Advances in Multiferroic Nanomaterials Assembled with Clusters

As an entirely new perspective of multifunctional materials, multiferroics have attracted a great deal of attention. With the rapidly developing microand nano-electro-mechanical system (MEMS&NEMS), the new kinds of microand nanodevices and functionalities aroused extensive research activity in the area of multiferroics. As an ideal building block to assemble the nanostructure, cluster exhibits particular physical properties related to the cluster size at nanoscale, which is efficient in controlling the multiferroic properties for nanomaterials. This review focuses on our recent advances in multiferroic nanomaterials assembled with clusters. In particular, the single phase multiferroic films and compound heterostructured multiferroic films assembled with clusters were introduced detailedly.This technique presents a new and efficient method to produce the nanostructuredmultiferroic materials for their potential application in NEMS devices.


Introduction
Multiferroics have attracted increasing attention due to simultaneous coexistence of ferromagnetic, ferroelectric, or ferroelastic ordering [1,2].Many researchers focused on the magnetoelectric effect driven by the prospect of controlling polarization by magnetic field and magnetization by electrical field [3], which opens up an entirely new perspective of magnetic/ferroelectric data storage media, spin-based devices (spintronics), magnetocapacitive devices, magnetic sensors, nonvolatile memories, random access memory, and so forth [4][5][6][7][8].Since its discovery a century ago, ferroelectricity has been linked to the ancient phenomena of magnetism.Attempts to combine the dipole and spin orders into one system started in the 1960s in Cr 2 O 3 single crystal [9,10], and other single phase multiferroics, including boracites (Ni 3 B 7 O 13 I, Cr 3 B 7 O 13 Cl) [10], fluorides (BaMF 4 , MMn, Fe, Co, Ni) [11,12], magnetite Fe 3 O 4 [13], (Y/Yb)MnO 3 [14], and BiFeO 3 [15], were identified in the following decades.However, such a combination in these multiferroics has been proven to be unexpectedly tough.
Moreover, by growing composite films combined with piezoelectric and magnetostrictive materials, the strong magnetoelectric coupling effect could be achieved due to product property.Much work has been done to prepare the composite films by combining perovskite ferroelectric oxides (e.g., Pb(Zr 0.52 Ti 0.48 )O 3 (PZT), BaTiO 3 ) with ferromagnetic oxides (e.g., CoFe 2 O 4 , La 0.67 Sr 0.33 MnO 3 ) [16][17][18][19][20][21]; however, due to the low magnetostriction of these ferromagnetic oxides and Ni metal, the reported magnetoelectric effects in these composite films are generally not strong.
As well known, rare earth iron alloy (R-Fe, R = rare earth element) possesses giant magnetostriction, being an order of magnitude greater than the ferromagnetic oxides [22].The previous investigations have shown that the magnetoelectric effect in the bulk laminate consisted of R-Fe alloy and ferroelectric oxide (e.g., Tb 0.30 Dy 0.70 Fe 2 (Terfenol-D)/PZT) with magnetoelectric coupling coefficient   of ∼4680 mV/cm⋅Oe is much larger than that of the all-oxide laminates (e.g., CoFe 2 O 4 /PZT; its   is ∼60 mV/cm⋅Oe) [23][24][25].However, with the applications in the micro-electro-mechanical system (MEMS) devices such as microtransducers, microactuators, and microsensors [26], the well-defined microstructures together with the tunable properties are necessary for the multiferroics.Therefore, for the laminated composite film (i.e., thin-film heterostructure), it could be expected that magnetoelectric effect would be enhanced significantly if the R-Fe alloy is used in the magnetostriction layer.Though the giant magnetostrictive films have been prepared by song conventional film preparation means [27][28][29][30], since the phase-formation temperature of R-Fe alloy is very high (the substrate is generally heated above 500 ∘ C), it is unavoidable to bring about serious oxygen diffusion from PZT oxide to Tb-Fe alloy.As a result, both magnetostriction in Tb-Fe alloy and piezoelectricity in PZT are seriously suppressed.Moreover, the serious oxygen diffusion would also generate a new interface layer, which further significantly decreases the magnetoelectric coupling efficiency [31].Therefore, a progress with low temperature and energy is necessary during deposition.Fortunately, we have developed an effective preparation method, namely, low energy cluster beam deposition (LECBD), to prepare the nanostructured magnetic, giant magnetostrictive, single phase multiferroic, and welldefined microstructured multiferroic heterostructured films [32][33][34][35][36][37][38].This paper aims to review the breakthroughs on the multiferroic nanostructure assembled with clusters.

Low Energy Cluster Beam Deposition
As a very important building block of nanomaterials, nanoclusters are aggregates of atoms or molecules of nanometric size, containing a number of constituent particles ranging from 10 to 10 6 [39][40][41].All the beam experiments on clusters have a cluster source, in which the clusters are produced.There are a variety of sources available including arc cluster ion source [42], laser vaporization cluster source [43,44], gas aggregation source [45,46], seeded supersonic nozzle source [47], ion sputtering source [48,49], and liquid metal ion source [50,51].Based on these we developed low energy cluster beam deposition method.A magnetron-sputtering-gasaggregation (MSGA) cluster source produce is used to produce cluster beam to assemble multiferroic films.The growth and deposition process of clusters is shown in Figure 1 using gas aggregation.A direct current (DC) pulse power was used as the sputtering power.As the sputtering gas, one stream of argon gas with 99.9% purity was introduced through a ring structure close to the surface of the target.Another stream of argon was fed as a buffer gas through a gas inlet near the magnetron discharge head.The cluster condensation and growth region was cooled with liquid nitrogen.A highly oriented cluster beam with a small divergent angle less than one degree was formed by differential pumping controlled by the skimmers.During the process of the deposition, the average velocity perpendicular to the substrate of each cluster is quite low (with less than 50 meV/atom corresponding to kinetic energy), and the velocity parallel to the substrate is about several meV/atom, which are both much lower than the molecular binding energy.The clusters are deposited on the substrate by a soft-landing manner and accumulated randomly but they do not coalesce with each other.
Based on this technique, various cluster-assembled nanostructured films such as metal and oxide have been prepared, which show peculiar properties different from the films prepared by the common methods [52][53][54][55].Since the size, mass, and the assembling manner of the clusters can be precisely tuned by changing the working gas flow, controlling the length of condensation region, changing the buffer gas, and so forth, it is possible to control the microstructures and properties of the cluster-assembled nanostructured films, which makes it an ideal candidate for the fabrication of single phase or heterostructured films.

Magnetic Films Assembled with Clusters
3.1.Giant Magnetostrictive R-Fe Films.The cubic Laves phase R-Fe (R = rare earth element such as Tb, Dy, Sm) compounds are well known to be a giant magnetostrictive material at room temperature, which could be widely used as actuators, transducers, dampers, and so forth [56,57].With the demand of the rapidly developing nano-electromechanical system (NEMS), much work has been done and various methods such as ion plating [27], ion beam sputtering [28], flash evaporation [29] and magnetron sputtering [58], and molecular beam epitaxy [59,60] have been developed for the preparation of R-Fe films.However, compared with the bulk materials, the saturation magnetostriction of the current R-Fe films is much lower while the magnetic driving field is still higher [58], which limits them to be further used.Fortunately, based on the LECBD technique, a welldefined Tb-Fe nanostructured film has been obtained, which  exhibits excellent magnetostriction, much higher than the common Tb-Fe films [34].Since the size, mass, and the assembling manner of the R-Fe clusters can be precisely tuned by changing the working gas flow, controlling the length of condensation region, changing the buffer gas, and so forth, it is possible to control the microstructures and magnetic properties of the cluster-assembled R-Fe nanostructured films, which makes it an ideal candidate for the fabrication of the magnetic NEMS devices.
A DC-magnetron-sputtering-gas-aggregation (MSGA) cluster source was used to produce the Tb-Fe cluster beam, which was finally deposited on the Si(100) substrate at room temperature to form the nanofilm.In order to tune the cluster size, the length of the condensing growth region  was set as 80 mm, 95 mm, and 110 mm, respectively.Figure 2 presents the SEM images and size distributions of the typical Tb-Fe films prepared under different length of the condensing growth region .One can clearly observe two facts: (i) all films are assembled by the spherical nanoparticles, which are distributed uniformly and monodispersely in the film; (ii) with the increase of the condensing growth region length, the size of the nanoparticle increases, being in the ranges of 31∼36 nm for  = 110 mm, 28∼33 nm for  = 95 mm, and 23∼28 nm for  = 80 mm, respectively.Meanwhile, we note that the particle size distribution was almost lognormal.The formation of such nanoparticle film is attributed to the unique LECBD preparation process.And the length of the cluster growth region significantly influences the size of the Tb-Fe clusters for the films.In fact, the growth of the clusters as well as their size distribution is mainly determined by the cluster residence time and its distribution [61,62].With increasing the length of the condensing growth region, the cluster residence time in the condensing growth region increases, and thus the collision among metal ion, Tb-Fe vapor, carrier gas, and free clusters becomes more sufficient, leading to the bigger size of the clusters.
It has been confirmed that all present nanoparticleassembled Tb-Fe films exhibit higher magnetostriction comparing to the common nonnanostructured films prepared by other methods [63][64][65].And we observe that the magnetostrictive behavior and piezomagnetic coefficient evidently vary with the average size of the nanoparticle.Figure 3 gives the magnetostriction and piezomagnetic coefficient on the magnetic field for the films with various particle sizes.With increasing the particle size, the saturation magnetostriction   and the saturation magnetic field   change, for example,   ∼ 816 × 10 higher magnetostriction and piezomagnetic coefficient at low magnetic field.It suggests that the dependence of the magnetostriction and piezomagnetic coefficient on the particle size could be attributed to the difference of the magnetization characteristic for these films.Figure 4 presents the field dependent magnetization at room temperature for the films with the particle sizes of 25 nm, 30 nm, and 35 nm.It is shown that the degree of magnetization anisotropy for the film is significantly affected by the particles size.Both in-plane and out-of-plane saturation magnetization change, as well as the coercivity with variation of the particle size.For the films with particles size of 30 nm, the degree of magnetic anisotropy is the maximum and the difference between in-plane and outof-plane saturation magnetization is maximum.The easy axis is out-of-plane.Thus particle size dependence of the magnetic anisotropy for the present films should be correlative to the exchange coupling effects between the nanoparticles in the film [66].Thus the film with  = 30 nm may show the highest degree of magnetic anisotropy because the exchange coupling distance is twice of the domain wall width (RFe ∼ 15 nm) for magnetic nanoparticles [67].Therefore, for the film with  = 30 nm, it has higher magnetic anisotropy than the other films.It needs far higher magnetic field to rotate the spin into the applied field.Therefore, the magnetostrictive coefficient of this film is lower than the other films at a low magnetic field, but, its saturation magnetostriction is the highest, which could be ascribed to the higher energy of anisotropy exchange interaction [68].

Enhanced Ferromagnetism of BiFeO 3
Films Assembled with Clusters.BiFeO 3 (BFO) is one of the most outstanding single-phase lead-free multiferroics due to its high ferroelectric Curie ( FE ∼ 1103 K) [69] and Neel (  ∼ 643 K) temperatures [70].However, for BFO materials, antiferromagnetism and a superimposed incommensurate cycloid spin structure with a periodicity of 62 nm along the [1 1 0] ℎ axis cancel the macroscopic magnetization at room temperature, which restricts its applications [71].Some investigations show that weak ferromagnetism is observed in some limited-dimension materials such as nanowires and nanoparticles due to the partial destruction of the spiral periodicity [72][73][74], which demonstrates a possible way to enhance ferromagnetism in single-phase multiferroics.Thus, as a size controllable building block of nanomaterials, clusters become a candidate to assemble multiferroics.Therefore, using LECBD technique, we have prepared the well-defined BiFeO 3 nanostructured films assembled with 0-characteristic-dimension clusters, and then the films were annealed at 600 ∘ C. As we expected, the ferromagnetism of the as-prepared BiFeO 3 films is enhanced [38].
Figure 5 gives the morphologies of cluster-assembled BiFeO 3 nanostructured films before annealing.It can be seen that the films are assembled with clusters, which are nearly spherical and densely packed to form the uniformly continuous films, whereas each individual cluster is still clearly distinguishable.The population versus the size reveals that the average size of the nanoparticles is ∼22 nm for asdeposited films and ∼25.5 nm for the annealed films and is attributed to the fact that the size of cluster increases derive from the improvement of crystallizing during the annealing process.
Figure 6 present the XRD patterns of the typical asdeposited and annealed nanostructured films assembled with clusters.They show that both present films are polycrystalline and all of the observed diffraction peaks can be indexed to a perovskite structure.And the as-deposited BFO nanostructured films and other common films belonging to the rhombohedral structure with space group R-3c (161) prepared by other methods annealed BFO films transform to the coexistence of tetragonal and orthorhombic symmetry structure as (104) and (110) diffraction peaks are not obviously split, which is observed by expanding the view of the XRD pattern around 2 = 32.6 ∘ in the inset of Figure 6.At the same time, the lattice constant of cluster-assembled BiFeO 3 films is  = 5.491 Å, smaller than those of the films prepared by other methods.It suggests that there exists a crystal distortion for the cluster-assembled BFO films, giving rise to a transition from the rhombohedral structure to tetragonal one [75][76][77], which means the crystal structure changes from a high symmetry state to a low symmetry state compared to bulk BFO materials.Thus the crystal distortion is due to the size effect of the clusters with the smaller characteristic size, which partially destroys the long-range cycloid spin structure with a periodicity of 62 nm in the rhombohedral structure with space group R-3c (161).It is such crystal distortion of the as-prepared films that brings about the enhancement in magnetization.
Figure 7 shows the magnetic hysteresis loops for the cluster-assembled BFO nanostructured films measured at 5 K and 300 K.As can be seen, obvious ferromagnetism is observed for the cluster-assembled BFO nanostructured films not only at 5 K but also at room temperature.In Particular, the saturation magnetization of the BFO films at room temperature reaches 108 emu/cc, which is comparable with that of the present films with 125 emu/cc at 5 K.More importantly, the large magnetization of 81 emu/cc is obtained at a magnetic field of 3000 Oe at room temperature, which is a larger response than the common films prepared by other methods [78][79][80].Such enhanced room temperature ferromagnetism is attributed to the fact the average size of BFO clusters is much less than the long-range cycloid order of 62 nm along the [1 1 0] ℎ axis that the periodicity of the spin cycloid is broken [81].Antiferromagnetic materials are considered as the combination of one sublattice with spins along one direction and another with spins along the opposite direction.If no spin canting is considered, the spins of these two sublattices compensate each other so that the net magnetization inside the material would become zero [82].However, the long-range antiferromagnetic order is frequently interrupted at the cluster surfaces, which forms the uncompensated surface spins.For the cluster-assembled BFO films with the average size of 25.5 nm, the uncompensated surface spins become very significant due to the very large surface to volume ratio for the clusters.The uncompensated spins at the surface enhance the contribution to the nanoparticle's overall magnetization.Besides, structural distortion and change of lattice parameter due to the size effect for the clusterassembled nanostructured films [83] lead to the release of the latent magnetization locked within the cycloid.Then the ferromagnetism of nanostructured films is significantly enhanced.

Multiferroic Film Heterostructure Assembled with Clusters
It is well known that composite films combined with piezoelectric and magnetostrictive materials can obtain stronger magnetoelectric effect than single phase materials [84] by the magnetic-mechanical-electric coupling product interaction via the stress mediation.Some composite films combined by perovskite ferroelectric oxides (e.g., Pb(Zr 0.52 Ti 0.48 )O 3 (PZT), BaTiO 3 ) with ferromagnetic oxides (e.g., CoFe 2 O 4 , La 0.67 Sr 0.33 MnO 3 ) [18,21,85,86] did not acquire strong magnetoelectric effect due to low magnetostriction of the ferromagnetic oxides.Since we had prepared giant magnetostrictive R-Fe films using low energy cluster beam deposition, it is possible to prepare the well-defined microstructured thinfilm multiferroic heterostructure consisting of R-Fe alloy and ferroelectric oxide.And the substrate is ferroelectric oxide; the degree of the interfacial reaction or diffusion between Tb-Fe alloy and ferroelectric oxide would be greatly suppressed due to the low temperature and energy during LECBD progress.Thus well-defined microstructure of thinfilm heterostructure as well as strong magnetoelectric effect would be obtained.
4.1.Tb-Fe/PZT Thin-Film Heterostructure.Tb-Fe nanocluster beam was deposited onto the surface of the PZT film through the open holes of the mask by LECBD progress.After deposition, not taking off the mask, a Pt electrode layer was deposited on the Tb-Fe dots via pulse laser deposition.Figure 8 presents the surface SEM image of the Tb-Fe layer in the heterostructure.It shows that the Tb-Fe layer is compactly assembled by the regular spherical nanoclusters, which are distributed uniformly and adjacent with each other.The structure of the thin-film heterostructure is sketched in Insert (a) of Figure 8. Insert (b) of Figure 8 shows the cross-sectional SEM image of the thin-film heterostructure.One observes that the interface between Tb-Fe and PZT layers is clear and no transition layer is observed, which is benefit from the LECBD progress.During this process, the phase formation of Tb-Fe nanoclusters (or nanoparticles) is achieved in the condensation chamber with high temperature, while the deposition of Tb-Fe nanocluster beam onto the substrate is achieved in another high vacuum chamber with low energy  and low temperature (e.g., room temperature).Both processes are independent of each other.It is easy to understand no reaction between Tb-Fe and PZT layers.
No destroying between Tb-Fe and PZT layers gives a feasibility of well ferroelectric and ferromagnetic properties.Figure 9 gives the polarization versus electric field hysteresis loops and magnetic hysteresis loops for the Tb-Fe/PZT thinfilm heterostructure.It shows that the well-defined ferroelectric loops are observed.The saturation polarization and remanent polarization for Tb-Fe/PZT thin-film heterostructure have a very slight decrease compared with the pure PZT film.Such slight decrease in ferroelectric properties of the heterostructure should be attributed to the increase of oxygen vacancy concentration in PZT layer, which brings about difficulty for the mobility of domain walls in a certain degree and further leads to the decrease in polarization [87].Insert of Figure 9(a) shows that the leakage current density in the heterostructure is quite low, for example, only being ∼1.5 × 10 −4 A/cm 2 even under the higher electric field of 30 MV/m.In spite of this, we found that the leakage current density in the heterostructure was still higher than that of the pure PZT film, which indicates the increase of free carrier density in PZT layer of the heterostructure [88].
Besides, the heterostructure exhibits the well-defined magnetic hysteresis loops.It shows that both in-plane and out-of-plane coercive field are the same as only   ∼ 60 Oe, much lower than that of the bulk Tb-Fe alloy, while the in-plane and out-of-plane saturation magnetizations are, respectively, ∼38 emu/cm 3 and ∼47 emu/cm 3 .We notice that the magnetization character of the heterostructure is almost comparable to the pure nanostructured Tb-Fe film prepared by LECBD process.Since magnetoelectric effect in a two-phase composite mainly originates from the interfacial stress transfer between the magnetostrictive and the ferroelectric phase, the high magnetostriction and ferroelectrics are beneficial to the magnetoelectric coupling.A strong magnetoelectric coupling could be obtained in the thin-film heterostructure.
Figure 10 plots the magnetic bias  bias dependence of the induced voltage increment |Δ ME | at a given ac magnetic field frequency  = 1.0kHz.It shows that thin-film heterostructure exhibits strong magnetoelectric coupling.The calculated maximum increment of the magnetoelectric voltage coefficient is as high as ∼140 mV/cm⋅Oe, larger than that of the reported all-oxide ferroelectric-ferromagnetic composite film [16][17][18].So strong magnetoelectric effect in Tb-Fe/PZT thin-film heterostructure is evidently beneficial from the unique LECBD process.Based on this process, not only could the interface reaction be availably avoided on the maximum degree, but also both ferroelectric and magnetostrictive properties for PZT and Tb-Fe could be maintained well.Insert of Figure 10 shows the  bias dependence of piezomagnetic coefficient  (= / bias ) for the pure Tb-Fe nanostructured film prepared by LECBD process.Both |Δ ME | in heterostructure and  in Tb-Fe film have the similar change trend with  bias .This indicates that the magnetoelectric coupling in the heterostructure should be dominated by the magnetic-mechanical-electric transform through the stress-mediated transfer.
4.2.Sm-Fe/PVDF Thin-Film Heterostructure.For Si based magnetoelectric composited films, the couple efficiency between ferroelectric and ferromagnetic phases was depressed due to the stress clamping effect of the hard substrate.Therefore a flexible polyvinylidene fluoride (PVDF) film may be used instead of the hard substrate due to its small Young's modulus.Thus the magnetoelectric coupling between the ferroelectric and ferromagnetic phases will almost be not influenced.Moreover, piezoelectric voltage constant ( 31 ) of PVDF film is an order higher than that of ordinary PZT film, which allows it to generate a bigger voltage output under a small stress.This indicates that PVDF film is suitable to act as the piezoelectric phase in the magnetoelectric thin-film heterostructure.
The flexible PVDF/Sm-Fe heterostructural film was prepared by depositing Sm-Fe nanocluster beam onto the PVDF film at room temperature using LECBD technique.Though it is very easy to destroy the PVDF polymer substrate, it can be avoidable during LECBD progress with quite low energy and low temperature.Figure 11 shows the cross-section SEM image of the Sm-Fe/PVDF film.It can clearly be observed that the interface between the PVDF film and Sm-Fe layer is clear and no evident transition layer appears, indicating that the PVDF film does not get destroyed during the process of LECBD.The well-defined heterostructure makes it possible to generate the strong magnetoelectric effect.
The Sm-Fe film exhibits strong negative magnetostrictive effect with a saturation value of ∼750 × 10 −6 at magnetic field of ∼7.0 kOe as shown in Figure 12.Inset of Figure 12 shows that the Sm-Fe/PVDF film exhibits distinct magnetic anisotropy with an in-plane magnetic easy axis, which obviously makes the magnetoelectric coupling in the Sm-Fe/PVDF film be more efficient under an in-plane magnetic field.For thin-film heterostructure, a large magnetoelectric voltage output can be obtained.Figure 13 gives the magnetoelectric voltage output increment |Δ ME | value as a function of  bias for the Sm-Fe/PVDF film.It is seen that the film exhibits a large voltage output under the external magnetic bias.The |Δ ME | value increases with increasing  bias , reaching the maximum value of |Δ ME | ∼ 210 V at  bias = 2.3 kOe, and then drops.Compared with the previous investigations, the magnetoelectric voltage output in the present Sm-Fe/PVDF film is remarkably large, almost being two orders higher than that of typical all-oxide PZT/CoFe 2 O 4 /PZT film deposited on the hard wafer [89].
Therefore, by using the flexible PVDF polymer film as the substrate, the substrate clamping effect on the magnetoelectric coupling of the heterostructural film is completely eliminated.The heterostructural film exhibits large magnetoelectric voltage output, which is mainly attributed to the large piezoelectric voltage constant in the piezoelectric PVDF layer and high magnetic anisotropy with in-plane magnetic easy axis as well as the giant negative magnetostriction in the ferromagnetic Sm-Fe layer.

Conclusions
In a conclusion, the single phase multiferroic films and compound heterostructured multiferroic films assembled with clusters were prepared by low energy cluster beam deposition.It shows that the multiferroic properties of the thin-films can be controlled or improved by tuning the size of the clusters.And the structure of the thin-film heterostructure would not be destroyed due to low temperature and energy during LECBD progress.The LECBD technique provides an ideal avenue to prepare multiferroic nanostructure and facilitates their applications on NEMS devices.

Figure 1 :
Figure 1: The sketched diagram of the growth and deposition process of clusters.

Figure 2 :
Figure 2: SEM images of the typical as-deposited Tb-Fe films and the graph of population versus size distribution of the nanoparticles at different growth region length.(a) 110 mm, (b) 950 mm (c), and 80 mm ([36]).

Figure 3 :
Figure 3: The dependence of magnetostriction and piezomagnetic coefficient for the Tb-Fe nanostructured film on various particle sizes.

Figure 4 :
Figure 4: Magnetic hysteresis loops for the Tb-Fe nanostructured film assembled by the clusters (a) with 35 nm in diameter, (b) with 30 nm in diameter, and (c) with 25 nm in diameter.

Figure 5 :Figure 6 :
Figure 5: (a) Typical SEM image of as-deposited BFO nanostructured films, (b) the films after annealing, and the inset is the graph of population versus size distribution of the clusters.

Magnetization (10 3 AFigure 7 :
Figure 7: The magnetization dependence on the magnetic field of the typical cluster-assembled BFO nanostructured films (a) at low temperature of 5 K, (b) at 300 K.The inset is the expand view of the magnetic hysteresis.

Figure 8 :
Figure 8: The surface SEM image of the Tb-Fe layer in the thinfilm heterostructure.Insert (a) is a sketch of the heterostructure, and Insert (b) is the typical cross-sectional SEM image of the heterostructure.

Figure 9 :Figure 10 :
Figure 9: (a) Polarization versus electric field hysteresis (-) loops for the thin-film heterostructure.Insert is the variation of leakage current density with the applied electric field.(b) The field dependent magnetization (-) curves for the thin-film heterostructure.

Figure 13 :
Figure 13: Induced voltage increment |Δ ME | as a function of magnetic bias  bias .