Multifunctional magnetoelectric materials for device applications

Two independent events marked the birth of the ME: (i) In 1888 Röntgen discovered that a moving dielectric became magnetised when placed in an electric field [10]; the opposite effect was observed 17 years later (the polarisation of a moving dielectric in a magnetic field) [11]. (ii) In 1894 Curie pointed out the possibility of the intrinsic ME behaviour of crystals on the basis of symmetry considerations, in which the crystals can be polarised in the presence of a magnetic field, and vice-versa. Later, Dzyaloshinskii provided theoretical details of the ME in a specific material—Cr₂O₃ [12]; subsequently, in 1960, Astrov reported the first experimental observation of the ME effect in Cr₂O₃, and he showed experimental confirmation of an electric field induced magnetisation [13, 14], and Rado et al [15, 16] quickly confirmed the converse magnetic field induced polarisation. The subsequent search for alternative ME materials led scientists to synthesise new single phase compounds and they found multiferroic and ME behaviour in several families of materials: The Pb-family [17–24] perovskite oxide structure; Bi compounds [1, 25–28]; rare earth (RE) manganites [29–32]; mixed perovskite solid solutions [33–45]; REMn₂O₅ family [46–52], phosphates [53, 54], boracites [55–59], fluoride family [60–65], spinel chalcogenides [66–71], and delafossites, [72–74]. Table 1 summarises the characteristics of each family with some typical examples and references. Most of the compounds listed in table 1 have drawbacks: (i) they are multiferroic only at low temperature; (ii) they have very weak ferroelectric and/or ferromagnetic response; and (iii) their magnetoelectric coupling constant is too low for practical applications. Several review articles summarise the general aspects of single-phase multiferroic materials and the ME coupling effect [7, 75–78].

Perovskite solid solutions have been an active area of research due to the possibility of exploring new materials with multifunctional applications [18, 19]; Sanchez et al [39] combined the best qualities of both lead iron tantalate with those of PZT, synthesising (PbZr_0.53Ti_0.47 O₃) _(1−x)–(PbFe_0.5Ta_0.5O₃)_x (PZTFT). PZTFT with variable x was prepared by a conventional solid-state route. PZTFT is a single-phase (figure 1(a)), low-loss material; it showed both ferroelectric (figure 1(b)) and ferromagnetic (figure 1(c)) ordering at room temperature with magnetoelectric coupling (figure 1(d)), with a very low leakage current even at 550 K, such that perfect square hysteresis at 550 K was observed. Temperature-dependent XRD revealed a structural phase transition from tetragonal to orthorhombic under cooling. PZTFT shows a classic textbook example of several sequential phase transitions: cubic-tetragonal (ca. 1300 K) to tetragonal-orthorhombic (520 K for x = 0.3 and 475 K for x = 0.4); and orthorhombic-rhombohedral (230–270 K)—a sequence similar to that in barium titanate. ME coupling is of the same order of magnitude as in the single phase multiferroic PFT. High resolution transmission electron microscopy (HRTEM) studies are being carried out to verify the possibility of secondary phases or clusters at the nanoscale level. The inset from figure 2(a) shows the selected area electron diffraction (SAED) pattern of the ceramic PZTFT; these studies suggest no evidence of secondary diffraction patterns in the PZTFT material at nanoscale. The PZTFT multiferroic is the lowest-loss room-temperature multiferroic known, which is a great advantage for magnetoelectric devices.

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Evans et al [43] showed a significant change in the ferroelectric domains of PZTFT lamella taken from a ceramic grain using the focussed ion beam technique (FIB) under a moderate external magnetic field using lateral piezoresponse force microscopy (LPFM). The images in figure 2(a) present results before (upper) and after (lower) the application of the 18-kOe (1.8 T) magnetic field; a clear change in ferroelectric domain states is observed. The LPFM amplitude images of the same region of the PZTFT single-crystal lamella (the left and middle panels) show variations in the local in-plane piezoelectric activity under the magnetic field. The domains or packets of domains and domain walls are clearly visible, and their orientations are distinct. Various cantilever orientations were used to scan the LPFM images; tip geometries are shown schematically in blue. The right-hand side images in figure 2 are the in-plane PFM phase signal deduced from the amplitude images. Various local polarisation directions are mapped and shown in the right-hand panels. The directions of the local polarisations are shown for all four quadrants (grey: left and up; lime green: left and down; purple: right and up; brown: right and down). Ferroelectric domains were preferentially grown in the left and down direction (lime green) under the application of external magnetic fields. These results successfully demonstrate strong and explicit ME coupling at the nanoscale for ferroelectric domains where these domains switch with moderate magnetic fields at room temperature.

In a subsequent experiment Evans et al examined the behaviour of ferroelectric domains on the same PZTFT single-crystal lamellae with capacitor structure under the application of both electric and magnetic fields [44]. Figure 2(b) shows the domain configurations and their magnitude after the application of successive electric fields (blue and green arrows) ((i)  −25 V, (ii) +25 V, (iii)  −25 V). A consistent change in in-plane domain orientations and magnitudes was observed under E-fields, which can be easily switched back and forth under E-fields. The application of a magnetic field ((iv) +3 kOe) efficiently switched the electric polarisation; however, the reversal of the magnetic field ((v)  −3 kOe) shows only a modest change in the ferroelectric domains (see figure 2(b) upper). These authors quantified the domain changes by counting the 'yellow' phase pixels in each image (see figure 2(b) lower). The changes in the populations of domains (yellow phase) are shown in the lower portion of figure 2(b) for various successive bias voltages and magnetic fields. It is remarkable that a magnetic field applied perpendicular to the PZTFT lamella can induce the switching of the ferroelectric domains, which is comparable to that produced by electric fields—clearly there is significant room-temperature magnetoelectric coupling, but magnetic switching fatigues easily.

Recently two theoretical works were published related to PbZr_0.53Ti_0.47O₃)_(1−x)–(PbFe_0.5Ta_0.5O₃)_x (PZTFT) and (PbZr_0.53Ti_0.47O₃)_(1−x)–(PbFe_0.5Nb_0.5O₃)_x (PZTFN) single-phase multiferroic magnetoelectric materials. Morozovska's group [79] published a theoretical study in which they presented a phase diagram for PZTFT and PZTFN materials. They established the boundaries between paraelectric, ferroelectric, paramagnetic, antiferromagnetic, ferromagnetic and magnetoelectric phases. However, their predicted dome structures are not confirmed experimentally. On the other hand, Kuzian et al [80] proposed that the room temperature magnetism in these systems can be due to the existence of regions with a special chemical order that results in the ordered spins of antiferromagnetic interacting Fe³⁺ S = 5/2 spins.

In order to compensate the deficiencies of the natural multiferroics at ambient temperatures the fabrication of artificial multiferroics to enhance magnetoelectric effects opens up the possibility of tailoring the properties using two different compounds, one being ferromagnetic and other being ferroelectric [8, 26]. The aim of this technique is to create materials that display both properties of the parent compounds and their cross coupling, but the cross coupling is generally indirect via strain (magnetostriction plus electrostriction and/or piezoelectricity) and not direct polarisation-magnetisation (MP) interaction. A magnetic field applied to the composites will induce magnetostriction, which produces piezoelectric and/or electrostrictive responses. This ME property of the ferroelectric-ferromagnetic composite is known as a product-property of the composite [81]. The ME composites could have various connectivity schemes, but the common connectivity schemes are: (i) 0-3 type particulate composite where the piezoelectric/magnetic particles are embedded in a matrix of magnetic/piezoelectric phases; (ii) 2-2 type laminate ceramic composites consisting of the piezoelectric and magnetic oxide layers; and (iii) 1-3 type 'fibers' of one phase embedded in the matrix of another phase [8]. The composite structures open up new avenues for tailoring the ME response through the choice of phase properties, volume fraction, shape, connectivity and microstructure of the constituents. The room-temperature ME coupling coefficients of composite structures have been found to be at least three to five orders of magnitude higher than ME coupling for single-phase compounds [75]. This idea was initially developed in the ceramic-composite (0-3 type) [82–102], and later laminated multilayers were investigated [103–114].

The first work on the ME composite was done at the Philips laboratory [82–85] the ME composites were prepared by the unidirectional solidification of a eutectic composition of the quaternary system Fe–Co–Ti–Ba–O; the ME coefficient is $\text{d}E/\text{d}H$ = 130 mV cm⁻¹ Oe⁻¹ [82–84], which is superior to that of single-phase materials such as Cr₂O₃. In 1978 they reported on the sintered ME composite of BaTiO₃ and Ni(Co,Mn)Fe₂O₄ with excess TiO₂ in terms of the particle size effect, the cooling rate and the mole ratios of both phases [84]. After the pioneering experiment on BTO/CFO [82–85], a variety of ferroelectric/ferrite bulk compositions werefabricated consisting of ferroelectric phases such as BaTiO₃ (BTO), PbZr_1−xTi_xO₃ (PZT), PbTiO₃ (PT), polyvinylidenefluoride (PVDF) and ferromagnetic phases such as CoFe₂O₄ (CFO), Tb_1−xDy_xFe₂-Terfenol-D, NiFe₂O₄ (NFO), CuFe₂O₄ (CuFO) and LaMnO₃ (LMO). Although bulk composite materials were considered to exhibit promising (larger) ME effects, so far the observed ME coefficients in ceramic composites are ten times lower than theoretical calculation, which is mainly due to their inherent fabrication problems, such as atomic scale interfacial diffusion during the growth process, chemical reactions between the constituent starting materials during sintering processes, or the interdifusion of the phases. However, important efforts have been made to obtain the desired properties of individual constituents such as ferroelectric (good piezoelectric, high electromechanical coupling coefficients) and ferrite phases (good piezomagnetic, high magnetomechanical coupling coefficients, high resistivity), as well as the improvement of parameters related to the composite materials, via carefully chosen constituent materials, sintering processes, grain size, mole ratios, thermal expansion, mismatch between phases and the uniform distribution of the magnetostrictive phase within a piezoelectric matrix.

As a good example, Ryu et al [100] published an improvement of ME properties with a more homogeneous dispersion of the magnetostrictive phase (Ni_0.8Zn_0.2Fe₂O₄) into a piezoelectric matrix 0.9Pb(Zr_0.52Ti_0.48)O₃–0.1Pb(Zn_1/3Nb_2/3)O₃ (see figures 3(a) and (b)) and Ramanaa et al [99] synthesised Ni_0.83Co_0.15Cu_0.02Fe_1.9O₄ (NCCF)/PZT; they added Co and Cu to NiFeO₃ to increase the resistivity of the ferrite phase (NCCF), obtaining a maximum ME coefficient of 3.15 V cm⁻¹ Oe⁻¹ in the composite containing 0.5NCCF + 0.5PZT, as shown in figure 2(c). Due to the improved engineering process, a viable ME response can be observed in multiferroic ME composites above room temperature. Various ME bulk composites in different systems have been investigated; the first part of table 2 shows the list of some bulk composite that have been investigated over the last forty years.

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Although composite layers of ferromagnets and ferroelectrics make excellent devices as transducers, actuators and low magnetic field detectors (comparable to SDQUIDs), their speeds are generally unknown and apt to be slow, since their elastic coupling is limited by the speed of sound (ferroelectric domain wall speeds cannot be supersonic, although magnetic walls can be). Thus, they are unlikely to be useful as multiferroic magnetoelectric random access memories. Moreover, they are unlikely to be useful for voltage-controlled magnetic tunnel junctions (MTJs), since the total thickness of a tunnel junction must be  <6 nm, and interfaces greatly reduce tunneling currents. Thus, artificial superlattices and FE/FM layer structures are not promising for two important classes of magnetoelectric devices: These require single-crystal or single-phase epitaxial film multiferroics.

Yttrium manganite, YMnO₃ (YMO): this ABO₃ oxide belongs to the RMnO₃ (R = rare-earth element) system, which can be divided into two subsystems in which the crystal structure is mainly determined by the size of the R cation. For a larger R size (R = La, Dy) an orthorhombic perovskite structure is adopted, whereas for a smaller R (R = Sc, Y,Ho, Lu) the structure is hexagonal. One of the typical rare-earth manganites studied in thin-film form is YMnO₃; its structure can be hexagonal (ferroelectric) or orthorhombic (non-ferroelectric) depending on the epitaxial strain. Hexagonal YMO undergoes a paraelectric-ferroelectric phase transition at T_c ~ 900 K, and it displays an antiferromagnetic transition around 70 K. That is, YMO is a room-temperature ferroelectric and low-temperature multiferroic [119]. Aken et al [120] reported that the ferroelectricity mechanism in YMO is driven entirely by electrostatic and size effects (dipole-dipole interaction and oxygen rotations), rather the usual changes in chemical bonding associated with FE phase transition in perovskite oxide; although a corrected and complete analysis of the phase transitions sequence of YMO with the possible existence of intermediate phases, i.e. P6₃mc (FE) and P6₃ /mcm (paraelectric) between P6₃cm (FE) and P6₃/mmc (paraelectric), was reported subsequently by Fennie and Rabe [121]. The FE thin films are expected to be more suitable dielectric materials for metal-ferroelectric-semiconductor field-effect transistor (MFSFET) structures due to the absence of volatile components such as Pb, Ti or Ta, which can easily diffuse into semiconductors. Fujimura et al [4] proposed YMnO₃ thin films as a new candidate for nonvolatile memory devices, using rf magnetron sputtering. They fabricated epitaxial (0 0 0 1) YMnO₃ films on (1 1 1) MgO, (0 0 0 1)ZnO : Al/(0 0 0 1), sapphire, and polycrystalline films on (1 1 1)Pt /(1 1 1)MgO. The dielectric properties of the epitaxial and polycrystalline YMnO₃ films were almost the same. After Fujimura's publication in 1996, YMO thin films were synthesised via a wide variety of substrates and growth techniques [117]. Lee et al [122] used rf sputtering to grow c-axis oriented Pt /YMO/Y₂O₃/Si and Pt/YMO/Si—that is, metal/ferroelectric/insulator/semiconductor (MEFIS) and metal/ferroelectric/ semiconductor (MFS) structures, respectively. Electrical properties showed the memory window of the MEFIS is greater than that of the MFS capacitor. Later, Yoo et al [123], using the same growth technique and substrate utilised in reference 124, found that c-axis/polycrystalline (bi-layer) YMO thin films showed a better memory window than both purely c-axis oriented and purely polycrystalline YMO thin films. Epitaxial (0 0 0 1) YMO thin films on (1 1 1)Pt/(0 0 0 1)sapphire (epi-YMO/Pt) and Y₂O₃/Si (epi/YMO/Si) and YMO oriented polycrystalline films on (1 1 1)Pt/ZrO₂/SiO₂/Si were grown by using the PLD technique [124]; excellent ferroelectric properties were obtained in epitaxial films compared to oriented polycrystalline films. The crystallinity and CV hysteresis of the epi-YMO/Pt and epi/YMO/Si thin films were almost the same. Epitaxial YMO thin film is a ferroelectric material suitable for MEFIS applications. Dho et al [125] found that the growth orientation and surface morphology of YMO films were sensitively dependent on the substrate (lattice mismatch) and deposition conditions (oxygen background pressure); that is, for (1 1 1) SrTiO₃ (STO) substrates, the orthorhombic YMO phase competes with the hexagonal phase, which was induced by the strong compressive stress. YMO thin films were also synthesised by sol–gel processes using alkoxides on Pt(1 1 1)/Ti/SiO₂/Si [126]. It was found that higher sintering temperatures improve the ferroelectric polarisation and crystal crystallinity with preferential orientation. The highly c-axis oriented YMnO₃ thin films illustrated higher remanent polarisation (2P_r = 3.6 μ cm⁻²) compared with polycrystalline YMnO₃ thin films. More recently, Uusi-Esko et al [127] used atomic layer deposition (ALD) to grow both the hexagonal and orthorhombic forms of YMnO₃. On Si(1 0 0) substrates the product was the hexagonal phase of YMnO₃; whereas on LaAlO₃(1 0 0) and STO (1 0 0) substrates, the metastable orthorhombic YMnO₃ phase was formed. Foncuberta's group [128] grew orthorhombic epitaxial YMO [0 0 1] (c-axis) and [1 0 0] (a-axis) textured films on conducting Nb : STO substrates. They showed a bc-cycloidal magnetic order (bc plane) exists in YMnO₃ thin films and can be switched to ac-cycloid (ac plane, where a, b and c represent the directions of the x-, y-, z-axes)) by an appropriate magnetic field. This finding showed that a non-collinear spin arrangement in thin films allows switchable electrical polarisation and tunability of their dielectric response by magnetic fields; however, these experiments were carried out at 5 K. Finally, Wadati et al [129] fabricated thin films (40 nm) of YMnO₃ on a YAlO₃ (0 1 0) substrate by PLD. They reported two successive commensurate and incommensurate magnetic phase transitions below 35 K and 45 K, respectively, suggesting the existence of E-type cycloidal states. These results suggest that the large polarisation below 35 K was mainly due to the presence of magnetic ordering in epitaxial thin films. These films show highly correlated spin-electric polarization phenomena below 35 K, make them suitable candidates for next generation ferroelectric-gated field-effect FETs [122]. However, the high fabrication temperature (⩾800 °C) makes it impractical for integration into silicon technology [4, 119–128]. Further studies to achieve robust ferroelectric properties and room-temperature multiferroicity in manganites are pending.

The single-phase multiferroic that has been most studied in the last decade is BFO due to its multiferroic and potential magnetoelectric properties. BFO is a fully recognised room-temperature multiferroic that has all three ferroic order parameters—ferroelectric/ferroelastic (T_c = 1103 K) [130], antiferromagnetic (T_N = 643 K) [131]—and exhibits weak ferromagnetism at room temperature; however, the cross coupling between these ferroic parameters in single-phase form is very weak and poorly understood. Bulk BFO single crystals possess a rhombohedral perovskite structure (a = b = c = 5.63 Å, α = β = γ = 59.4°) [132]. In single-crystal form an early report found the spontaneous polarisation is ~6.1 μC cm⁻² along the (1 1 1) direction at 77 K [133], but this is known now to have simply been a poor sample. The ferroelectricity in BFO is due to the stereo-chemically-active 6s lone pair of Bi³⁺. Studies during the 1980s indicated the magnetic nature of BFO is a G-type antiferromagnetic order, wherein Fe³⁺ ions are surrounded by six neighbouring Fe³⁺ ions with spin anti-parallel to the central ion [134]. The symmetry also allows a canting of the antiferromagnetic sublattices, resulting in a macroscopic magnetisation 'weak ferromagnetism' [135]. In 2002, Palkar et al [136] reported weak ferroelectric properties in BFO thin films deposited on a Pt/TiO₂/SiO₂/Si substrate, and magnetoelectric properties were demonstrated by an anomaly in the dielectric constant in the vicinity of the Néel temperature; later, Yun et al [137] using the same substrate and technique as Palkar but lower oxygen pressure during deposition (0.01–0.1 Torr), obtained good current-voltage characteristics and an improvement in ferroelectric properties, high remanent polarisation (P_r), 2P_r ~ 71.3 μC cm⁻² and coercive field (Ec), 2E_c ~ 125 kV cm⁻¹. However, in 2003 Wang et al [25] reported epitaxial monoclinic BFO thin films grown on SrRuO₃/STO(1 0 0) substrates by PLD, with a surprisingly large electric polarisation response up to 2P_r ~ 120 μC cm⁻², which is one order of magnitude higher than the value of 6.1 initially reported from bulk BFO single crystal [130, 133]. These films also show enhanced thickness-dependent magnetism compared to the bulk, which is attributed to the mismatch strain induced by heteroepitaxy. This study has led to a growing interest in BFO thin films, which has endured until the present day, almost a decade after its publication. Later, Li et al [138] investigated the effects of the orientation of the STO substrate on crystallography and the ferroelectrical properties of BFO. BFO films grown on (1 1 1) had a rhombohedral structure like single crystals; whereas films grown on (1 0 1) or (0 0 1) were monoclinically distorted from the rhombohedral structure, attributed to the epitaxial constraint; the remanent polarisation in each case was 55, 80 and 100 μC cm⁻², respectively. Afterwards, a multilayer film of BiFeO₃/La_0.7Sr_0.3MnO₃/SrTiO₃ was deposited on a Si substrate by pulsed laser deposition. The BiFeO₃ film showed a low leakage-current density, and 2P_r ~ 110 μC cm⁻² was observed at room temperature [139] On the other hand, Shvartsman et al [140] showed large ferroelectric polarisation ~40 μC cm⁻² in ceramic BFO, a value close to the theoretically predicted value. Since the highest values of polarisation were obtained in ceramic, polycrystalline and epitaxial films, these results indicated the larger polarisation is not related to the strain but it is an intrinsic property of BFO, a result supported by first-principles calculation [141].

However, the major drawbacks for the BFO device are high leakage current, a tendency towards fatigue and thermal decomposition near the coercive field, which have been addressed by doped BFO, for example with Pr or Mn doping [142, 143]. Due to its exceptional ferroelectric properties, multiferroic nature, potential ME coupling and lead-free character, BFO remains a potential candidate for the next generation of ferroelectric memory applications. Recently Sando et al [144] reviewed work on BiFeO₃ epitaxial thin films, where they discussed the ferroelectric properties and ferroelectric photovoltaic response in strained or doped thin films, the correlation between strain, magnetic spins and electric polarisation, wide range optical properties, optical dielectric response, bandgaps, photovoltaic effects, and advances in the design of prototype devices for electronics, spintronics and photonics.

Another multiferroic single-phase material family very recently studied in thin-film form are lead-based solid solution perovskites (SSPs). To our knowledge the first publication on Pb-SSP thin films was from Ashok et al [37]. They reported single-phase polycrystalline (PbZr_0.53,Ti_0.47O₃)_0.8–(PbFe_0.67W_0.33O₃)_0.2, (0.8PZT/0.2PFW) synthesised by chemical solution deposition, a new room-temperature single-phase multiferroic magnetoelectric material. Later, the multiferroic properties of the single-phase 0.8PZT/0.2PFW system were confirmed by Lee et al [145, 146] by growing epitaxial 0.8PZT/0.2PFW films on a SRO coated STO (0 0 1) substrate. And (PbZr_0.53Ti_0.47O₃)_0.60–(PbFe_0.5Ta_0.5 O₃)_0.4, (0.6PZT/0.2PFT) highly oriented thin film was synthesised by PLD on La_0.67Sr_0.33CoO₃ coated MgO substrates. These films show near room temperature a frequency dependent dielectric maximum, moderate polarisation and a weak magnetic moment, as well as multiferroic relaxor characteristics [147]. The synthesis of single-phase solid solution materials using conventional and relaxor ferroelectrics might open a new way to realising a room-temperature multiferroic material with strong magnetoelectric coupling.

Martinez et al [151, 189, 190] investigated the structural analysis and multiferroic and magnetoelectric properties of Ba_0.7Sr_0.3TiO₃/La_0.7Sr_0.3MnO₃ superlattice (SL) thin films grown on LaNiO₃ (LNO) coated (1 0 0) MgO substrates by pulsed laser deposition. The thickness of the superlattice was kept constant (300 nm) irrespective of the modulation period in different SL-configurations. X-ray diffraction along with cross-sectional TEM of the (BST_20uc/LSMO_10uc)₂₅ show that SL structure was present in the thin films (figure 7(a)). The direct ME measurement illustrates a strong response of superlattice films, figure 7(b) shows the typical ME response of one of these SLs: a maximum peak for α_E,33 and α_E,31 at ~250 Oe and ~90 Oe, respectively, was seen, which further decreases monotonically to zero with an increase in the bias magnetic field (H). A similar H-dependent behaviour of the ME coefficients was seen for the superlattices with other periodicities (i.e. Λ = 18, 24 and 36 nm). The experimental data fitted well to a modified free-body model, (solid lines in figure 7(b)). From figure 7(c), the ME values follow a hyperbolic behaviour which increases for the longitudinal (α_E33) until Λ = 24 nm with further decrease in periodicities. A similar but inverse character is present in the case of the transverse ME coupling (α_E31). However, the evolution of the ME coefficient as a function of periodicity requires further research on interface-microstructure-property relations; at present it is very poorly understood. These results showed the substrate clamping and the resulting weakening of ME coupling that are usually encountered in piezoelectric-magnetostrictive bilayers was not observed in the systems studied here. The ME voltage coefficients are in the range 35–300 mV cm⁻¹ Oe for these MLs structures.

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Multiferroic ME materials offer the opportunity to study novel physical phenomena, and they present the possibility for their application in new multi-functional devices [215]: for example, transducers converting between magnetic and electric fields, attenuators, filters, field probes and data recording devices based on the electrical control of magnetisation, and vice versa [216]. With the presence of more than one ferroic parameter in multiferroics, the cross coupling can be utilised to design several novel types of memory elements [9] since we know that spontaneous polarisation and magnetic spins are used to program binary information in FeRAM (ferroelectric random access memory), and MRAM (magnetic random access memory). If a system has both ferroic orders with bilinear cross coupling, one can design at least four-state logic states in a single element. One can design the best multiferroic (MeRAM) memory elements with electrical write and magnetic read logic states with various spin orientations and polarisation directions. However, to realise the MeRAM device, researchers have to overcome many underlying challenges at the FE and FM interfaces and integration with silicon technology. Mathur [214] proposed novel simple single-domain multiferroic crystals with simple multiferroic domain dynamics under various external electrical and magnetic fields; however, until now most multiferroic systems show complex domain structures. Figure 8(a) illustrates the electrical control of ferromagnetism in multilayer films of the ferroelectric-ferroelastic and ferromagnetic sublayers. In multilayer structures piezoelectricity, electrostriction and magnetostriction each play an important role in modifying the magnetic spins and polarisations. Under an external E-field, the ferroelectric-ferroelastic layer produces mechanical strain in the FE layer. These FE layers coupled with the FM layer alter the magnetic spins via magnetostriction, which in turn changes the preferred orientations of the magnetic dipoles and therefore the macroscopic magnetisation. Bibes et al [215] explained the basic operation of a magnetoelectric random access memory (MeRAM). Figure 8(b) shows the process of encoding the binary information utilising the various magnetisation directions of the bottom ferromagnetic layer (blue). They proposed that the read process can be developed by exploiting the resistance of the magnetic trilayer (R_p when the spins of both magnetic layers are parallel), and written by applying a voltage across the multiferroic ferroelectric-antiferromagnetic layer (FE-AFM; green). They also proposed that if the strong coupling between the spins of multiferroics (small white arrows) and the bottom ferromagnetic layer exist, ferroelectric polarisation (since P is coupled with the spins shown in white) of multiferroics can be utilised to reverse the ferromagnetic spins in the trilayer from parallel to antiparallel. These coupled spins and polarisation can be easily utilised to encode various logic states for MeRAM.

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