaC films over a wide carbon content range.¹³⁵ Figures 6(g) and 6(h) show the carbon content dependence on magnetostriction constants of FeGaC thin films as a function of the biased magnetic field. As the carbon content increases, the saturation magnetostriction constants of FeGaC films first increase to a maximum value of 81.2 ppm and then decrease to 22 ppm. The piezomagnetic coefficients also have the same trend and have a maximum value of 9.71 ppm/Oe. The ΔE effect of FeGaB and FeGaC films with the increasing thickness was measured and is displayed in Figs. 6(i) and 6(j). As the film thickness increased from 100 to 500 nm, the maximum ΔE of FeGaB films decreased from 123 to 62 GPa, while the value of FeGaC films increased from 89 to 119 GPa. This behavior makes FeGaC films better candidates for microwave device applications, such as ME antennas, tunable inductors, and magnetic sensors.

Although many papers have been published on magnetostrictive thin films, there are still several opportunities and challenges that need to be addressed in the future. The piezomagnetic coefficient, coercive field, and ferromagnetic resonance (FMR) linewidth are the essential properties in developing novel thin-film magnetostrictive materials. The summary of a variety of magnetostrictive materials that have been investigated so far in terms of these properties is presented in Fig. 7. The desired magnetostrictive materials are required to have a large magnetostriction constant, high piezomagnetic coefficient, low coercive field, and narrow FMR linewidth. The focus of studies in rare earth magnetostrictive materials tends to be on the light rare-earth-based materials, such as SmFe, because of the shortage of heavy rare earth sources. FeGa and FeCo systems, which have large magnetostriction constant and low coercivity, have been extensively investigated and are the most promising candidates for rare-earth-free magnetostrictive films. Apart from the development of new materials, novel structure designs such as multilayers consisting of the soft magnetic layer and large magnetostrictive layer are also promising for ME devices.

One of the hottest research studies focusing on spintronics and multiferroics is the control of magnetization in ferromagnetic materials by applying an electric field. The realization of this behavior in ME composite thin films can be achieved through charge-driven, exchange bias-induced, or strain-mediated ME coupling. For the charge-driven ME effect in the 2–2-type laminate ultrathin films, the accumulation of charges results in a change in the interface magnetization due to spin-dependent screening of an electric field. Such a charge-driven ME effect has been obtained in the ME heterostructures consisting of the ferromagnetic film and piezoelectric layer by both first-principles calculations^137–139 and experiments.^140,141 Rondinelli et al. demonstrated a linear ME effect, which arises from a carrier-mediated mechanism, of the interface between a dielectric and a spin-polarized metal.¹³⁷ They elucidated this effect at the interface of SrRuO₃/SrTiO₃ and illustrated its origin by using first-principles density functional calculations. The spatial coexistence of magnetism and dielectric polarization also suggests a new type of interfacial multiferroic. By applying the first-principles calculations to ferromagnetic Fe(001), Ni(001), and Co(0001) ultrathin films in the presence of an electric field, a surface ME effect was revealed due to spin-dependent screening of the electric field at the metal surfaces.¹³⁸ Significant changes in the surface magnetization and magnetocrystalline anisotropy of the ferromagnetic metals were discovered because of the presence of the external electric field. The density and spin polarization of the charge carriers near the Fermi level of the films determine the sign and magnitude of the surface ME coefficient.

Reversible control of the magnetic properties of a PZT (250 nm)/LSMO (4 nm) heterostructure was demonstrated by Molegraaf et al. via an electronic charge-modulation ME effect.¹⁴⁰ The magnetism of the LSMO thin film, which includes the modulation of the magnetization amplitude and onset of ferromagnetic order, can be switched on or off by applying an electric field in the composite system. This system can also be utilized to modulate spin polarization of itinerant magnetic systems due to the change in the band filling of the magnetic material based on this carrier-driven mechanism. The sensitivity of a strongly correlated LSMO film to a competing electronic ground state is used to realize the charge-driven ME effect in this heterostructure. More recently, Nan et al. observed a strain and charge co-mediated ME coupling in ultrathin ferromagnetic/ferroelectric heterostructures with significantly enhanced ME coupling.¹⁴¹ They demonstrated the quantification of strain and surface charge co-mediated ME coupling on the ultrathin Ni_0.79Fe_0.21/PMN-PT interface by using a control sample of Ni_0.79Fe_0.21/Cu/PMN-PT with only strain-mediated ME coupling. A large effective magnetic field change of 375 Oe was induced by the application of a high voltage in the heterostructure, which is due to the existence of the surface charge at the interface. A strong correlation of the pure surface charge modification of magnetism to the polarization of PMN-Pt was established by distinguishing the ME coupling mechanisms. As shown in Fig. 8(a), a Cu layer is inserted in between the NiFe ultrathin film and the PMN-PT substrate to eliminate the screening charge at the interface. Therefore, a symmetric “butterfly” curve of the effective FMR field was observed due to the pure strain mediated ME coupling. As a comparison, in Fig. 8(b), an asymmetric curve of the effective FMR field was achieved when the isolating Cu layer was removed. The maximum H_eff tunability was increased from ∼202 to ∼375 Oe. More interestingly, at the zero electric field, the effective FMR field of NiFe/Cu/PMN-PT remained unchanged due to the linear piezoelectric effect, while in NiFe/PMN-PT, there were two effective FMR fields that were caused by the remnant electric polarization of PMN-PT. The magnetic anisotropy was modified by the polarization-induced surface charge on the NiFe/PMN-PT interface via the screening charge effect. Thus, a strain and charge co-mediated ME coupling could exist on the NiFe/PMN-PT interface. The angular dependence of the FMR field was measured under different electric fields and is shown in Figs. 8(c)–8(f) to further our understanding of the charge-driven ME effect. As shown in Figs. 8(c) and 8(e), a uniaxial magnetic anisotropy with the easy axis along the [100] direction was indicated for NiFe/Cu/PMN-PT with an impulse electric field of ±8 kV/cm. There was no magnetic anisotropy change for these two cases, which was consistent with the symmetric “butterfly” curve in Fig. 8(a). However, under an electric field of 2 kV/cm, the in-plane magnetic anisotropy was tuned with a value of ∼45 Oe, which was in accordance with the FMR field response in Fig. 8(a). The same uniaxial anisotropy behavior was observed in NiFe/PMN-PT, as displayed in Figs. 8(d) and 8(f). However, in comparison with the case under the −8 kV/cm electric field, a high effective FMR field under the +8 kV/cm impulse electric field was achieved. This indicated an out-of-plane magnetic anisotropy change that was induced by the surface charge. The co-existence of strain and charge co-mediated ME coupling in ferromagnetic/piezoelectric heterostructures could facilitate the development of non-volatile ME devices with significantly enhanced performance.

The exchange bias is the exchange interaction between the antiferromagnet and the ferromagnet at their interface and has been widely used in magnetic recording to pin the state of the readback heads. This effect has also been employed for manipulating the magnetic properties by applying an electric field in ME composite systems. The idea of applying the exchange bias in the ME composite structures comes from the research studies on the single-phase ME materials with antiferromagnetic order, as well as the electric field control of exchange bias in ME composites. The perpendicular exchange bias of the ME heterostructure Cr₂O₃(111)/(Co/Pt)₃ was electrically reversed after field cooling to below the Neel temperature.¹⁴² Based on this mechanism, Chen et al. proposed novel voltage-controlled spintronic devices with low power consumption and nonvolatile logic states: magnetic random access memory cells and magnetic logic devices.¹⁴³ The magnetotransport properties of Permalloy and the exchange bias of YMnO₃/Permalloy could be directly controlled by an electric field.¹⁴⁴ However, all these phenomena were observed at low temperatures. Later on, by combining the multiferroic BFO and ferromagnetic layer (e.g., CoFeB,¹⁴⁵ LSMO¹⁴⁶), the magnetic properties could be controlled by an electric field at room temperature, which was realized through the ferroelectric–antiferromagnetic coupling or the strain-mediated ME coupling. In 2011, Liu et al. demonstrated the electric field control of exchange coupling and the coercive field in FeMn/Ni₈₀Fe₂₀/FeGaB/PMN-PT heterostructures at room temperature.¹⁴⁷ This deterministic magnetization switching and dynamic magnetization rotation could be explained by the competition between the unidirectional anisotropy accompanied by the exchange coupling and the electric field-induced uniaxial anisotropy. The exchange biasing of ME composites was also utilized to replace the external DC magnetic bias fields in ME magnetic sensors.¹⁴⁸ The maximum piezomagnetic coefficient occurs at zero magnetic fields by shifting the magnetostriction curve with the exchange bias field. More recently, Toyoki et al. reported the isothermal ME switching of the perpendicular exchange bias in Pt/Co/α-Cr₂O₃/Pt stacked films by the simultaneous application of electric and magnetic fields.¹⁴⁹ They also addressed the switching mechanism by doing pulse voltage measurements, which indicated the dominant of the antiferromagnetic domain propagation during the switching process.

Magnetoelectric random access memories (MERAMs) combine the advantages of ferroelectric random access memories (FeRAMs) and magnetic random access memories (MRAMs), which have the electric field-induced nonvolatile magnetization switching. Near 180°, magnetization switching at room temperature was first realized by utilizing the electric field modulating the exchange bias in novel atomic force microscopy (AFM)/FM/FE heterostructures.¹⁴⁷ The angular dependence of the exchange bias under different electric fields is shown in Fig. 9(a). The exchange bias H_ex was highly affected by the θ angle of the electric field between 0° and 90°. A maximum exchange bias shift of 42 Oe was achieved at θ = 55°. As displayed in Fig. 9(b), the exchange bias field was measured as a function of the switching number of the electric field at 0 and 6 kV cm⁻¹ to confirm the repeatability of the phenomenon, which indicates a repeatable and robust exchange bias change. The electric field control of magnetization in the time domain under a bias magnetic field of 28 Oe at θ = 55° is presented in Fig. 9(c). When the electric field was reduced from 6 to 4 kV cm⁻¹, near 180°, deterministic magnetization switching was realized and illustrated by the magnetization loops in the inset of Fig. 9(c). A continuously reversible magnetization switching could be realized by employing a magnetic impulse field. Figure 9(d) shows the dynamic magnetization switching in the ferromagnetic film as a response of a square wave of the electric field and a magnetic pulse at an external magnetic bias field of 28 Oe. The electric field control of the exchange bias and deterministic magnetization switching at room temperature in AFM/FM/FE multiferroic heterostructures paves a new way for electric field writing of novel memory and spintronic devices.

Compared to the charge-mediated and exchange bias-mediated ME coupling, the strain-mediated ME coupling is more exploited in many novel ME devices. As an electric field is applied to the ferroelectric phase, the induced strain due to the piezoelectric effect would be transferred to the magnetic phase, which would change the magnetic anisotropy via magnetostriction and vice versa. It is well known that the ME effect in bulk ME composites is via elastic interaction. However, there are a variety of mechanisms that are responsible for the ME coupling in the thin-film ME composites. For example, residual stress due to the lattice or thermal expansion mismatch between the film and the substrate of the thin-film ME composites is always considered for understanding the ME response. The theoretical results of the phase electric field model clarify that the electric polarization induced by the magnetic field is extremely affected by substrate constraint, morphology, and film thickness, which indicates that the ME coupling in nanocomposite films can be controlled by numerous degrees of freedom.^150,151 It is understood that the strain-mediated ME effect could be suppressed by the substrate-imposed mechanical clamping. More work on the influence of the constraint stress on ME coupling is required to thoroughly explore the ME mechanism in the thin-film ME composites.

In the 2–2-type thin-film laminate composite of AlN (∼1.8 µm)/FeCoSiB (∼1.75 µm) heterostructure, which was deposited on Si substrates via magnetron sputtering, an extremely high ME voltage coefficient of 737 V cm⁻¹ Oe⁻¹ at the resonance of 753 Hz was obtained.¹³² Most works of electric field tuning of magnetism are reported in the 2–2-type film-on-substrate system with a ferroelectric substrate/magnetic film heterostructure. The ferroelectric substrates include single crystals (e.g., PMN-PT, PZN-PT, and PZT) or ceramics, and the magnetic films involve oxide-based films (e.g., LSMO, Fe₃O₄, and CFO) and metallic films (e.g., Ni, Fe, and FeGaB). In such ME heterostructures, the strain-mediated ME effect was investigated by electric-field-induced changes in different magnetisms, such as magnetic anisotropy, magnetization, and coercive field. The first demonstration of changes in M–H loops induced by applying the electric field was observed in the LSMO/BTO system.¹⁵² Eerenstein et al. observed a large magnetic change in LSMO films due to the strain coupling via ferroelastic BTO domains. Later on, Thiele et al. demonstrated the strain-mediated modification of magnetization in the LSMO/PMN-PT composite heterostructure by application of an electric field.¹⁵³ The butterfly-shaped M–E loop, which corresponds to the piezo-strain curve of the piezoelectric substrate, clearly confirms the significant role of the elastic strains for the ME coupling in the heterostructure. Ferrite Fe₃O₄ and CFO films grown on the PMN-PT substrate were also demonstrated for large and reversible changes in magnetization under an electric field.¹⁵⁴ Wang et al. reported a remarkable magnetism change in CFO/PMN-PT epitaxial ME heterostructures due to the polarization reorientation-induced strains. The maximum strains along in-plane 100 and in-plane $01̄1$ were found to be −1.3% and 0.64%, respectively. A large irreversible change in the magnetic coercivity of 580 Oe was observed along the in-plane 100 direction. After annealing at 470 K, the magnetic properties recovered their original status. The schematics of the polarization reorientation-induced strain of single-crystal PMN-PT within various planes are illustrated in Figs. 10(a)–10(c). As shown in Fig. 10(b), the four possible polarization projections in the (⁠$x⃗,y⃗$⁠) plane will be degenerated into two directions along $x⃗$ under application of a sufficiently large electric field. Figure 10(c) displays a similar situation for the (⁠$y⃗,z⃗$⁠) plane. A comparison of XRD results before and after poling is presented in Fig. 10(d), which indicates the transformation of ferroelectric domains in the PMN-PT substrate. Thus, the strains in the ME heterostructure are induced. Figure 10(e) summarizes remanence-to-saturation magnetization ratio M_r/M_s vs electric field along a different axis. When the electric field is larger than 5 kV cm⁻¹, M_r/M_s along $y⃗$ became larger than that along $x⃗$ that means the magnetic easy axis rotated from $x⃗$ to $y⃗$⁠. In addition, the change in M_r/M_s along $y⃗$ was much larger than that along $x⃗$⁠. This is also confirmed by the larger calculated strain along $y⃗$⁠. Both the values and changes of M_r/M_s along $z⃗$ were small over the entire electric field range, which is due to the difficulty in changing the magnetic shape anisotropy of thin-film architecture. Figure 10(f) shows the change in the magnetic coercive field as a function of the electric field along various directions. These data are inconsistent with the results of M_r/M_s in Fig. 10(e).

Analogously, various metallic thin films, which are normally polycrystalline or amorphous, have been used to realize the strain-mediated ME coupling.^100,101,155 For example, Liu et al. recently reported preliminary results on the electric field-induced change of magnetization and FMR properties on a novel amorphous FeGaB/PZN-PT(001) ME heterostructure.¹⁰¹ As shown in Fig. 11(a), normalized magnetic hysteresis loops of amorphous FeGaB/PZN-PT(001) under different electric fields indicate that a large effective magnetic field is induced by the application of electric fields. The FMR spectrum under various electric and magnetic fields were measured and are presented in Fig. 11(b). By controlling the applied electric and magnetic bias fields, any FMR frequency within the range between 2.8 and 15.9 GHz can be achieved. Hysteresis loops of electric field dependence of FMR frequency under a magnetic bias field of 50 Oe and FMR field at 12 GHz are shown in Fig. 11(c). Due to the linear converse piezoelectric effect of PZN-PT single crystal, these two loops exhibit a linear behavior at low electric fields. A sudden change in both FMR field and frequency was observed when the electric field reached a critical threshold of ∼5.8 kV cm⁻¹, which implies the appearance of rhombohedral-to-orthorhombic phase transition in PZN-PT(011) with a large lattice change and giant ME coupling effect. Agreeing with Fig. 11(c), Fig. 11(d) shows the normalized magnetization loop as a function of the electric field under a magnetic bias field of 200 Oe. The memory-type dynamic magnetization switching with an impulse electric field is demonstrated with two stable states, as displayed in Fig. 11(e). The demonstrated giant FMR tunability and nonvolatile dynamic magnetization switching through strain-mediated ME coupling make FeGaB/PZN-PT composites great candidates for next-generation voltage-tunable devices. More recently, Cui et al. successfully manipulated the magnetism of a Ni ring with a 1000 nm outer diameter, 700 nm inner diameter, and 15 nm thickness by using surface electrodes to produce localized strain in a Ni ring/PZT thin-film (1 µm) ME bilayer.¹⁵⁵ One of the “onion” domain walls was moved by applying a voltage to the electrodes. This demonstration encourages the development of novel strain-mediated ME devices with complex architectures. The conceptual schematic of the Ni ring/PZT heterostructure is shown in Fig. 12(a). A highly localized strain can be generated by applying a voltage to one pair of top electrodes. The inset presents the average principal strain field under different configurations. As shown in Fig. 12(b), the domain structure of a Ni ring under a 1200 ppm biaxial strain was simulated by using a micromagnetic model based on the ME coupling and Landau–Lifshitz–Gilbert (LLG) equation. The formation of an “onion” state in the initialized Ni ring is observed in Fig. 12(b). When the biaxial strain was applied in the direction of θ = 30°, the magnetization aligned with the direction of compressive strain and rotated counterclockwise by 60°. The magnetization reversed to its original state when the strain was removed. The atomic force microscopy (AFM) image of the fabricated device is shown in Fig. 12(c), and the surface profiles of the Ni ring and PZT thin film, as indicated in Fig. 12(c), are presented in Fig. 12(d). Magnetic force microscopy (MFM) images of the Ni ring with 0 and 25 V applied to the A–A electrodes and 25 V applied to the B–B electrodes are displayed in Fig. 12(e), respectively. By using patterned electrodes on top of the Ni ring/PZT thin film heterostructure, the magnetic domain of the Ni ring could be rotated forward and backward.

As a significant component of wireless communication systems, the antenna is ubiquitous in our daily life. However, a critical challenge of the conventional antennas driving by electrical current or voltage is the antenna volume miniaturization. For conventional antennas, the dimension should be at least one-tenth of the free space wavelength of electromagnetic (EM) waves, to keep a good radiation efficiency and enhance the directivity.^34,156 This brings difficulty in compact antenna designs, which require small antenna volume and high efficiency at the same time.

The ME antenna with mechanical strain as intermediation brings a new approach to solve this problem for the impressive miniaturization, low power consumption, and high theoretical radiation efficiency.^157,158 The practical ME antenna based on the suspended acoustic resonator was first designed by Nan et al. for very-high-frequency (VHF, 30–300 MHz) band and ultra-high-frequency (UHF, 0.3–3 GHz) band in 2017.³² In addition, the ME antenna based on the bulk surface acoustic wave (SAW) resonator was demonstrated by Dong et al. for very-low-frequency (VLF, 3–30 kHz) band in 2020.³³ Those ME antennas utilize the acoustic resonance inside the resonator, the wavelength of which is five orders of magnitude smaller than the wavelength of the EM wave at the same frequency, leading to a several orders smaller volume over conventional antennas.

Based on the microelectromechanical systems (MEMS) technology, the practical ME antennas for VHF (Very High Frequency, 30–300 MHz) band and UHF (Ultra-High Frequency, 300–3000 MHz) band were fabricated, as shown in Fig. 13. Depending on the different resonance modes, the ME antennas were named the nano-plate resonator (NPR) antenna [Fig. 13(a)] and the thin-film bulk acoustic resonator (FBAR) antenna [Fig. 13(d)]. For both antennas, the resonators were consisted of FeGaB as the ferromagnetic layer and AlN as the piezoelectric layer due to the high magnetostriction coefficient, piezoelectricity, and Q-factor of these two materials. The electric driving field is applied across the piezoelectric material, so the generated acoustic wave propagates in solids, which is called the bulk acoustic wave (BAW). However, the resonance directions of the two types are different. For NPR antenna, the d₃₁ mode is utilized. Therefore, the acoustic resonance happens in-plane, and the resonance frequency is determined by the width or length of the resonator. While at the FBAR mode, the acoustic resonance is out-of-plane due to the d₃₃ resonance mode. Hence, the antenna thickness contributes to the operation frequency. In this way, designers have great flexibility in choosing the operation frequency. According to ME coupling, the magnetic domain rotation is the radiation source of the ME antennas. During the receiving process, the magnetic field of the EM wave is detected by the ferromagnetic material, leading to an induced mechanical strain in the ferromagnetic layer based on the magnetostriction. This strain is transferred to the piezoelectric layer and results in an ac voltage output, according to the direct ME coupling. On the other hand, during the transmitting process, the ME antenna is driven by the ac input electric field, and an oscillation strain is generated inside the piezoelectric layer. Similarly, this strain is transferred to the ferromagnetic layer and leads to an inverse magnetostriction effect, which can radiate the EM wave. Hence, the ME antenna performs as a magnetic dipole, which was also proved by the measured antenna polarization in Ref. 153. In Ref. 153, an NPR antenna for 60 MHz and an FBAR antenna for 2.5 GHz were reported, as shown in Figs. 13(b) and 13(e), respectively. In Fig. 13(c), a peak induced output voltage of 180 µV was observed at resonance from NPR antenna, with an ME coupling coefficient of 6 kV/Oe cm. From the FBAR antenna, an antenna gain of −18 dBi was calculated by using the gain comparison method at resonance, as shown in Fig. 13(f), and the efficiency was calculated as 0.403%. By comparing with the control devices, both NPR and FBAR antennas show several orders of magnitude stronger output signals, which proves that the antenna performance is dominated by the ME coupling.

To improve the antenna performance, a solidly mount resonator (SMR) antenna was introduced by adding a Bragg reflector under the acoustic resonator of the FBAR antenna by Liang et al. in 2020.³⁷ The Bragg reflector is an acoustic wave reflector, with which the acoustic wave can be reflected back to the FBAR resonator instead of being dissipated into the substrate. According to this, a 10-dB signal enhancement was detected with the same experiment setup with the released FBAR antenna. Moreover, the efficiency enhancement is also related to the more orderly aligned magnetic domain. For the released FBAR antenna, the resonator always curved up or down due to the unavoidable mechanical stress of the thin film, leading to a disordered magnetic domain inside the curved film. Hence, the equivalent magnetization is decreased by the disordered magnetic domain. However, the ME resonator of the SMR antenna is totally fixed to the substrate; therefore, the magnetic domain can be easily aligned to one direction.

Based on the NPR antenna, Chen et al. designed an antenna array for implantable wireless communication.³⁸ At present, the 402–405 MHz band is picked for medical implant communication service (MICS). Therefore, the FBAR structure is not suitable for this band because the ME composite becomes too thick at this frequency range. However, the main problem of the NPR antenna is the high electrical impedance. Hence, an antenna array with 16 elements connected in parallel was utilized for impedance matching. An antenna gain of −54.82 dBi was achieved at the resonance frequency of 371 MHz. Compared to the state-of-art compact antennas for implantable devices, the volume of the ME antenna is about three orders smaller. Moreover, another benefit is the stable operating frequency. For conventional antennas, the resonance frequency is related to the permittivity of the environment, but for the ME antenna, it is only decided by the acoustic wave. Hence, the ME antenna has a constant operating frequency inside the human body.

In conclusion, ME antennas provide a two orders smaller antenna volume than conventional compact antennas. Therefore, they have a great potential for applications such as wireless medical implants, wearable systems, and portable devices. Based on the flexibility of the frequency design, the ME antenna is also a good choice for multiband antennas by changing the geometric dimensions of each resonator in one ME antenna array.¹⁵⁹ Moreover, the MEMS fabrication process of ME antennas is compatible with the CMOS circuits, benefitting the integration.

Since the free-space wavelength of VLF (Very Low Frequency, 3–30 kHz) is in the range of 10–100 km, physically huge radiation towers with large power consumption become necessary for electrically small VLF antennas to reach an acceptable radiation efficiency.³³ For example, the U.S. Navy’s VLF transmitter Cutler operates at 24 kHz, which spreads over 8 km² and requires 1.8 MW power as input. For this reason, even with the good penetration into the conductive ground and water, the VLF band can only be utilized in the one-way transmission from the base station to the terminals. To solve this problem, more and more attention is paid to VLF ME antennas recently.

In 2016, the idea of the VLF ME antenna was first put forward by Sun and Li,¹⁶⁰ and a practical device was reported by Dong et al. in 2020.³³ This VLF antenna consists of Metglas as the ferromagnetic layer and PZT as the piezoelectric layer, as shown in Fig. 14(a). Unlike VHF antennas, interdigital electrode (IDE) fingers were utilized in VLF antennas. Therefore, the electric field is applied on the surface of the PZT fibers, resulting in a surface acoustic wave (SAW), and the resonance frequency is determined by the pitch size of the IDE fingers. The radiation source of the VLF antenna is the magnetic domain rotation, controlled by the ME coupling, which is the same as the VHF and UHF antennas. A clear receiving peak was detected experimentally at the resonance frequency of 23.95 kHz with a great signal-to-noise ratio (SNR) of 92.3 dB, as shown in Fig. 14(c). In Fig. 14(d), a low limit of detection (LoD) of 180 fT was achieved, which means a high sensitivity to the electric field and allows long-distance communication. In Ref. 154, a maximum transmitting distance of 120 m was reported. Additionally, with the antenna array structure to increase the radiation intensity and low noise receiver, the distance could reach up to ∼10 km with the theoretical model.

To even improve the antenna performance, the non-linear antenna modulation (NAM) was developed by the Northeastern group.³³ This NAM takes advantage of the nonlinear time-variant relation between mechanical strain and magnetization by mixing the data signal and carrier signal directly at the electromagnetic resonance in the antenna without external mixers. The second harmonic output signal from the antenna is utilized for the modulation. Therefore, different from the conventional modulation methods, the data rate of which is limited by the linear Q-factor and bandwidth, the ME antenna with NAM outputs a stronger sideband signal for the high data rate.

With the development of the ME composite with a high coupling coefficient, magnetic-field sensors become more and more attractive as an alternative to the recent sensors depending on Hall effect, superconducting quantum interference device (SQUID), fluxgate, and so on due to the low power consumption and operation at room temperature. Nowadays, the research focuses of ME sensors are increasing the sensitivity at low frequency and extending the operation bandwidth.

Depending on the sensing principles, the ME magnetic sensor can be classified into three categories. The first type is directly based on the ME coupling, which is usually used for ac field detection.^161–165 Here, the voltage output from the ME composite is used to represent the magnitude of the magnetic field. Hence, the sensitivity is determined by the ME coefficient, which is related to the magnetic bias field and operation frequency. For example, a magnetic field of 23 nT was detected by Zhao et al. at the mechanical resonance frequency of 333 Hz with a ME coupling coefficient up to 1.8 V/(Oe cm) under a dc bias field of 90 Oe.¹⁶¹ Yarar et al. introduced a low-temperature deposition method of the AlN thin film with a reversed deposition sequence to improve the quality of each layer of the ME composite in 2016.¹⁶³ Consequently, the LoD was improved to 400 fT/$Hz$ at the resonance frequency of 867 Hz. Chu et al. reported a bulk ME sensor in 2016.⁹² The LoD reaches as low as 135 fT at the resonance frequency of 23.23 kHz. Here, the ME composite was consisted of PMN-PT single crystal and Metglas fibers in novel (1–1) connection. The Metglas alloy was laser-treated for a high mechanical Q-factor due to the nanocrystallization, followed by a reduced resonance loss and enhanced ME coupling coefficient. Additionally, both demagnetization and eddy current loss were reduced by the (1–1) connection. Another direct measuring ME sensor with a high ME coefficient [1704 V/(Oe cm)] and low equivalent magnetic noise (92 fT/$Hz$⁠) at mechanical resonance (6862 Hz) was reported by Turutin et al. in 2018,²¹⁸ which used a y + 140° cut lithium niobate plate and Metglas as the ME composite. An annealing process was introduced for the preparation of the antiparallel polarized bidomain LiNbO₃ crystal for the high sensitivity.

However, since the ME coefficient decays rapidly at off-resonance frequencies, the low sensitivity for dc or low-frequency field becomes the main issue of the first type of the ME sensor. One solution to this problem is converting the dc magnetic field up to the mechanical resonance frequency of ME sensors,^166,167 which is the second type of the ME sensor. The first ME sensor with frequency conversion was introduced by Jahns et al.,¹⁶⁶ by using the nonlinear characteristic of the magnetostriction curve. The sensitivity was enhanced by around three orders down to 1 nT/$Hz$ for low-frequency detection. However, additional noise was also modulated to the resonance frequency, which impairs the sensitivity. In 2018, Hayes et al. reported an electrically modulated ME sensor based on a cantilever beam with a pickup coil for signal readout.²⁰ Two high order modes of resonance at 515.7 and 520.7 kHz were utilized to enhance the induced voltage of the cantilever. The minimum detectable signal of 1.2 nT at 200 mHz was achieved without the magnetic bias field. Chu et al. reported an amplitude modulation method (AMM) for the quasi-static magnetic field in 2019.²¹⁹ The low frequency magnetic signal is demodulated from the output of the ME sensor at the resonance frequency. Therefore, the measured LoD is 100 pT at 100 mHz.

Another sensing theory for the dc or low-frequency magnetic field is based on the delta-E effect as the third type of the ME sensor.^19,168–171 The delta-E effect represents Young’s modulus change in the magnetostrictive materials with the magnetization under an external magnetic field. Hence, the dc signal is mixed up to the resonance frequency, and the low-frequency 1/f noise and acoustic disturbance are excluded from the measurement. An extremely low magnetic noise bulk ME sensor was demonstrated by Wang et al. in 2011,¹⁶⁴ with the ME composite consisted of Metglas and the PMN-PT fiber. The resonance frequency was set to 1 kHz with a maximum ME coefficient of 52 V/(Oe cm). The noise sources of this ME sensor are dielectric loss noise and DC leakage resistance noise. The measured equivalent magnetic noise is 5.1 pT/$Hz$ at 1 Hz. The first integratable magnetic sensor based on delta-E effect was reported by Gojdka et al. in 2011¹⁶⁸ by sputtering a FeCoSiB layer on a Si cantilever. Then, in 2013, Nan et al. demonstrated a sensor combining ME effect and delta-E effect with a resonance frequency of 215 MHz,¹⁹ as shown in Fig. 15. The sensor consists of the FeGaB/Al₂O₃ multilayer as the magnetostrictive layer, AlN as the piezoelectric layer, and Pt as interdigital electrodes. With an applied magnetic field, a resonance frequency shift occurs due to Young’s modulus change from delta-E effect, translated to an input admittance change at driving frequency, as shown in Figs. 15(c) and 15(d), which is the readout of the ME sensor. A limit of detection of 300 pT was observed under a dc bias field of 5 Oe, as shown in Fig. 15(e), which was 600 pT under the zero bias field. Additionally, another method to represent the sensitivity is using the frequency shift, expressed as $dfdH$⁠, where f is the resonance frequency and H is the measured field. Since the magnetostriction coefficient of the magnetostrictive layer is usually several orders lower than Young’s modulus change due to the delta-E effect, the frequency shift induced by magnetostriction is negligible. A sensitivity of 100 Hz/mT with a limit of detection of 12 nT/$Hz$ at 10 Hz was reported by Jahns based on a ME cantilever.¹⁶⁹ Li et al. demonstrated a ME sensor based on the AlN/FeGaB resonator with a dc field sensitivity of 2.8 Hz/nT and a limit of detection of 800 pT.¹⁷¹ 

Magnetic random-access memory (MRAM) is usually regarded as a nonvolatile “universal memory,” which has the potential to replace all kinds of the state-of-art memories, including static random-access memory (SRAM), dynamic random-access memory (DRAM), cache memory, and flash memory, due to the high reading/writing speed and endurance.^42,177,178 However, for most of the MRAM driving by current, such as spin-transfer-torque (STT), the high writing energy still limits the area density due to the requirement of a large access transistor for high writing current, followed by a heating dissipation problem.^42,173,174 Magnetoelectric RAM (MeRAM) is a reasonable solution to this problem by using voltage control of magnetization instead of large writing current.^175–178 

A MeRAM was reported by Hu et al. in 2011 by combining the ME coupling with a magnetoresistive memory, using phase-field simulations,¹⁷⁵ as shown in Fig. 16. On the top of the ferroelectric element (PMN-PT), the magnetostrictive layer (Ni) consists of two magnetic layers, separated by a nonmagnetic spacer. The magnetization of the top layer is fixed, while that of the bottom layer is free. By switching the magnetization direction of the bottom layer, the electric resistance of the magnetic trilayer shows different statuses, where the binary information is stored. During the reading process, the resistance level is directly read by the circuit. While, during the writing process, an electric voltage is applied across the ferroelectric layer, resulting in a magnetization change in the bottom free layer through ME coupling. Here, in Fig. 16(b), a resistance change of ∼2.5% was observed with almost 90° magnetization switching in the free layer with various thicknesses from 5 to 35 nm. The power consumption of this MeRAM is mainly from the capacitor charging of the ferromagnetic layer, leading to an ultra-low level of 0.16 fJ/bit. A high storage capacity of 88 Gb/in.² and a short operation time of less than 10 ns were achieved. Moreover, with the development of the nanostructures, the 180° magnetization switch has already been realized.^147,184,185 In this case, both the resistance change and the device reliability are improved because of the better magnetization stability compared with the 90° switch. Additionally, unlike the MeRAM based on ferromagnetic materials mentioned above, anti-ferromagnetic materials show another approach for the memory. By using the anti-ferromagnet Cr₂O₃, an AF-MeRAM was reported by Kosub et al. with a 50-fold reduction of the writing threshold compared with ferromagnetic memories.⁴¹ 

By replacing the nonmagnetic spacer between the two ferromagnetic materials with a ferroelectric layer, a voltage controlled multiferroic tunnel junction (VC-MTJ) is created. Different from using mechanical strain as intermediation, this VC-MTJ utilizes the charge accumulation and depletion at the interface to control the electron orbitals, leading to the magnetic anisotropy change due to the spin–orbit control.⁴³ Amiri et al. demonstrated a VC-MTJ with the measured switching energy less than 40 fJ/bit in 2015.¹⁸¹ Then, in 2016, the write energy was even scaled down to 6 fJ/bit by Grezes et al. by a very low Ohmic loss from a high resistance-area product, which diminishes the STT contributions.⁴⁴ Contemporarily, the device diameter was decreased to 50 nm and the reported switching time was 0.5 ns. In 2016, Wang et al. made a comparison between VC-MTJ and STT-RAM,¹⁷⁴ in which the VC-MTJ shows a 83% faster writing speed, 67.4% less writing energy, 138% faster reading speed, and 28.2% less reading energy. Compared with MeRAM, this VC-MTJ has a much simpler structure for fabrication, leading to a higher area density. However, the reliability problem from the dielectric breakdown in the ferroelectric layer is still a challenge.

For the MeRAMs, due to the coexistence of the ferromagnetic phase and piezoelectric phase, the binary information can be stored in the direction of magnetizations, the direction of polarization, and the level of electric resistance. Therefore, it brings a possibility to store four logic states or even more in one single device.¹⁸² Different from these, the ME coefficient is an alternative choice for binary information storage. A MeRAM using the multiple states of the ME coefficient was designed by Shen et al.^183,184 By combining the two magnetization directions and two polarizations, four different states of the ME coefficient are available for the storage.

To realize the Internet of Things (IoT), energy harvesting is necessary to replace the heavy, bulky power charger or battery for applications such as medical implants and wearable devices,^172,185 which collects the energy from the environment, in the forms of EM wave, vibration, heat and as on, and converts them to electric output. Among all the research studies that have been done, the ME coupling based energy harvester is attractive due to the high output power.

Based on the direct ME coupling, it is obvious that the ME energy harvester can easily collect energy from EM waves or magnetic fields, similar to the ME sensor. Li et al. reported a ME energy harvest in 2010,¹⁸⁶ which is consisted of a magnetostrictive Terfenol-D plate, piezoelectric PZT plates, and an ultrasonic horn. Here, mechanical vibration is generated from the Terfenol-D plate by the external magnetic field, collected by the ultrasonic horn, and then transferred to the PZT plates, resulting in an electric voltage output. A weak power output of 20 µW was observed under a magnetic field of 1 Oe. Li et al. also designed an energy harvester directly based on the FeNi/PZT ME composite,¹⁸⁷ which shows a much higher output power (61.64 µW under 0.2 Oe) than the former structure with an ultrasonic horn as intermediation. A ME cantilever with NdFeB magnets attached at the tip was demonstrated by Liu et al. as another approach for the energy harvester for the low-frequency magnetic field,¹⁸⁸ in which a maximum power density of 11.73 µW/(Oe² cm³) was achieved at the resonance frequency (<100 Hz). Lasheras et al. introduced a ME energy harvester based on FeCoSiB/PVDF as the ME laminated composite,¹⁸⁹ which shows that the output power density at resonance frequency decreases with the length of the ME composite (1.5, 0.2, and 0.054 mW/cm³ at 3, 1, and 0.5 cm, respectively). A ME dual-band energy harvester combined with the ME sensor was demonstrated by Zaeimbashi et al.,¹⁹⁰ as shown in Fig. 17. This energy harvester is based on the VHF and UHF ME antenna mentioned above with the same materials to achieve the best ME coupling behavior. Depending on the geometric dimensions of the antenna resonator (250 × 174 × 1 µm³), it performs as an energy harvester at the FBAR mode (2.51 GHz) and as an ME sensor at the NPR mode (63.6 MHz). It shows a 1–2 orders of magnitude better than any reported miniaturized micro-coils in wireless power transfer efficiency at the same frequency, and even, it is misaligned or rotated. Hence, this energy harvester has a great potential on biomedical implants to realize wireless charging, magnetic sensing, and data transmission at the same time.

With an applied external magnetic field from permanent magnets, the ME energy harvester can also be utilized to collect kinetic energy. Dong et al. first reported a design for both magnetic and mechanical energies in 2008,³⁹ with FeCoSiC/PZT as the ME composite, as shown in Fig. 18. An open circuit output voltage of 8 V_pp was detected under the 2 Oe magnetic field and a vibration amplitude of 50 mg, at 20 Hz. Dai et al. reported another vibration energy harvester using the Terfenol-D/PZT/Terfenol-D composite transducer, operating at the resonance of the cantilever structure,¹⁹¹ which produces a power of 2.11 mW at the resonance frequency of 51 Hz with 1 g acceleration. One issue of these two designs is that they can only collect energy from one single direction of motions. Therefore, several bi-axial energy harvesters were demonstrated based on various approaches, such as permanent-magnet/ball-bearing arrangement,¹⁹² circular cross-section cantilever rod,¹⁹³ and multi-cantilever beams.¹⁹⁴ Additionally, a three-dimensional nonlinear harvester was designed by Lin et al. based on a three-dimensional magnetic interaction and spring force.¹⁹⁵ 

At present, most of the energy harvesters are still suffering from the narrow operation bandwidth, which means that only the energy at operation frequency can be collected. To collect more energy, a multi-modal harvester was reported by Bai et al. by using a spiral-shaped cantilever.¹⁹⁶ Five peak values were observed among the frequency region of 15–70 Hz. Similarly, Zhang and Chen reported a wideband energy harvester using a series of ME composite fibers with different lengths.¹⁹⁷ Hence, each fiber has its own resonance frequency, and the overlap of all the operation peaks broadens the bandwidth of the whole device. Moreover, another method for the wideband vibration harvester is using the nonlinear interaction between fixed magnets and movable magnets.^193,195 By this method, the magnetic field applied on the ME composites also changes with the vibration.

The tunable inductor is one of the basic passive components in analog circuits, which allows the operating frequency tuning in communication terminals. However, compared with the tunable capacitor due to the low Q-factor and large device area, there is a limitation on the practical application of tunable inductors. Nowadays, inductors with the MEMS switch are a popular approach for the tunability and high Q-factor;^198–200 however, the inductance tunability of these designs is discrete, and the inductance density is low due to the absence of the magnetic core. Another method is controlling the magnetic flux density across the inductor coil by the DC bias current,^201,202 secondary coil,^203,204 or floating metal plate.²⁰⁵ The most significant problem with this method is the high power consumption, and additionally, the tunability is usually low.

The ME tunable inductor is a reliable solution to balance the tunability and power consumption by choosing a proper ME composite. The first ME tunable inductor was reported by Lou et al.²⁵ in 2009, which is a solenoid inductor with the Metglas/PZT composite as the magnetic core. With the increasing electric field across the PZT slab, the permeability decreases according to the converse ME coupling, leading to an inductance reduction. A maximum tunability of 450% was achieved, and the operation frequency was extended from kHz to MHz by ∼1000 times due to the FMR frequency increasing. With the combination of MEMS technology, the inductor volume can be easily miniaturized. Hence, an integrated tunable inductor for RF circuits was introduced by Chen et al. in 2020,²⁹ as shown in Fig. 19. Unlike the bulk inductor, the FeGaB/Al₂O₃ multilayer was utilized as a ferromagnetic layer in this integrated inductor because the multilayer offers lower eddy current loss and better magnetic properties compared to the single layer thin film.²⁰⁶ The thickness of the FeGaB/Al₂O₃ multilayer is 2.5 µm, and the thickness of the PMN-PT slab is 500 µm. In Figs. 19(c) and 19(d), with a tuning voltage from 0 to 500 V, corresponding to the electric field from 0 to 10 kV/cm, a maximum inductance tunability of 191% was observed at 1.5 GHz, while the Q-factor increased by ∼80%.

In wireless communication systems, the filter is an indispensable component to pick out the desired frequency. Research studies have been done on magnetic tuning on the filter with ferrites. However, the large power consumption and slow tuning are still an open question.^22,207–209 Hence, filters with ME composites become more and more attractive due to the near-zero power consumption, rapid tuning, low noise, and compatibility to CMOS technology.^22,210

In 2005, the first bandpass filter based on the YIG/PMN-PT composite was reported by Srinivasan et al.,²¹¹ in which the input–output coupling was realized by the FMR-corresponded external bias magnetic field on the YIG. With the bias electric field of 100 kV/cm, a maximum frequency tunability of 1.4 GHz and the lowest insertion loss of 2.5 dB were achieved. In 2015, a nonreciprocal dual H- and E-field tunable bandpass filter was designed by Lin et al.,²¹² as shown in Fig. 20. The NiZn-ferrite and PMN-PT were utilized as the ME composite. The nonreciprocity comes from the 45° rotation of the ferrite film from the magnetostatic surface wave (MSSW) and bias magnetic field, which operates in the stop band of the magnetostatic back volume wave (MSBVW). Hence, the reflected wave and standing wave resonance are diminished, as shown in Fig. 20(c). Therefore, a difference of 15.8 dB between S₂₁ and S₁₂ was observed at resonance, as shown in Fig. 20(d). The frequency tunability of 5 MHz/Oe under the H-field and 55 MHz/(kV/cm) under the E-field was reported. Additionally, unlike the filters coupled by FMR resonance, an integrated bandpass filter based on acoustic wave coupling was reported by Lin et al. in 2016,²¹ as shown in Fig. 21. Two FeGaB/AlN ME composites were placed in parallel with the 2 µm gap. By sharing the same piezoelectric layer, when one ME composite is excited at resonance in the in-plane contour mode, the acoustic wave is generated and transferred to the other ME composite, followed by a voltage output. Both H-field and E-field tunings are realized by Young’s modulus change of ME composites, leading to a resonance frequency shift, where the tunability of 5 kHz/Oe and 2.3 kHz/V was extracted.

The phase shifter is one of the most important components in systems such as phased array antennas, beamforming networks, and power dividers to control the phase difference between each element in the systems. There are multiple approaches to realize the phase shift, for example, based on Faraday rotation for electromagnetic waves, latching ferrites, magnetostatic wave propagation, and ferromagnetic resonance.²³ For all these, the magnetic layer is the key component. Hence, magnetic field tuning can be easily achieved by applying an external magnetic tuning field to the devices. However, the bulky device volume and high power consumption force researchers to find a more efficient tuning method. Therefore, electric field tuning based on ME coupling is turned out to be a reasonable solution.^{23,24,213,214}

The first electric field tunable, low loss, ME phase shifter operating close to FMR frequency was demonstrated by Tatarenko et al. in 2006,²³ in which YIG/PZT was used as the ME composite, as shown in Fig. 22. A phase shift between 90° and 180° and an insertion loss of 1.5–4 dB were observed within the frequency range of 5–10 GHz under a bias electric field of 5–8 kV/cm. Yang et al. reported another FMR phase shifter with the two-layer PMN-PT structure using a bending mode, which can reach a phase shift of 119° under an electric field of 11 kV/cm.²¹³ In addition, a tunable phase shifter based on spin-wave propagation was designed by Ustinov et al. in 2007. A high phase shift of 650° was achieved between 4.5 and 8 GHz; however, the high insertion loss of 20 dB is the main problem.

Although this review paper aims to introduce the most recent progress in magnetoelectric materials, phenomena, and devices, it is extremely difficult to cover all aspects due to the rapid development of this topic. Table I summarizes the ME voltage coefficients of current ME materials with various configurations, and Table II provides a summary of characteristics for some of the reviewed ME devices. The ME materials, especially ME composites with large ME coefficients at room temperature, provide great opportunities for practical device applications, such as ME antennas, ME magnetic sensors, ME random access memories, and tunable RF/microwave devices. There have been a variety of ME devices developed and mentioned above. Many opportunities and challenges still remain for further investigation in the coming years. The main trend for the ME society is to explore new ME materials and devices for practical applications by involving researchers and industries profoundly. Since the ever-increasing interest in ME thin films in the last decade, many open challenges and questions have become highly critical, for example, precise control of thin films’ growth including their crystal orientation, composition, and atomic structures.; manipulation of domain structures and activities; size effect of the ME effect in thin films; dynamic behaviors of ME coupling; and further understanding of different ME mechanisms in thin-film ME systems. From the materials point of view, new piezoelectric materials, such as AlScN with a high piezoelectric coefficient and low loss tangent, and new magnetostrictive materials, such as FeGaC and CoFeC with a large magnetostriction constant and narrow FMR linewidth, are desired for obtaining strong ME coupling. From the perspective of device applications, integration and scale-up with existing silicon processing flows and electronics, which desire low-temperature process methods, are more than welcome. From the science point of view, understanding, modeling, and characterizing of various devices based on piezoelectric/magnetostrictive ME heterostructures are particularly valuable for the multiferroic society. In addition, flexible ME materials and multifunctional devices compatible with smart wearable systems are of great importance in the fields of healthcare, security, the Internet of Things, etc. In summary, the involvement of many researchers and exponential growth in the number of publications in this area indicate their potential functionality as materials and devices. There exist a bright future and great challenges for magnetoelectric materials, phenomena, and devices, which will have huge influences on our daily life.

X.L. and H.C. contributed equally to this work.

The financial support from the NSF TANMS ERC under Award No. 1160504 and the W. M. Keck Foundation is acknowledged.

The authors declare no conflict of interest.

The data that support the findings of this study are available from the corresponding author upon reasonable request.