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Introduction

Ferromagnetic thin films exhibit a stable and switchable magnetization that memory devices and sensors use to store information and detect magnetic fields. Ferroelectric layers, on the other hand, allow for a variety of intriguing applications by virtue of their piezoelectric, dielectric, and polarization switching properties. While each of these material groups is utilized in many practical applications, research on hybrid structures that contain both ferroic order states is still in its infancy. Yet, the coexistence of ferromagnetism and ferroelectricity in so-called multiferroic materials promises to unveil new physical phenomena and provide additional functionalities to novel electronic devices. One particularly promising prospect of efficiently coupled multiphase systems is the ability to tailor magnetic properties in an applied electric field and to control ferro- and dielectric effects by the application of a magnetic field. The scientific significance of ferromagnetic/ferroelectric phase coexistence is illustrated by an intense revitalization of studies on magnetoelectric coupling in recent years. Efficient coupling at the interfaces of two intrinsically very different materials can result in behavior that is very unusual, if not unprecedented, in naturally occurring compounds. The exploration of these effects offers significant opportunities for innovations in spintronics. In this chapter, the main developments within the field of ferromagnetic/ferroelectric heterostructures are reviewed.

Multiferroic Materials

While ordered electronic states such as ferromagnetism and ferroelectricity have long been a centerpiece of solid-state and material physics due to their fundamental relevance in the understanding of phase control and related thermodynamic properties, studies on multiple ferroic order coexistence have been far more limited. The reasons for this are related to the mutual exclusivity of the conventional mechanisms that drive ferromagnetism and ferroelectricity [1] and the inability of early studies to establish strong magnetoelectric (ME) coupling effects [2]. Driven by advances in thin-film growth techniques and improved computational capabilities, studies on multiferroics, however, have greatly intensified during the last decade. This has led to the identification of new single-phase materials with different mechanisms for the stabilization of multiple- order coexistence. In one class of multiferroic materials, magnetism and ferroelectricity occur independently from each other. As a result, the ferroic ordering temperatures differ significantly, and ME coupling between both ordering states tends to be weak. Examples of multiferroic materials that belong to this class include BiFeO3 and YMnO3. In a second, more recently discovered class of single-phase multiferroic materials, the ferroelectric polarization is induced by a spiraling or collinear magnetic spin structure. Examples include TbMnO3, Ni3V2O6, TbMn2O5, and YMn2O5. Due to the direct link between magnetism and ferroelectricity in these materials, ME coupling can be strong, but the induced polarization is small. Reviews on the physics of single-phase multiferroic materials can be found in Refs. [3–9]. For spintronic applications, materials that combine robust ferromagnetic and ferroelectric polarizations at room temperature and strong ME coupling are required. These attributes are more readily obtained in hybrid material systems, in which ferromagnetic and ferroelectric compounds are artificially assembled. This chapter focuses on ferromagnetic/ferroelectric heterostructures with emphasis on electric-field control of magnetism and transport phenomena. Electric-field effects in ferromagnetic thin films with dielectric gate oxides, which are also under intense investigation (see e.g., Refs. [10–19]), are outside the scope of this review.

Ferromagnetic/Ferroelectric Heterostructures

In hybrid ferromagnetic/ferroelectric material systems, ME coupling originates from direct or indirect interactions between two dissimilar ferroic phases at the heterostructure interfaces. Each material constituent of artificially assembled hybrids can be independently optimized for high-temperature operation, which facilitates their integration into practical devices. Moreover, since a wide variety of ferromagnetic and ferroelectric materials are available, the nature and strength of ME interactions can be systematically altered and maximized. This has led to the engineering of large ME responses that exceed those of single-phase multiferroic materials by several orders of magnitude [20–22].

At a macroscopic level, electric-field control of magnetism is often characterized by the converse ME coupling coefficient (α), which is defined as the change in magnetization upon the application of an electric field, i.e.,

$$ \alpha ={\mu}_0\Delta M/\Delta E $$
(1)

In SI, the unit of the converse ME coupling coefficient is sm−1. The change in magnetization (ΔM) can be the result of an electric-field induced modification of the saturation magnetization, the exchange interaction, or the magnetic anisotropy. Large converse ME coupling coefficients have been obtained for vertical nanopillar arrays and horizontal thin-film heterostructures. Nanopillar arrays are often prepared by self-assembly during simultaneous deposition of two immiscible magnetic and ferroelectric compounds. Prototypical examples include combinations of ferroelectric perovskites (e.g., BaTiO3, PbTiO3, and BiFeO3) and magnetic spinels (e.g., CoFe2O4, NiFe2O4, MgFe2O4, and Fe3O4) [23–33]. Integration of such nanocomposites on silicon substrates has been demonstrated [34]. Besides self-assembly, ordered arrays of magnetic/ferroelectric nanostructures have also been patterned using lithographic techniques [35–37] and hierarchical templating by polymer films [38].

For spintronic applications, electric-field control of magnetism in thin-film heterostructures is appealing because the layered geometry closely mimics the architecture of most spintronic devices (e.g., magnetic spin valves, magnetic tunnel junctions, and magnetic field-effect structures). Hence, the integration of horizontal ferromagnetic/ferroelectric thin-film hybrids into functional spintronic structures is more viable than materials that couple via vertically aligned interfaces. In particular, electric-field induced magnetic switching, magnetic domain wall motion, and dynamic spin precession are topics of intense current interest. In the last decade, researchers have successfully addressed these magnetic functions using the spin-transfer torque (STT) effect . In this actuation scheme, a spin-polarized current is passed through a magnetic thin film or magnetic domain wall, which results in current-induced magnetic switching, continuous spin precession, or the motion of magnetic domain walls under appropriate experimental conditions. The STT phenomenon now forms the basis for magnetic random access memories (MRAMs), tunable microwave oscillators, and magnetic nanowire device concepts [39, 40]. Employing electric currents, however, is inevitably accompanied by energy dissipation, and in this context, electric-field induced magnetic effects without major current flow are desirable. In ferromagnetic/ferroelectric thin-film heterostructures, a bias voltage is applied across the ferroelectric layer to alter the magnetic properties of an adjacent ferromagnetic film via ME coupling. Since the leakage current through the insulating ferroelectric layer is small, electric-field control of magnetism has the advantage of low power consumption. In addition, the integration of ferromagnetic/ferroelectric hybrid structures in practical devices opens up routes toward the combined use of both ferroic order parameters. Proposals in this direction include novel magnetic memories in which the data is written electrically and read magnetically [41–44], four-state memory cells based on multiferroic tunnel junctions [45–49], and electric-field tunable microwave devices [50–52].

In ferromagnetic/ferroelectric thin-film heterostructures, three converse ME coupling mechanisms have been explored, namely, (1) electric-field induced charge modulation, (2) electric-field controlled exchange interactions, and (3) piezoelectric or ferroelastic strain transfer. All coupling mechanisms can result in a modification of the saturation magnetization, the exchange interaction, or the magnetic anisotropy. Since charge modulation and exchange bias are both interface effects, electric-field control of magnetism via these ME coupling mechanisms is limited to thin ferromagnetic films. Moreover, exchange bias and ferroelastic strain transfer can be used to attain strong ferromagnetic–ferroelectric domain correlations. The prospects of this phenomenon are discussed in the section “Ferromagnetic/Ferroelectric Domain Coupling.”

ME Coupling Based on Charge Modulation

At ferromagnetic/ferroelectric interfaces, ME coupling effects may originate from pure electronic mechanisms. Ab initio calculations and experiments indicate that electric fields can actively modify the magnetic and electronic properties of a variety of magnetic materials, including metallic ferromagnets [53–69], oxides [70–91], and dilute magnetic semiconductors [92–101]. One of the effects is related to the screening of electric fields by the accumulation or depletion of charge carriers in magnetic films. In ferromagnetic metals, electric fields are screened effectively by a high density of spin-polarized carriers. As a result, the spin imbalance at the Fermi level changes in an ultrathin region near the film interface, which alters the magnetic moment or magnetic anisotropy. For freestanding Fe, Ni, and Co films, the strength of the interface ME coupling coefficient is of the order \( \alpha =1.6-3\times {10}^{-22}\mathrm{s} \) [58]. Much larger values have been obtained for metallic ferromagnetic films on ferroelectric films or substrates. This difference is related to the proportionality between the screening charge of the metal and the dielectric constant of the ferroelectric material (typically, ϵ r = 100–1,000). For ferromagnetic/ferroelectric heterostructures, another electric-field effect originates from electronic hybridization between 3D transition metal atoms at the interface. For example, first-principle calculations based on density functional theory indicate that the magnetic moment of Fe atoms at a Fe/BaTiO3 interface changes by about 5 % due to a shift in the Fe–Ti bond length during ferroelectric polarization reversal [53]. Similar effects have been found for Co2MnSi/BaTiO3 [55], Fe/PbTiO3 [56, 62, 66], Fe3O4/BaTiO3 [57], and Co/PbZr x Ti1−x O3 [67]. Markedly larger ME coupling effects based on ionic displacements at a Fe/BaTiO3 interface are reported by Radaelli and coworkers [68]. In this work, it is convincingly demonstrated that exchange coupling in the interfacial-oxidized Fe layer can reversibly switch between antiferromagnetic and ferromagnetic upon out-of-plane polarization reversal in the BaTiO3 layer.

Electric-field effects based on charge modulation are particularly prominent in doped manganites due to strong lattice-spin-charge coupling. The accumulation or depletion of charge carriers near the interface of manganite films changes the hole doping concentration, a parameter that is normally controlled by substitution of La ions of the LaMnO3 parent compound with alkaline earth ions. As a result, polarization reversal in an adjacent ferroelectric film can change the magnetic and electronic ground state of manganites when the material is positioned near one of its phase transitions. An example is shown in Fig. 1. First-principle calculations based on density functional theory indicate that the magnetic interface structure of La0.5 A 0.5MnO3/BaTiO3 (A = Sr, Ca, or Ba) is ferromagnetic when the polarization points toward the La0.5 A 0.5MnO3 layer, while antiferromagnetically aligned Mn moments are obtained after polarization reversal [70, 71, 85]. According to the phase diagrams of La1−x A x MnO3 [102], the ferromagnetic-to-antiferromagnetic conversion is accompanied by a metal-to-insulator transition. This effect can be used to induce large tunneling electroresistance in ferroelectric tunnel junctions (section “Ferroelectric Tunnel Junctions”) [85, 86].

Fig. 1
figure 1

Illustration of an electrically induced magnetic reconstruction at the La0.5Ca0.5MnO3/BaTiO3 interface (Reproduced from [85] with permission from Nature Publishing Group)

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Electrostatic control of manganite thin films has also been observed in experiments [74–91]. For example, the temperature of magnetic phase transitions and the magnetoresistance of La0.8Sr0.2MnO3 change upon polarization reversal in PbZr0.2Ti0.8O3/La0.8Sr0.2MnO3 field-effect structures [74, 75]. Magneto-optical Kerr effect measurements on similar ferromagnetic–ferroelectric bilayers confirm these observations [77]. The latter study also demonstrates hysteretic switching between two magnetization states in an applied electric field. X-ray absorption near edge spectroscopy (XANES) measurements indicate that this effect can be ascribed to an electrostatic modulation of the valence state of Mn ions [79]. A more detailed discussion on charge-mediated ME coupling effects is given in Ref. [22].

ME Coupling Based on Exchange Interactions

Many single-phase multiferroic materials are antiferromagnetic. Intrinsic coupling between the ferroelectric polarization and the antiferromagnetic spin lattice in such materials can therefore be utilized to electrically control the exchange bias interaction with an adjacent ferromagnetic film. In conventional ferromagnetic/antiferromagnetic heterostructures, exchange bias manifests itself most prominently by a shift of the magnetic hysteresis loop along the magnetic field axis [103, 104]. The addition of voltage control over this interlayer coupling phenomenon is of interest to spintronic applications, in particular if the magnetic changes are reversible and isothermal. Multiferroic materials that have been explored for studies on exchange bias include YMnO3 [105], LuMnO3 [106], and BiFeO3 [107–117]. For NiFe/YMnO3, the application of an electric field during cooling through the Néel temperature reduces the exchange bias field. The change in exchange bias has been attributed to a decrease of coupled antiferromagnetic/ferroelectric domain walls, which act as the main pinning centers for the magnetization of the NiFe film [105]. A similar effect, namely the unpinning of the NiFe film magnetization by electric-field induced motion of antiferromagnetic/ferroelectric domain walls, can explain full reversal of the exchange bias direction in NiFe/LuMnO3 under the simultaneous application of magnetic and electric fields [106].

Room temperature exchange coupling effects have been obtained using BiFeO3, which exhibits a Néel temperature of 643 K. The origin of exchange bias in metallic ferromagnetic films on BiFeO3 depends on the type of ferroelectric domain walls in the BiFeO3 crystal. If the domains are predominantly separated by 109° walls, the exchange bias field is inversely proportional to the ferroelectric domain size [108, 109]. This observation suggests that uncompensated spins in the domain walls are the main source of the exchange bias effect. For 71° walls, on the other hand, no shift in the hysteresis loop is measured [108, 113]. In this case, exchange interactions between the ferromagnetic film and BiFeO3 result in an enhancement of the coercive field, which is explained by direct coupling to the canted moment of BiFeO3 domains. The orientation of the canted moment in BiFeO3 is strongly linked to the direction of ferroelectric polarization. As a consequence, rotation of the polarization produces a lateral modulation of exchange anisotropy in an adjacent ferromagnetic film. This effect can lead to ferroelectric/ferromagnetic domain correlations (section “Ferromagnetic/Ferroelectric Domain Coupling”), which form a strong basis for electric-field controlled magnetic switching in exchange-coupled systems [107, 110, 113, 116]. Ferroic domain correlation were first demonstrated in Co0.9Fe0.1/BiFeO3 using a combination of piezoresponse force microscopy (PFM) and X-ray magnetic circular dichroism (XMCD) with photoemission electron microscopy (PEEM) [107]. In this work, the application of an in-plane electric field resulted in 71° polarization switching inside the BiFeO3 layer, causing 90° rotations of the ferroelectric and magnetic domain walls. In a subsequent study by the same group, additional anisotropic magnetoresistance measurements were used to illustrate that opposite 71° ferroelectric switching events in neighboring domains can be used to reverse the net magnetization of a Co0.9Fe0.1 film via local 90° magnetization rotation inside the domains. An even higher degree of electric-field control was recently obtained by strain-engineering of double switching events in BiFeO3, leading to full magnetization reversal in an adjacent ferromagnetic film [116]. Moreover, integration of such exchange-coupled bilayers in magnetic spin valves resulted in nearly equal electric-field and magnetic-field switchable magnetoresistance effects. A detailed review of electric-field control of magnetism using BiFeO3-based heterostructures can be found elsewhere [117].

Finally, it is noted that electric-field control of exchange bias is not limited to multiferroic materials. In fact, some of the early studies focused on Cr2O3 [118, 119], which is a magnetoelectric antiferromagnet below 307 K. Reversible, isothermal, and global electric-field control of exchange bias has been obtained in Pd/Co multilayers deposited on the (0001) surface of a Cr2O3 single crystal [120].

ME Coupling Based on Strain Transfer

Electric-field control of magnetism using strain transfer from a piezoelectric or ferroelectric material is based on the generation of magnetoelastic anisotropy in an adjacent ferromagnetic film via inverse magnetostriction. Strain-induced changes of the atomic and electronic structure of ferromagnets can also alter other magnetic properties. This is most apparent for perovskite manganites such as La1−x Sr x MnO3 [121–125], La1−x Ca x MnO3 [122, 126], La1−x Sr x CoO3 [127], and La1−x Ba x MnO3 [128], for which electric-field induced changes of the Curie temperature and colossal magnetoresistance have been reported. Contrary to charge modulation and exchange bias interactions, ME coupling via strain transfer can be efficient up to relatively large magnetic film thickness (>100 nm) [125, 129]. The electric-field dependence of strain transfer from a piezoelectric material or a ferroelectric material with ferroelastic domains differs. The application of an electric field across a piezoelectric material produces a butterfly-shaped piezostrain curve (Fig. 2a). The magnetic response of an adjacent magnetic film tends to mimic this strain curve [122]. Consequently, the change of magnetization is approximately linear and mostly reversible in an applied electric field. Removing the electric field from the piezoelectric medium releases the piezostrain in the magnetic film, which restores the anisotropy of the piezoelectrically unstrained film. Thus, in the absence of other symmetry breaking anisotropy contributions, the electric-field induced magnetic state does not persist when the field is turned off. This volatility, however, can be circumvented by carefully designed anisotropy configurations.

Fig. 2
figure 2

Schematic illustration of the strain transfer curve of a piezoelectric material (a) and the variation of the in-plane lattice parameter during 90° in-plane polarization rotation in a tetragonal ferroelectric material (b). In the latter case, non-volatile switching between two ferroelastic domains can be used to alter the direction of uniaxial strain in an adjacent ferromagnetic film

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The most used piezoelectric material is (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT), which is a well-known relaxor ferroelectric with excellent electromechanical and piezoelectric properties for compositions near the morphotropic phase boundary (0.25 ≤ × ≤0.35) [130]. Piezostrain transfer from PMN-PT has been utilized to tune the magnetic properties of manganite [121, 122, 125, 126], ferrite [51, 131–135], and metallic ferromagnetic films [136–139] and to alter the electrical resistance of magnetic oxides [121, 123, 124, 126–128, 134]. Besides crystalline substrates, commercial piezoelectric actuators have also been used to study voltage control of magnetic anisotropy [140–147].

Phenomenological models based on Landau free-energy thermodynamic theory [148–151] and phase field simulations [43, 44] have been used to analyze electric-field control of magnetism in ferromagnetic/piezoelectric heterostructures. By considering strain-induced variations of the magnetoelastic anisotropy energy, it is foreseen that the magnetic easy axis of CoFe2O4 and Ni can be reoriented from an in-plane to an out-of-plane direction [148, 149]. In-plane rotations of the magnetic easy axis at relatively small applied electric fields are also calculated for various other magnetic materials [150, 151]. Moreover, the temporal evolution of the magnetization configuration can be calculated by solving the Landau-Lifshitz-Gilbert equation in phase-field simulations. For nanometer-sized Ni elements on PMN-PT, switching times of the order of 1 ns have been predicted using this method [43, 44].

Potential applications of electric-field controlled ferromagnetic/piezoelectric heterostructures include electrically tunable microwave devices based on ferromagnetic resonance (FMR) and ME random access memory (MERAM). For example, giant electric-field tuning of the FMR frequency from 1.75 to 7.57 GHz in zero applied magnetic field for FeGaB films on (011) PZN-PT substrates (piezoelectric material similar to PMN-PT) has been demonstrated [50]. The wide-band tuning range in this experiment is ascribed to the large magnetostriction of FeGaB, which transforms the uniaxial piezostrain into a large in-plane magnetoelastic anisotropy. Similar results are obtained for Fe3O4 on PMN-PT and PZN-PT [51]. MERAM devices require nonvolatile magnetic switching in an applied electric field. Despite the intrinsic volatility of piezostrain, stable magnetic switching can be realized when a reversal to the original magnetic state is prevented by a competing magnetic anisotropy. The desired anisotropy configuration can be provided by a static magnetic field [142] or by other anisotropy contributions such as magnetocrystalline anisotropy [144] or exchange bias [152]. Other proposals for electric-field controlled deterministic magnetic switching involve the use of bistable piezostrain of partially poled piezoelectric layers [43, 44, 137], the hysteretic strain-voltage dependence of piezoelectric actuators [143], or dynamic strain effects in ferromagnetic films with perpendicular anisotropy [153]. Non-volatility can also be obtained by electric-field induced structural transitions between rhombohedral and orthorhombic phases in PMN-PT or PZN-PT crystals [135, 154]

Ferromagnetic/piezoelectric heterostructures have also been used to electrically alter the motion of magnetic domain walls [144, 155–158]. Electric-field control over the velocity of magnetic-field or current-driven magnetic domain walls is particularly efficient in the thermally activated dynamic creep regime. Here, the motion of magnetic domain walls depends sensitively on the disorder-induced pinning energy barrier and the depinning field [159], which can be tuned by transfer of piezoelectric strain and inverse magnetostriction. Local control over the pinning and depinning of magnetic domain walls has been realized by the patterning of side electrodes on hybrid PbZr0.5Ti0.5O3/magnetic spin-valve structures [157]. Voltage-controlled magnetic domain wall gates and traps based on these concepts provide promising prospects for magnetic logic and memory technologies.

The characteristics of strain transfer from a ferroelectric material with ferroelastic domains are different from the mostly linear piezoelectric response. If the polarization reversal process involves the nucleation and growth of ferroelastic domains, i.e., domains that are separated by non-180° domain walls, the in-plane crystal lattice changes during ferroelectric switching (Fig. 2b). This hysteretic switching effect can be used to alter the magnetic properties of an adjacent ferromagnetic film in a nonvolatile way. The magnitude of transferrable strain depends on the ferroelectric material. For example, the tetragonal lattices of PbTiO3 \( \left(a=b=3.905 \mathring{\mathrm{A}}, c=4.156 \mathring{\mathrm{A}} \right) \) [160] and BaTiO3 \( \left(a=b=3.991 \mathring{\mathrm{A}}, c=4.035 \mathring{\mathrm{A}} \right) \) [161] provide a maximum uniaxial strain of 6.4 % and 1.1 % at room temperature. The strength of the induced magnetoelastic anisotropy depends on the efficiency of strain transfer and the magnetostrictive and elastic properties of the ferromagnetic material. Importantly, strain transfer from ferroelastic domains is not uniform but laterally modulated, which is schematically illustrated in Fig. 3. The local character of strain transfer allows for the imprinting of ferroelectric domains into ferromagnetic films and strong pinning of magnetic domain walls on top of ferroelectric domain boundaries. Before discussing these microscopic phenomena (section “Ferromagnetic/Ferroelectric Domain Coupling”), macroscopic measurements of strain-coupled ferromagnetic-ferroelectric heterostructures are reviewed first.

Fig. 3
figure 3

Schematic illustration of domain patterns in tetragonal ferroelectric materials (e.g., PbTiO3 and BiTiO3 at room temperature) with a (001) crystal orientation. Polarization reversal between two out-of-plane states can be used for electrostatic control of magnetic properties (section “ME Coupling Based on Charge Modulation”), but the domain pattern in (a) does not modulate the lattice strain of an adjacent ferromagnetic film. Ferroelastic a 1 – a 2 (b) and a − c (c) domain structures, on the other hand, can be used to attain ferromagnetic/ferroelectric domain correlations (section “Ferromagnetic/Ferroelectric Domain Coupling”)

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One popular approach in studies on elastic interactions between a ferroelectric material and a ferromagnetic film utilizes the structural phase transitions of BaTiO3 substrates. The lattice structure of single-crystal BaTiO3 changes as a function of decreasing temperature from cubic to tetragonal at 393 K, then from tetragonal to orthorhombic at 278 K, and finally from orthorhombic to rhombohedral at 183 K [162]. The concurrent changes of the BaTiO3 domain pattern at these phase transitions alter the strain state of the ferromagnetic film, and via inverse magnetostriction, this can lead to local magnetic switching. In an early report by Lee and co-workers [163], the macroscopic response of La0.67Sr0.33MnO3 films during cool down from 400 to 5 K was measured using SQUID magnetometry (Fig. 4). The abrupt changes in film magnetization at the phase transitions of BaTiO3 are due to in-plane rotations of magnetic anisotropy caused by lattice distortions in the BaTiO3 substrate. Similar magnetic effects are reported by other groups for a variety of materials. Besides La1−x Sr x MnO3 [164], these include La1−x Ca x MnO3 [165], Fe3O4 [166–168], Fe [169–174], Sr2CrReO6 [175], CoFe2O4 [176], SmCo [177], and exchange-biased Co/CoO bilayers [178]. Instant variations in sample magnetization at the phase transitions of BaTiO3 are a common feature in these experiments, illustrating significant elastic coupling between the ferroelectric substrate and the ferromagnetic film. Most of the studies also report on coincident shifts in the coercive field and the remanent magnetization [166, 169, 172–175, 178]. These observations clearly indicate that abrupt changes in the ferroelastic domain pattern alter the strength and/or orientation of magnetic anisotropy. Macroscopic measurements, however, only reveal the average magnetic response. Due to the strong local character of strain transfer from ferroelastic domains, the change in magnetization varies from one domain to the other. Moreover, a variety of ferroelectric domain transformations can occur at the BaTiO3 phase transitions, which complicates the interpretation of macroscopic data. Lahtinen et al. reported on temperature-induced local magnetic effects in CoFe films on BaTiO3 substrates [179]. Optical polarization microscopy measurements in this study indicate local magnetization rotation by 90° during sample cooling and heating through the structural phase transitions of BaTiO3.

Fig. 4
figure 4

Magnetization as a function of temperature for a 50 nm thick La0.67Sr0.33MnO3 film on a BaTiO3 (001) substrate. The inset shows magnetic hysteresis loops for temperatures below (T1) and above (T2) the orthorhombic-tetragonal structural phase transition of BaTiO3 (Reproduced with permission from [163]. Copyright 2000, AIP Publishing LLC.)

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Several experiments on electric-field control of magnetic films on top of BaTiO3 substrates have been conducted [164, 169, 171, 173, 180–185]. Eerenstein and coworkers measured the magnetic response of La0.67Sr0.33MnO3 films during the application of an out-of-plane electric field across the ferroelectric substrate using vibrating sample magnetometry (VSM) [164]. Sharp magnetic switching was obtained for electric fields in the range of 4–10 kVcm−1 depending on sample temperature. Taniyama et al. reported on electric-field induced magnetic switching in rectangular Fe dots on BaTiO3 [180]. In these experiments, a piezoresponse force microscope was used to apply local electric fields and the magnetic response was imaged using magnetic force microscopy. Electrical switching between single- and multidomain magnetic structures is demonstrated and ascribed to polarization reversal in the underlying ferroelectric substrate. In most experiments, the electric field is applied perpendicular to the BaTiO3 substrate plane. Abrupt switching from in-plane to out-of-plane polarization alters the ferroelastic strain state in this configuration and via inverse magnetostriction the magnetoelastic anisotropy and coercive magnetic field are affected. ME coupling induced by the application of an in-plane electric field has been studied using suspended BaTiO3/FeGa thin-film bilayer structures [186].

Besides anisotropy control, electric-field induced shifts of magnetic phase transitions can also be realized by strain transfer from ferroelastic domains. Reversible switching between antiferromagnetic and ferromagnetic order was recently demonstrated for FeRh films on BaTiO3 substrates near a transition temperature of 350 K (Fig. 5) [187]. Tweaking of the magnetic phase in these experiments is ascribed to the growth of ferroelectric c domains at the expense of a domains in an out-of-plane electric field. Because of the giant change of magnetization during the electric-field induced ordering transition, the converse ME coupling coefficient is much larger than that of hybrid material systems based on anisotropy modulation.

Fig. 5
figure 5

Voltage dependence of magnetization in a FeRh/BaTiO3 heterostructure at a temperature of 385 K. The change in magnetization is induced by ferroelastic domain switching in the BaTiO3 substrate, as indicated by X-ray diffraction analysis (Reproduced from [187] with permission from Nature Publishing Group)

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In addition to BaTiO3-based systems, electric-field control of magnetism via ferroelastic domain switching has also been demonstrated using PMN-PT and PZN-PT substrates [52, 188–191], providing large and nonvolatile magnetoelectric coupling effects. Moreover, strain-induced correlations between ferroelectric stripe domains in a BiFeO3 layer and magnetic domains of a La0.7Sr0.3MnO3 film have been imaged [192].

Ferromagnetic/Ferroelectric Domain Coupling

The local character of some ME coupling mechanisms and the direct link between the direction of ferroelectric polarization and the orientation of ME-induced magnetic anisotropy open up routes toward the design of ferromagnetic/ferroelectric heterostructures with correlated domain structures. In these hybrid material systems, rotation of the ferroelectric polarization alters the strength, orientation, and/or symmetry of the magnetic anisotropy in an adjacent ferromagnetic film. Moreover, the nearly instant change of magnetic anisotropy at ferroelectric domain boundaries creates a strong pinning potential for magnetic domain walls. Electric-field control of local magnetic switching, the writing and erasure of magnetic domain patterns, and the motion of magnetic domain walls can therefore be realized. In this section, the physics of domain pattern transfer in ferromagnetic/ferroelectric heterostructures is reviewed and the prospects for spintronic devices are discussed.

Domain Pattern Transfer

Domain pattern transfer from a ferroelectric material to a ferromagnetic film has been demonstrated in exchange-coupled CoFe/BiFeO3 [107, 110, 113, 115, 116, 193] and strain-mediated ferromagnetic/BaTiO3 [182–184, 194–199] and La0.7Sr0.3MnO3/BiFeO3 [192] heterostructures. Exchange interactions between the canted magnetic moment of BiFeO3 domains and an adjacent CoFe film can produce the required lateral modulation of magnetic anisotropy. The direct link between the direction of ferroelectric polarization and the orientation of the canted moment allows for electric-field control of magnetic domain patterns and local magnetization in this hybrid material system. Electric-field induced magnetic switching in CoFe/BiFeO3 hybrids depends on the orientation of the BiFeO3 film, the type of ferroelectric switching event (71° or 109° polarization rotation), and the direction of the applied electric field. The magnetic anisotropy strength of exchange-coupled heterostructures decreases with CoFe film thickness due to the interfacial character of the ME coupling mechanism. As a result, domain correlations vanish for relatively thin ferromagnetic films.

In strain-based systems, the ferroelastic domains of a ferroelectric material modulate the magnetoelastic anisotropy of an adjacent magnetic film via inverse magnetostriction. Full imprinting of ferroelastic domains into a magnetic film was first demonstrated for a CoFe film on top of a BaTiO3 substrate with regular a 1 − a 2 domains (Fig. 6) [182]. The a 1 − a 2 domain pattern of tetragonal BaTiO3 is characterized by 90° rotations of the ferroelectric polarization and uniaxial lattice elongation in the substrate plane (Fig. 3b). Domain correlations are obtained if the induced magnetoelastic anisotropy (Kme) dominates other magnetic energies, including the magnetocrystalline anisotropy (Kmc) and exchange and magnetostatic interactions between magnetic domains. Maximization of the anisotropy figure of merit Kme/Kmc thus provides a possible route towards the engineering of robust ferromagnetic/ferroelectric domain coupling. Ferroelastic a − c stripe domains of BaTiO3 can also be used to manipulate magnetic microstructures (Fig. 3c) [194, 195]. In this domain pattern, the ferroelectric polarization alternates between in-plane and out-of-plane. Because the out-of-plane c domains exhibit cubic in-plane structural symmetry, strain transfer from such domains induces a biaxial magnetic anisotropy in the adjacent ferromagnetic film. Imprinting of ferroelastic a − c stripe patterns is therefore due to an abrupt change in anisotropy symmetry and strength at domain boundaries rather than a rotation of the uniaxial magnetoelastic anisotropy axis (a 1 − a 2 domains).

Fig. 6
figure 6

Full domain pattern transfer from a ferroelectric BaTiO3 substrate to a ferromagnetic CoFe thin film. Polarization microscopy and Kerr microscopy images show the domain structure of the ferroelectric (FE) and the domain pattern of the ferromagnet during several stages of the magnetization reversal process (R1, S1, R2, S2). The hysteresis curve represents an average magnetic response of many domains. The arrows in the images indicate the orientation of ferroelectric polarization (FE) and magnetization in the remanent states (R1 and R2) and during abrupt magnetic switching (S1 and S2) (Reproduced from [182] with permission from John Wiley and Sons)

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Strain-induced domain pattern transfer has been demonstrated for various ferromagnetic materials. Besides polycrystalline CoFe films [182–184], these include epitaxial Fe [194], epitaxial CoFe2O4 and NiFe2O4 [195], epitaxial manganites [192, 197], polycrystalline Ni [196] and NiFe [199], and amorphous CoFeB [198]. Magnetization reversal in these heterostructures is characterized by coherent magnetization rotation followed by abrupt magnetic switching within the domains (if Kme is sufficiently large). During this process, the magnetic domain walls are fully immobilized by strong pinning onto ferroelectric domain boundaries (Fig. 6). Since the magnetization of neighboring magnetic domains rotate in opposite directions, the total spin rotation within magnetic domain walls changes as a function of magnetic field strength [200]. Moreover, because of strong magnetic domain wall pinning, two distinctive magnetic microstructures can be initialized. Head-to-tail domain walls are formed when a magnetic field is applied perpendicular to the stripe domains. In this case, the width of magnetic domain walls is mostly determined by the exchange stiffness and the strength of Kme. A magnetic field parallel to the stripe domains stabilizes alternating head-to-head and tail-to-tail domain walls. In this configuration, the width of the walls is mainly defined by magnetostatic interactions and magnetic anisotropy. Deterministic switching between magnetic walls with different width and energy can therefore be realized by in-plane rotation of the magnetic field [200]. This high degree of tunability could open the door to new magnetic devices wherein domain walls are utilized as functional and controllable elements.

Size Dependence of Domain Pattern Transfer

The physics of domain pattern transfer in hybrid ferromagnetic/ferroelectric materials is governed by a competition between the strength of the induced magnetic anisotropy and other relevant energies within the magnetic film. In particular, exchange and magnetostatic interactions oppose the formation of regular magnetic domains. For small ferroelectric domains, ferromagnetic coupling between neighboring domains exceeds the magnetic anisotropy and, hence, domain pattern transfer is no longer obtained. The cross-over from strong ferromagnetic/ferroelectric domain correlations to uniform film magnetization occurs when the width of the ferroelectric domains (Δ) becomes comparable to the width of the magnetic domain walls (δ) (Fig. 7) [201]. Two different scaling regimes are accessible. If the magnetic domains are separated by head-to-tail domain walls, the anisotropy and exchange energy determine the magnetic microstructure. In this case, the remanent spin rotation between neighboring domains diminishes when \( \Delta \approx \delta \approx \pi \sqrt{A/2{K}_{me}} \), which is the width of 90° Néel walls when magnetostatic interactions are omitted [202]. Based on this analysis, a phase diagram for domain pattern transfer as a function of magnetic anisotropy can be constructed, as illustrated in Fig. 7c. For head-to-head and tail-to-tail magnetic domain walls, breakdown of domain pattern transfer is mainly determined by the anisotropy and magnetostatic energy of the system. Because magnetostatic coupling between domains extends over a longer distance than exchange interactions, the magnetization of neighboring domains are forced to align parallel at considerable larger domain width. In this case, domain pattern transfer breaks down when \( \Delta \approx \delta \approx \pi {\mu}_0{M}_s^2t/8{K}_{me} \), which approximates half the width of 180° charged domain walls [203]. Thus contrary to uncharged walls, the critical length scale for domain patterns with magnetically charged walls increases linearly with ferromagnetic film thickness.

Fig. 7
figure 7

(a) Micromagnetic simulations illustrating the breakdown of domain pattern transfer with decreasing ferroelectric domain width (Δ). (b) Dependence of domain wall spin rotation on Δ. (c) Phase diagram of domain pattern transfer as a function of magnetic anisotropy strength. The transition from a well-defined magnetic stripe pattern to uniform magnetization occurs when Δ ≈ δ. The symbols and line indicate simulation data for δ and a calculation based on \( \delta \approx \pi \sqrt{A/2{K}_{me}} \)

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Electric-Field Control of Local Magnetic Switching and Magnetic Domain Patterns

The strong link between the direction of ferroelectric polarization and the orientation of magnetic anisotropy in hybrid materials with correlated domain structures enables electric-field control of local magnetic switching and magnetic domain patterns. Electric-field induced changes in ferroelectric domains are transferred to the ferromagnetic film if ME coupling at the interface is effective. In that case, concurrent rotations of the in-plane ferroelectric polarization (or its projection) and the magnetic anisotropy axis can trigger magnetic switching in zero magnetic field. In exchange-coupled CoFe/BiFeO3 heterostructures, switching depends on the alignment between the ferroelectric polarization and the canted magnetic moment inside BiFeO3 domains and interface exchange interactions with the magnetization of the CoFe film [48, 49, 107, 110, 113, 116]. For example, in the experiments of Ref. [113], the in-plane projection of ferroelectric polarization and easy anisotropy axis are collinear. Application of an in-plane electric field to this hybrid system results in 71° polarization switching between two <111> directions in BiFeO3, which corresponds to a 90° rotation of the projected polarization in the (001) plane. Because of efficient ME coupling at the interface, the local magnetization of the CoFe film is forced to rotate by 90°. Full magnetization reversal in CoFe, i.e., switching by 180°, requires the engineering of more complicated double switching events in BiFeO3, which was successfully demonstrated by Heron and coworkers [116].

Strain coupling to ferroelastic domains of a ferroelectric material offers another route towards non-volatile magnetic switching. Application of an out-of-plane electric field to a CoFe/BaTiO3 heterostructure with fully correlated a 1 − a 2 domains (Fig. 6), for example, deterministically rotates the in-plane magnetization of the CoFe domains by 90° [182–184]. The regular magnetic stripe pattern is conserved during this switching event. However, when the ferroelectric polarization relaxes back into the plane of the BaTiO3 substrate, the magnetic domain pattern disappears. The writing and erasure of regular magnetic stripes in zero magnetic field is reversible and it is fully explained by considering local strain transfer from ferroelastic BaTiO3 domains to the CoFe film and modifications of magnetic anisotropy via inverse magnetostriction.

Electric-Field Driven Magnetic Domain Wall Motion

Domain coupling between a ferromagnetic film and a ferroelectric material also provides a platform for electric-field control of magnetic domain wall motion [184, 204, 205]. Abrupt changes in magnetic anisotropy at ferroelectric domain boundaries create a strong pinning potential for magnetic domain walls. This pinning effect fully immobilizes magnetic domain walls during magnetization reversal in an external magnetic field (section “Domain Pattern Transfer”). However, if a ferroelectric domain boundary is moved laterally by an applied electric field, the magnetic domain wall is forced to move along by a concurrent displacement of the pinning potential. An example of reversible electric-field driven magnetic domain wall motion is shown in Fig. 8. In this experiment, an epitaxial Fe film is elastically coupled to an a − c domain structure of a BaTiO3 substrate and an out-of-plane electric field is applied. If the electric field is aligned along the direction of ferroelectric polarization in the c domain (negative voltage pulse), the c domain grows at the expense of the neighboring a domain by lateral domain wall motion. A positive bias voltage, on the other hand, shrinks the c domain by moving the ferroelectric boundary in the opposite direction. Strong elastic pinning necessitates that the magnetic domain wall in the Fe film strictly follows the displacement of the ferroelectric domain boundary. Other configurations such as the motion of a 1 − a 2 magnetic domain walls driven by in-plane electric fields can also be considered, but this requires a network of planar electrodes and has not been explored yet. Initial studies on the dynamics of pinned magnetic/ferroelectric domain walls indicate several effects, including the emission of monochromatic spin waves, domain wall depinning, and oscillatory motion at high velocities [204, 205]. Since electric-field driven magnetic domain wall motion in hybrid heterostructures is only emerging, it is anticipated to gain scientific interest in the coming years.

Fig. 8
figure 8

Reversible electric-field driven magnetic domain wall motion in a 20 nm thick Fe film on a BaTiO3 substrate. The Kerr microscopy images show the domain wall position after application of positive (blue dots) and negative (red dots) voltage pulses across the BaTiO3 substrate. The dependence of magnetic domain wall velocity on electric field strength is shown in the graph. All measurements were conducted in zero magnetic field (Reproduced from Franke et al., Reversible Electric-Field-Driven Magnetic Domain-Wall Motion [204]. doi:http://dx.doi.org/10.1103/PhysRevX.5.011010)

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Ferroelectric Tunnel Junctions

Ferromagnetic/ferroelectric thin-film heterostructures are often used in ferroelectric tunnel junctions (FTJs). In the most general form, an FTJ consists of a thin ferroelectric tunnel barrier and two conducting electrodes. Switching of the out-of-plane ferroelectric polarization by a bias voltage changes the junction resistance, an effect known as tunneling electroresistance (TER) . Several mechanisms can contribute to TER [206], including (a) an electrostatic effect due to electric field-induced polarization reversal in the ferroelectric barrier, (b) an interface effect resulting from ionic displacements within the interface layers of the electrodes, and (c) a piezoelectric effect that alters the effective width of the tunnel barrier. In most experimental realizations [48, 49, 64, 85, 86, 207–219], the FTJ consists of a BaTiO3, PbTiO3, or PbZr x Ti1−x O3 barrier grown on top of a La1−x Sr x MnO3 bottom electrode (SrRuO3 in Ref. [209–211]). The top contact is either a metal or another conducting oxide. Epitaxial barrier/La1−x Sr x MnO3 combinations are used to stabilize the out-of-plane ferroelectric polarization of the tunnel barrier via compressive in-plane lattice strain. Using piezo-response force microscopy (PFM), Garcia et al. have shown that the ferroelectric polarization of ultrathin BaTiO3 films on La0.67Sr0.33MnO3 can be retained down to a film thickness of only 1 nm [207]. Junctions with single-phase multiferroic tunnel barriers have also been studied [45, 220–224].

In FTJs with a metallic top electrode, a TER effect is caused by incomplete screening of polarization charges at the barrier/electrode interfaces, which for inherently different electrode materials leads to an asymmetrical deformation of the barrier potential [225, 226]. In this case, reversal of the barrier polarization produces two distinctive barrier heights and consequently two different tunnel barrier resistances. This scenario is supported by an exponential increase of the TER effect with tunnel barrier thickness [207]. The TER of FTJs with an asymmetrical barrier can be considerably larger than the tunneling magnetoresistance (TMR) of conventional magnetic tunnel junctions (MTJs). The maximum TMR effect at room temperature is about 600 % for MgO-based MTJs with CoFeB electrodes [227], which corresponds to an OFF/ON ratio of 7. However, for FTJs with a La0.67Sr0.33MnO3 bottom electrode, a BaTiO3 tunnel barrier, and a Co top electrode, OFF/ON ratios as high as 100 have been obtained (Fig. 9) [214]. Moreover, ferroelectric switching between the two resistance states only requires a current density of about 104 Acm−2, which is considerably smaller than the critical current density for spin-transfer torque writing in MTJs (≈ 106 Acm−2). The large, stable, and reproducible TER effect underpins the potential of FTJs for data storage applications. Further advances in strain engineering and careful control of electrical boundary conditions are anticipated to further enhance the performance of FTJs beyond the current state-of-the-art.

Fig. 9
figure 9

OFF and ON resistance states of nanoscale FTJs with a 10 nm Co/2 nm BaTiO3/30 nm La0.67Sr0.33MnO3 structure (Reproduced from [214] with permission from Nature Publishing Group)

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The resistance of FTJs with two ferromagnetic electrodes also changes in an applied magnetic field. The magnitude or even sign of the TMR effect can change upon polarization reversal in the ferroelectric tunnel barrier [48, 49, 64, 228]. Experiments on Co/PbZr0.2Ti0.8O3/La0.7Sr0.3MnO3 indicate that the TMR response is negative when the polarization points toward the Co electrode, while positive TMR is measured after ferroelectric switching into the opposite direction (Fig. 10) [49]. The polarization-induced modification of the TMR effect can be attributed to an anti-aligned induced magnetic moment on the Ti ions at the Co interface or a spin-dependent electrostatic screening effect in the interfacial layers of La0.7Sr0.3MnO3. Support for the first scenario has been obtained by X-ray resonant magnetic scattering experiments [228] and first-principles calculations [53, 55–57, 66]. It has been argued that a combination of deterministic TER and TMR effects in single tunnel junctions could be utilized for the design of four-state memory cells.

Fig. 10
figure 10

Electric-field induced reversal of TMR in a Co/PbZr0.2Ti0.8O3/La0.7Sr0.3MnO3 tunnel junction. Negative TMR is obtained when the ferroelectric polarization of the PbZr0.2Ti0.8O3 tunnel barrier points towards the Co top electrode. Polarization reversal by a voltage pulse of +3 V changes the sign of the TMR effect (Reproduced from [214] with permission from Nature Publishing Group)

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Besides metallic electrode/ferroelectric barrier/La1−x Sr x MnO3 junctions, large TER effects have also been obtained in all-oxide FTJs. Yin et al. reported on a TER response of 5,000 % at 40 K in 30 nm La0.7Sr0.3MnO3/0.4–2 nm La0.5Ca0.5MnO3/3 nm BaTiO3/50 nm La0.7Sr0.3MnO3 [85]. The TER of this heterostructure originates from electrostatic charge modulation in the La0.5Ca0.5MnO3 insertion layer. When the barrier polarization points toward La0.5Ca0.5MnO3, the layer is ferromagnetic and metallic. Polarization reversal away from the La0.5Ca0.5MnO3/BaTiO3 interface results in local hole accumulation, which changes the phase of the manganite layer to antiferromagnetic and insulating. As the junction resistance depends exponentially on the effective barrier width, large effects are readily obtained when only a few atomic layers of La0.5Ca0.5MnO3 are affected by polarization reversal. As discussed in section “ME Coupling Based on Charge Modulation,” the ability to induce phase transitions in thin-film manganites with appropriate doping concentration is supported by calculations and other experiments.

Finally, it is noted that giant TER effects have also been obtained for junctions wherein a ferroelectric BaTiO3 tunnel barrier is directly grown onto a semiconducting Nb-doped SrTiO3 substrate [229]. In this case, the effective tunnel barrier width is drastically altered by polarization-controlled accumulation or depletion of majority charge carriers at the semiconductor interface. The reported OFF/ON resistance ratio of FTJs with a semiconductor electrode is about 104 at room temperature.

Based on the recent progress in FTJs, their application in future memory and logic devices seems credible. Key advantages of FTJs include giant electroresistance, nondestructive readout, and low power usage. Moreover, the physical mechanisms behind TER are scalable to the nanometer range. Before commercialization, however, a number of scientific challenges related to the fatigue and retention characteristics of ultrathin ferroelectric films need to be solved.

Summary

Theoretical and experimental investigations of ferromagnetic/ferroelectric heterostructures have drastically intensified in the last decade. The potential use of these hybrid materials as electric-field controllable elements in spintronic devices offers several benefits including low power consumption and giant electroresistance. Two research directions can be distinguished based on the alignment of ferroelectric polarization. In structures with in-plane polarization, correlations between ferromagnetic and ferroelectric domains can be attained via local ME coupling. This enables electric-field control of nonvolatile magnetic switching, writing of magnetic domain patterns, and reversible magnetic domain wall motion. For practical applications of these effects, open questions related to the dynamics of ferromagnetic/ferroelectric domain coupling need to be answered. Ferroelectric materials with out-of-plane polarization can be used to modulate charge carriers in the interfacial layers of an adjacent ferromagnetic film. Ferroelectric tunnel junctions are based on this concept. Recent progress on tunneling electroresistance at room temperature offers promising prospects for innovations in nanoelectronics.