Strain-gradient effects in nanoscale- engineered magnetoelectric materials Cite as: APL Mater. 9, 020903 (2021); https://doi.org/10.1063/5.0037421 Submitted: 13 November 2020 . Accepted: 22 January 2021 . Published Online: 12 February 2021 Aliona Nicolenco, Muireann de h-Óra, Chao Yun, Judith MacManus-Driscoll, and Jordi Sort COLLECTIONS Paper published as part of the special topic on Magnetoelectric Materials, Phenomena, and Devices ARTICLES YOU MAY BE INTERESTED IN Advances in magneto-ionic materials and perspectives for their application APL Materials 9, 030903 (2021); https://doi.org/10.1063/5.0042544 Ferroelectric/multiferroic self-assembled vertically aligned nanocomposites: Current and future status APL Materials 9, 030904 (2021); https://doi.org/10.1063/5.0035366 Emerging opportunities for voltage-driven magneto-ionic control in ferroic heterostructures APL Materials 9, 040904 (2021); https://doi.org/10.1063/5.0045820 APL Mater. 9, 020903 (2021); https://doi.org/10.1063/5.0037421 9, 020903 © 2021 Author(s). APL Materials PERSPECTIVE scitation.org/journal/apm Strain-gradient effects in nanoscale-engineered magnetoelectric materials Cite as: APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 Submitted: 13 November 2020 • Accepted: 22 January 2021 • Published Online: 12 February 2021 Aliona Nicolenco,1,2 Muireann de h-Óra,3 Chao Yun,3 Judith MacManus-Driscoll,3,a) and Jordi Sort1,4,a) AFFILIATIONS 1 Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2 Institute of Applied Physics, 2028 Chisinau, Moldova 3 Department of Materials Science and Metallurgy, University of Cambridge, CB3 OFS Cambridge, United Kingdom 4 Institució Catalana de Recerca i Estudis Avançats, Pg. Lluís Companys 23, 08010 Barcelona, Spain Note: This paper is part of the Special Topic on Magnetoelectric Materials, Phenomena, and Devices. a) Authors to whom correspondence should be addressed: jld35@cam.ac.uk and jordi.sort@uab.cat ABSTRACT Understanding strain gradient phenomena is of paramount importance in diverse areas of condensed matter physics. This effect is responsible for flexoelectricity in dielectric materials, and it plays a crucial role in the mechanical behavior of nanoscale-sized specimens. In magneto- electric composites, which comprise piezoelectric or ferroelectric (FE) materials coupled to magnetostrictive (MS) phases, the strain gradient can add to any uniform strain that is present to boost the strength of the coupling. Hence, it could be advantageous to develop new types of functionally graded multiferroic composites (for information technologies) or magnetic-field-driven flexoelectric/magnetostrictive platforms for wireless neurons/muscle cell stimulation (in biomedicine). In MS or FE materials with non-fully constrained geometries (e.g., cantilevers, porous layers, or vertically aligned patterned films), strain gradients can be generated by applying a magnetic field (to MS phases) or an elec- tric field (to, e.g., FE phases). While multiferroic composites operating using uniform strains have been extensively investigated in the past, examples of new nanoengineering strategies to achieve strain-gradient-mediated magnetoelectric effects that could ultimately lead to high flexomagnetoelectric effects are discussed in this Perspective. © 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0037421., s I. INTRODUCTION exploited in microelectromechanical systems and to reduce energy consumption of magnetic memories and spintronic devices.8 Magnetism and electricity have always had an intimate link. The idea of using strain transfer to induce a coupling between Particularly interesting is the coexistence of magnetic and elec- FE and MS phases in multiferroic heterostructures dates back to tric orders in magnetoelectric (ME) materials, which makes them 1972,9 a few years after the intrinsic magnetoelectric effect had able to respond, simultaneously, to external magnetic and electric been experimentally demonstrated for the first time in single-phase stimuli: (i) electric polarization can be modulated by the external Cr2 O3 10 (see Fig. 1). During subsequent years, particulate compos- magnetic field (direct ME effect, DME) and (ii) magnetic proper- ites, comprising either FE (e.g., BaTiO3 ) or MS (e.g., CoFe2 O4 ) ties can be largely controlled with an electric field (converse ME particles,11,12 were extensively studied for their potential applica- effect, CME).1 In conventional ME composites, the coupling between tions. However, the weak ME coupling in multiferroics (single-phase piezoelectric [or ferroelectric (FE)] and magnetostrictive (MS) con- and heterostructured) at room temperature and the high dielec- stituents is mediated by homogeneous interfacial strain and, in some tric losses have hampered practical applications of these materials. cases, by electric surface charge effects.2,3 DME effects are appealing During the 1990s, the interest in magnetoelectricity was revived for healthcare technologies,4 water remediation,5 energy harvest- again when a wide range of advanced experimental techniques for ing systems,6 and sensors/actuators,7 whereas CME effects can be synthesis and characterization of nanomaterials became available APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 9, 020903-1 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm FIG. 1. Timeline illustrating the major milestones in the investigation of the ME effect. [e.g., piezoresponse force microscopy, scanning transmission elec- use of flexible substrates can minimize this problem but high- tron microscopy, and advanced pulsed laser deposition (PLD) tech- quality FE/MS bilayers (specially containing oxide FE) are not easy niques] that triggered new theoretical advances (e.g., development to prepare on flexible substrates. To overcome the aforementioned of a density-functional theory), allowing a better understanding of challenges and thus to achieve large DME and CME effects with this phenomenon. low applied voltages, strain gradient effects in continuous (non- A further leap in the field occurred in 2000 when the con- patterned) films grown on rigid substrates could be used while verse magnetoelectric effect, experimentally demonstrated by Ohno circumventing the problems of substrate clamping. et al.13 and Weisheit et al.,14 was shown to be a suitable strategy In contrast to conventional piezoelectricity where the change to manipulate the magnetic properties of diluted semiconductors in polarization is induced by homogeneous strain, the gradient of and ultra-thin metallic films with voltage. Concurrently, laminated strain ultimately leads to the “flexoelectric effect,” which is universal composites based on new materials [e.g., Terfenol-D, Metglas or for all dielectric materials.23 The flexoelectric effect is proportional Pb(Mg1/3 Nb2/3 )O3 –PbTiO3 ] soon became available, leading to ME to the dielectric constant, and since FEs have very large dielectric coupling coefficients tens of times larger than in particulate com- constants, flexoelectricity is maximized for this class of materials. posites.15 Then, two-phase, vertical nanocomposite/nanostructured The flexoelectric coefficients in dielectrics have been measured to films (VANs) began to be explored.16 Many VAN reports have been be in the range 10−4 μC/m–10−5 μC/m in elastomers,24 100 μC/m in made over the last nearly 20 years, with attention focused on the piezoelectric BaSrTiO3 ,25 287 μC/m–418 μC/m in FE BaTiO3 ,26 and manipulation of vertical strain rather than lateral (horizontal) strain, even as high as 1000 μC/m in the oxygen-depleted BaTiO3-δ semi- which is the case for standard heterostructures,17 and advances in conductor, BTO-δ .27 Furthermore, there have been predictions that micro-/nano-thin film technology, with atomic-scale control of the flexoelectricity should significantly enhance the piezoelectric perfor- connectivity between the phases, have further contributed to the mance at the nanoscale,28,29 although direct evidence of this remains renaissance of magnetoelectricity. rather elusive due to the difficulties in generating strain gradients During the last 20 years, a large increase in the number of pub- in conventional clamped thin films. At the surface of a film under lications and patents covering magnetoelectric effects in the areas a mechanical force of 0.1 μN, the effective piezoelectric coefficient, of spintronics, memories, sensors, actuators, biomedical application, deff 33 , has been shown to be an order of magnitude larger in flexo- and many others has been observed (the number exceeds 20 000 electric SrTiO3 than in piezoelectric quartz.30 The flexoelectric effect according to the ISI Web of Science). Most of these works focus diminishes with distance, r, from the mechanical tip-to-surface con- on conventional multiferroic composites (where the ME effects tact (1/r3 for 3D geometries), hence the reason why flexoelectricity are mediated by homogeneous strain), magneto-ionics, or surface specifically dominates in thin films.31 charge effects. The effects of strain gradients in ME heterostruc- In terms of the impact of flexoelectricity on magnetoelectric tures still remain rather unexplored (only around 50 publications effects, there have been only a few experimental reports in the during the last five years). Nanoporous materials,18 polymer-based last few years of flexoelectricity combined with magnetism.20,32,33 composites,19 and VANs20 constitute the most promising materials The state-of-the-art in the development of these strain-gradient- for strain-gradient engineered ME composites and require deeper mediated magnetoelectric materials and future potential directions exploration. is discussed in this Perspective. Specifically, in Sec. II, we discuss There are several challenges associated with the operation of mechanically induced strain gradient effects in FE and MS con- conventional ME composites. In MS films directly grown onto FE tinuous layers that were traditionally studied separately and have substrates, the voltage required to generate ME effects is extremely not been combined yet to produce ME composites. In Sec. III, we high (e.g., 4 kV)21 due to the large thickness of the substrate (i.e., then focus on the strain-gradient-mediated ME bilayers based on in capacitors, the electric field is inversely proportional to the dielec- a mesoporous/nanoporous MS matrix partially filled with the FE tric thickness). This is not suitable for microelectronics, where much phase that can be prepared to boost strain gradient effects. When lower voltages (<10 V) are desirable to enhance energy efficiency grown onto rigid substrates, ME effects in such heterostructures and not burn the electronic components. If thin FE/MS bilayers are are mediated by strain-gradients instead of homogeneous strain. directly grown onto rigid (non-FE) substrates, then the required The effect is enhanced in high-aspect-ratio patterned elements, i.e., voltages are lower, but the attainable strain is small due to the VANs, where clamping occurs only right at the bottom part of the clamping with the substrate, thus also limiting ME effects.22 The structure, and so, lateral strains are developed along the vertical APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 9, 020903-2 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm direction, as it is discussed in detail in Sec. IV. Finally, we provide an case of complex 3D porous structures; (ii) porous materials show outlook for the possible application of the strain-gradient-mediated complex magnetostrictive behavior that is difficult to predict (mag- ME composites in Sec. V, and some general conclusions are given in netostriction can either increase or decrease or remain unchanged Sec. VI. dependently on the magnetostrictive constants and porosity degree) and sometimes even more difficult to measure;47 (iii) for CME, II. MECHANICALLY INDUCED STRAIN GRADIENTS the FE phase should not have electric pinholes (otherwise the elec- IN MAGNETOSTRICTIVE AND FERROELECTRIC tric charges are not accumulated to create the electric field), which MATERIALS sometimes may become a technological challenge. Nevertheless, MS meso-/nanoporous materials are excellent candidates to study the Strain gradients can be mechanically induced in bulk specimens strain-gradient induced ME effects, as it is discussed hereafter. or dense films by, for example, bending or nanoindentation. The An interesting example of this type of composite is the uniform highest possible strain gradients in materials with self-constrained deposition of piezoelectric lead zirconate titanate (PZT) into the (i.e., non-porous) geometries occur at the end of crack tips.34 The templated mesoporous MS CoFe2 O4 thin film for CME.45 Out-of- interplay between flexoelectricity and fracture behavior has been plane (OOP) magnetic measurements of this system revealed that, studied in some detail in several oxide materials (including bone or contrary to expectations based on the total PZT volume fraction, FE compounds).35,36 Crack-propagation in FE oxides can be either mesoporous CFO samples partially filled with PZT showed larger aided or obstructed by the orientation of the ferroelectric polar- changes in the magnetization than the sample with fully filled pores. ization. In other words, the strain-gradient at the tip of the crack The authors argued that the residual porosity in the composites induces a flexoelectric polarization either antiparallel or parallel to added mechanical flexibility enabling greater ME coupling, which the ferroelectric polar axis, thereby resulting in asymmetric crack can be interpreted as a consequence of strain gradient effects. Sim- formation.37 ilar results were also reported in mesoporous BiFeO3 single-phase In turn, the effects of nanoindentation strain gradients on the multiferroic on application of an electric field.48 magnetic properties of some specific alloys (FeAl, FeRh, etc.) have Another recent example is the growth of porous FeGa MS layers also been investigated in detail. FeAl undergoes an order-disorder by electrodeposition onto rigid Si/Cu substrates and the subsequent paramagnetic-to-ferromagnetic transition when subjected to plas- coating with the P(VDF-TrFE) FE polymer by spin coating.49 Under tic deformation at the atomic scale.38 FeRh exhibits a metamag- the magnetic field (DME), the FeGa was found to be compressed, on netic transition (from the antiferromagnetic to ferromagnetic state) average, by 0.033% [as evidenced by x-ray diffraction (XRD)]. The that can be also tuned by the strain gradient (i.e., a direct spa- experimental results revealed that while the bottom of the FeGa layer tial correlation between the metamagnetic transition temperature remains clamped, its air side exhibits a pronounced tetragonal defor- of this alloy and local strain values has been recently reported).39 mation, thanks to the residual nanoporosity existing between the The flexoelectric effects induced by nanoindentation in multifer- columnar grains of the electrodeposited films (see Fig. 2). It is worth roic materials could give rise to changes in the magnetic prop- mentioning that while the FE layer most likely experiences an homo- erties (i.e., to give flexomagnetism). The changes in the magnetic geneous strain due to its relatively large thickness (strain-gradient behavior of materials caused by inhomogeneous FE polarization effects are more pronounced at the nanoscale), the magnetic-field have been sometimes referred to as flexomagnetoelectric effects.40,41 induced strain gradient in nanoporous FeGa causes a change in the These have been reported in certain single phase multiferroics, but piezoresponse of the adjacent ferroelectric P(VDF-TrFE) layer, as their strength could be enhanced in suitably engineered composites evidenced by piezo-response force microscopy. (note that the strain-gradient effects in MS and FE materials so far These works thus reveal that, owing to their high mechanical have been mainly studied separately). In particular, one could try to flexibility, nanoporous materials offer unique opportunities for the control crack propagation as a means to tailor the performance of design of strain-gradient mediated ME structures. Specifically, MS magnetoelectric devices to achieve an optimized CME. porous matrices could be used to produce inorganic–organic com- posites by, e.g., infiltrating the FE polymers. Such heterostructures III. STRAIN GRADIENTS IN MAGNETOELECTRIC are expected to have a larger biocompatibility (see Sec. V for further COMPOSITES BASED ON MESOPOROUS AND details) due to the reduced Young’s modulus of the porous metallic NANOPOROUS MATERIALS counterpart.50 In addition, in high surface area composites, the flex- Mesoporous and nanoporous materials have recently attracted oelectricity caused by inhomogeneous strain generated by each MS much attention for the fabrication of ME composites due to their ligament can be added to piezoelectricity leading to an enhanced ME ability to accommodate various guest materials.42–44 It is worth men- effect. tioning that the vast majority of works deal with CME, where the changes in magnetic properties of the porous matrix are governed by electric surface charge accumulation or interface oxidation– IV. STRAIN GRADIENTS IN VERTICALLY ALIGNED reduction reactions.3,18 Indeed, in these cases, the presence of pores NANOCOMPOSITES brings about a drastic increase in the surface-to-volume ratio that Strain coupling between piezoelectric and magnetostrictive significantly enhances ME effects. Only a few studies were focused materials in VAN systems has been widely explored over many on the strain-mediated ME composites based on porous materi- years. There are two main types. The first type is made by chem- als.43,45,46 This is probably due to several factors: (i) a high-quality ical solution methods, which do not rely on epitaxial growth and interface should be created between the MS and FE phases to ensure where feature sizes are relatively large (>100 nm),51 and the second effective transfer of strain, which may not be straightforward in the type are VANs made by physical vapor deposition, with feature sizes APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 9, 020903-3 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm FIG. 2. Magnetoelectricity in a FeGa/P(VDF-TrFE) bilayer mediated by a strain gradient developed in the FeGa phase. (a) The topography image, (b) schematic illustration of the strain gradient development in each FeGa grain, (c) local piezo-response ampli- tude, and (d) phase loops obtained from the Fe–Ga/P(VDF-TrFE) heterostructure without (MF Off) and with (MF On) the application of a magnetic field of 0.1 T. Adapted from Ref. 49. of ∼10 nm–20 nm. Similar to the composites discussed in Sec. III pillar length, the polarization direction of the P(VDF-TrFE) pillars above, these VAN systems are substrate anchored and hence have could be reversed using magnetic fields. the potential for memory and sensor applications. Considering the physical vapor deposited systems, here ME There are only a few experimental works of the chemical- effects in VAN films have been obtained in many systems incor- method composite films that exploit the flexoelectric effect.33,52,53 porating FE (and hence piezoelectric) phases, such as BaTiO3 or Flexoelectricity is combined with magnetostriction to produce ver- BiFeO3 , with MS systems (CoFe2 O4 being the most common). The tically coupled ME composite materials. A notable example is the films are grown in the epitaxial form in a one step process by physi- work of Poddar et al. who fabricated Ni matrix/P(VDF-TrFE) pillar cal vapor deposition, and the VAN structure forms by self-assembly films.20 Periodic arrays of FE P(VDF-TrFE) square pillars (62 nm [schematic VAN structure shown in Fig. 4(a)]. Results for both the height and ∼185 nm lateral size) were obtained by nanoimprint DME effect54–59 and the CME effect60 have been achieved. The ME lithography, and the MS Ni matrix was made by electrodeposition coupling coefficients in such VAN structures are typically ∼10−9 [Fig. 3(a)]. The Ni matrix was physically clamped to a rigid substrate. s/m. Challenges for these systems are electrical leakage, and the need It was demonstrated that the polarization of the FE P(VDF-TrFE) to apply a magnetic field to realize the maximum ME coupling effect, can be locally switched by an external magnetic field applied to the not only for DME but also CME.60 composite due to transfer of inhomogeneous strain from the MS As far as known, strain-gradient-mediated/flexoelectric- Ni matrix. The strain induced in the P(VDF-TrFE) pillars increased mediated magnetoelectricity has not been studied in these self- from the bottom to the top, producing a strain gradient (and hence assembled VAN composites. However, there is much promise since the flexoelectric effect) along the z vertical axis. Finite element anal- VAN films have both vertical strain and thickness-dependent strain ysis demonstrated that as the distance from the substrate increases, gradient effects. Hence, it should be possible to induce either a flex- the Ni matrix contracts (negative vertical displacement field, U3 ), oelectric effect in a FE phase or a large strain gradient effect in a MS while the pillars experience a large expansion (positive U3 ), as shown phase. in Fig. 3(b). The strain in the pillars increased significantly with We consider in Fig. 4 a VAN film example from our ear- thickness [Fig. 3(c)]. From these data, the flexoelectrically gener- lier work where thickness-dependent strain and strain gradients ated electric field profile could be obtained [Fig. 3(d)]. Notably, have been measured.61 The system is La0.9 Ba0.1 MnO3 (LBMO, the largest changes occurred within the first 20 nm from the sub- matrix)/CeO2 (pillar) grown by pulsed laser deposition (PLD) from strate, which further supports that flexoelectric effects are more pro- a composite target on single crystal SrTiO3 . The LBMO film is insu- nounced in features with very small dimensions.23 Due to the strain lating, and based on the fact that FM 3d metals typically show MS gradient effects and the inhomogeneous ME coupling along the behavior,62 and insulating La0.8 Ba0.2 MnO3 63 shows a large MS effect APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 9, 020903-4 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm FIG. 3. Strain-gradient mediated Ni/P(VDF-TrFE) composite. (a) The SEM image of the heterostructure showing P(VDF-TrFE) nanopillars embedded in an electrodeposited Ni matrix. [(b)–(d)] Finite element analysis: (b) the vertical displacement field in the pillars and matrix normalized by the magnetostrictive strain, (c) average and maximum strains in the FE pillars along the vertical position, and (d) average and maximum strain-gradient-generated electric fields along the vertical position of the P(VDF-TrFE) pillar. Reprinted with the permission from Poddar et al., ACS Nano 12(1), 576–584 (2018). Copyright 2018. American Chemical Society. FIG. 4. One-step thin film process for inducing flexoelectricity via self-assembled vertically aligned nanocomposite (VAN) films. (a) The schematic of a VAN structure illustrating how vertical strain induced by the substrate relaxes as the film grows, whereas vertical strain induced by the vertical pillars stays constant. (b) The XRD plot for the exemplar system LBMO/CeO2 showing the increasing vertical strain with film thickness, switching from substrate-controlled to pillar controlled strain. The arrows indicate the positions of the LBMO (003) film peaks that overlap the STO (003) peak. (c) The percentage change in out-of-plane (OOP) strain vs the bulk material, with increasing thickness across three different regions of A, B, and C. (d) The schematic of the average strain state in a VAN film cross section with increasing film thickness in regions A, B, and C. (e) X-ray reciprocal space maps of the LBMO (103) peak for different thickness films in regions A, B, and C. The reciprocal peak broadening along the out-of-plane direction is indicated on each plot, as ΔQz (a measure of the non-uniformity of the OOP strain) and the values are shown in (c). APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 9, 020903-5 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm and La0.9 Ba0.1 MnO3 is also expected to be an MS phase. The CeO2 is parameter is close to saturation for the vertical strain level that the not, however, ferroelectric (it is an ionic conductor), and it is not pillars can provide. For this system, the OOP strain level for the possible to achieve a ME effect via strain coupling. On the other thickest film is ∼0.3%. In fact, it is possible to achieve >1% strains hand, the system of Fig. 4 simply serves to show the vertical strain in other perovskite VAN systems, e.g., BaTiO3 -based.69–71 effects in a typical VAN film. Figure 4(d) shows schematically the average strain state There is not a limitation that the MS phase must be the matrix schematically in a VAN film cross section with increasing film thick- and the FE phase must be the pillars. Indeed, the opposite case has ness. Considering that OOP strain is compresive for very thin films been more commonly studied (FE matrix and MS pillars).64 For and tensile for thick films, there will be a gradient of strain in the creating ME systems, both the FE and MS phases need to be near- relatively thick structures, progressing from compressive to tensile, insulating, otherwise leakage currents and Joule heating effects ham- as the distance from the rigid substrate increases. X-ray reciprocal per device performance. The pillar phases are typically 10 nm–20 nm space maps of the LBMO (103) peak for different thickness films in in diameter and of a similar pitch. This fine feature size ensures regions A, B, and C [Fig. 4(e)] were used to assess the variation in a huge vertical interfacial area for coupling effects with the matrix strain (or level of non-uniformity of strain) in the OOP direction phase. (from the FWHM of the reciprocal space peak along the z (OOP) As shown in Fig. 4(a), the LBMO matrix phase (blue) has direction), i.e., ΔQz and the values are shown as a function of thick- nanopillars of CeO2 (orange) grown within it, and the whole film ness in Fig. 4(c). In region B (film thickness 46 nm), ΔQz shows a is supported on the substrate (green). To achieve good quality epi- maximum value consistent with the largest mix of strain values in taxy and a clear phase separated structure, the films were grown at the transition region from substrate to pillar control, i.e., from OOP ∼700 ○ C. More generally, for VAN films to achieve epitaxy, the films compression to OOP tension. In region C [largest thickness film need to be grown above ∼600 ○ C, the actual temperature depending (110 nm)], most of the film is in tension OOP and is pillar domi- on the specific cations in the composite PLD target. Of all crystalline nated and so is more uniform, and so, ΔQz decreases, cf. region B. materials that can be deposited, the perovskite materials are grown Overall, a 110 nm thick film can provide a large strain gradient effect. most perfectly as a matrix in epitaxial film form on the most com- For the VAN example given here, the OOP strain value changes monly available substrates, i.e., perovskites. The pillars that grow from −0.3% at the bottom of the film to +0.3% at the top, i.e., 0.6% within the matrix are typically not perovskite structured; otherwise, difference, but as already mentioned, strain gradients of over 1% intermixing with the matrix is likely to occur. are possible, depending on the specific materials in the VAN film. VAN films offer very interesting strain effects that cannot be Hence, although not studied for inducing strain gradient effects, achieved in plain, single phase epitaxial films.65,66 This is because of there is a strong potential for VAN to achieve either a strain-gradient the presence of vertical epitaxy between the pillars and the matrix, flexoelectric effect in the FE material to achieve enhanced polariza- which is additive to the epitaxy of the matrix phase with the sub- tion or to achieve a large strain gradient in the MS material to achieve strate. Hence, there are 3D epitaxial effects. For very thin films, sub- enhanced MS. Both effects should lead to enhanced ME coupling. strate epitaxy dominates, but this strain relaxes as the film grows. The variable substrate strain effect and constant VAN pillar strain effect are shown schematically in Fig. 4(a) on the left hand and right V. BEYOND CONVENTIONAL hand of the film schematic. If two vertical strain components are PIEZOELECTRIC-MAGNETOSTRICTIVE COMPOSITES added, it is clear that the strain in the largest film thicknesses is In the recent years, stain-gradient effects have been studied in influenced only by the pillar effect. This is manifested in the XRD various MS magnetic and FE materials, leading to interesting effects plots of Fig. 4(b). Hence, the substrate diminishes with increasing such as flexomagnetism and flexoelectricity. However, there are only film thickness. a few systems where the strain gradients were studied in coupled We see that the LBMO (003) peak [indicated by arrows in MS/FE systems, i.e., in ME composites. Compared to the conven- Fig. 4(b)] moves from the right-hand side of the STO (003) sub- tional strain mediated ME systems where the effects are mediated strate peak (lattice parameter 3.905 Å) to its left as the film thickens, by homogeneous strain, the inhomogeneous strain can significantly indicating an increasing out-of-plane (OOP) lattice parameter. As enhance the performance of the composite films at the nanoscale, expected, the STO will tense the LBMO in-plane (LBMO bulk lattice when the features size falls below ∼50 nm. Interestingly, this could parameter is ∼3.875 Å,67 depending on the precise composition68 ), render functionally graded materials (with tunable ME properties leading to compression OOP (from Poisson effects) that relaxes with along the vertical direction), which are not possible to obtain using film thickness. Hence, the LBMO film OOP lattice compresses less conventional ME approaches. This opens up a new range of pos- with film thickness and, in fact, goes into tension. This is shown in sibilities for the utilization of strain-gradient mediated ME com- Fig. 4(c). The white dashed line shows approximately the position of posites. Specifically, two main applications of such materials can be switchover from compression to tension. We can label three differ- envisaged. ent regions of [Fig. 4(c)], A, B, and C. These same regions are also shown in Fig. 4(b). Region A is where epitaxy with the substrate dominates the A. Strain-graded ME composites for biomedical OOP lattice parameter, B is the mixed region where vertical epitaxy applications (DME) with the nanopillars begins to play a strong role in controlling the Wireless, non-invasive electric stimulation of living cells OOP strain but where substrate effects are not negligible, and C is (without implanted electrodes) is of paramount interest in the region where the nanopillars dominate the OOP strain in the biomedicine.72,73 Several studies (including in vivo tests)74 have upper part of film that is from the substrate. Here, the OOP lattice shown that ME core–shell nanoobjects, e.g., FeGa/P(VDF-TrFE) APL Mater. 9, 020903 (2021); doi: 10.1063/5.0037421 9, 020903-6 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm or CoFe2 O4 /BaTiO3 nanoparticles, can generate reasonable electric VI. CONCLUSIONS fields (∼1 kV/m), allowing optimum conversion from magnetic to The development of new nanoengineered FE/MS composites electric energy for minimally invasive localized treatments.4,74 In ME of different sorts, such as partially filled mesoporous films or ver- composites, by adding the effect of the strain gradient to the effect of tically aligned nanocomposite (VAN) structures, with the poten- strain itself, i.e., adding flexoelectricity to piezoelectricity, the attain- tial to exhibit large strain gradient effects, is likely to enhance able electrical polarization induced by magnetic fields can be largely currently available magnetoelectric phenomena for the holy grail enhanced.23 In fact, the inherent flexoelectricity of bone has been of high performance DME or CME devices. The proper inte- reported to play a central role in bone-crack self-repair.35 How- gration of strain gradients in this type of materials could result ever, DME combining flexoelectricity with magnetostriction has in voltage-driven functionally graded materials or in the rever- been largely unexploited. Nonetheless, it has been recently reported sal of electric polarization with magnetic fields or the analogous that the polarization in flexoelectric MS/FE heterostructures can be effects, i.e., the reversal of magnetization with voltage. Hence, flex- directly switched with an external magnetic field.20 This is generally omagnetoelectric materials and devices, governed by inhomoge- not possible using only piezoelectric/magnetostrictive composites. neous strains, are appealing candidates for the investigation and The possibility to locally switch polarization in some regions of the implementation in the near future. The range of applications of material while preserving the original polarization direction in the these materials could extend beyond information technologies. For others is related to local strain gradients, and it opens new avenues instance, their integration in the biomedical field could revolution- for tissue engineering applications, where magnetic fields (and mag- ize current technologies for cell stimulation, prompting the devel- netic field gradients) with different strengths and signs could allow opment of wireless electrostimulation of neurons or chemothera- tailoring cell proliferation in different regions or directions at differ- pies (e.g., electric-field-driven drug delivery), among others. Despite ent rates, depending on the locally induced variations of the electric intensive recent research efforts, this field remains still in its polarization. infancy and its potential is still to be demonstrated. Nevertheless, there are promising new avenues to follow, as outlined in this B. Strain-graded ME composites for energy-efficient Perspective. information technologies (CME) In magnetic storage devices and memories, the CME effect is used to reduce the coercivity (H C ) of the media so that the infor- ACKNOWLEDGMENTS mation can be stored under lower applied magnetic fields (which means using lower electric currents, thereby reducing Joule heat- This project has received funding from the European Union’s ing effects).8 In archetypical ME memories, each memory unit (bit) Horizon 2020 research and innovation program under the Marie behaves as a “single entity” with a single set of homogeneous prop- Sklodowska-Curie Grant Agreement No. 892661–MAGNUS. Finan- erties.75 Functionally graded magnetic materials, in which there is cial support by the European Commission (BeMAGIC H2020- a gradual variation of properties (e.g., H C ) across the thickness of MSCA-ITN-2019 No. 861145 project), the European Research the memory unit, emerged as an interesting class of materials to Council [SPIN-PORICS 2014-Consolidator Grant (No. 648454) and write information with lower magnetic fields (also improving the MAGIC-SWITCH 2019-Proof of Concept Grant (No. 875018)], signal-to-noise ratio) while still guaranteeing stability of the media, the Spanish Government (MAT2017-86357-C3-1-R and associated thanks to the counterpart that retains a large coercivity.76,77 In con- FEDER), and the Generalitat de Catalunya (Grant Nos. 2017- ventional functionally graded magnetic materials, the composition SGR-292 and 2018-LLAV-00032) is also acknowledged. J.M.M.-D. of the layers is progressively varied through the film thickness by, acknowledges support from the Royal Academy of Engineering— e.g., doping with non-magnetic elements (e.g., by diluting FePt with CIET1819_24, the Leverhulme Trust Grant No. RPG-2015-017, Cu).76 However, after fabrication, each memory unit prepared in EPSRC Grant Nos. EP/N004272/1, EP/T012218/1, EP/P007767/1, this way exhibits a unique (fixed) range of properties that is deter- and EP/M000524/1, and the Isaac Newton Trust in Cambridge mined by the gradient in composition. Strain gradients could be [minute 16.24(p) and RG96474]. used as a new strategy to surpass conventional functionally graded magnetic materials in which tunable ME effects will be induced in DATA AVAILABILITY FE/MS clamped heterostructures by means of the strain gradient. 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