Genome mapping and data mining in ferroics

Advances in high-performance, low-cost computing, high-capacity data storage, and high-speed data transfer have led to an explosion in data generation. It is predicted that worldwide data generation will double every year in the near future.^[ Reference Gantz and Reinsel ^{7 ]} Experimental and computational science has followed similar trends, and it is now possible for a single researcher to generate terabytes of data in a single day. Traditionally this data has been sorted and analyzed by “hand”, condensed to a manageable structure, and published as a few thousand words and a few figures. The raw data are, however, rarely curated or published in a systematic way. In turn, most scientific data are only analyzed and interpreted by a select group of researchers with access to the raw data. Such isolated “data nodes” preclude the formation of interconnected, networked segments of scientific knowledge between research groups, significantly limiting the scientific impact extracted from the data. Recently, there has been growing interest in applying data analytics such as unsupervised and supervised neural networks, genetic and evolutionary algorithms, statistics-based methods, and machine learning to rapidly mine data.^[ Reference Kalinin, Sumpter and Archibald ^{8 –} Reference Rondinelli, Poeppelmeier and Zunger ^{16 ]} There are considerable challenges, however, due to the significant complexity that has been developed in both the fields of materials science and data analytics. Advances in these approaches will rely heavily on those researchers who can bridge this gap and establish interacting “social networks” between these two communities [Fig. 2(a)]. Here we discuss how the assemblage of these networks could facilitate the discovery of new multifunctional materials and phenomena.

Figure 2. (a) Overview of networked combined computational and experimental approach to discovery of new multifunctional materials (Reprinted from [Reference Jain, Ong, Hautier, Chen, Richards, Dacek, Cholia, Gunter, Skinner, Ceder and Persson32], with the permission of AIP Publishing). (b) Graphical representation of the computed piezoelectric coefficients of 941 materials. A series of concentric circles indicate the maximum value of longitudinal piezoelectric modulus ||e _ij ||_max. Concentric circles correspond to moduli ||e _ij ||_max of 1, 2.5, 5,10, and 20 C/m². The compounds are segmented according to their crystal and point-group symmetry classes (Reprinted with permission from Ref. [Reference de Jong, Chen, Geerlings, Asta and Persson41]).

To date, many of the watershed events in the development of multifunctional ferroic materials have centered on the chance discovery of novel materials or classes of materials. In recent years, however, materials discovery and design has brought to bear an expansive set of theory, modeling, and computational (TMC) approaches including density functional theory (DFT) calculations,^[ Reference Resta, Vanderbilt, Ahn, Rabe and Triscone ^{17 ]} atomic-scale simulations (i.e., Monte Carlo,^[ Reference Liu, Wang, Chan and Choy ^{18 ]} molecular dynamics,^[ Reference Shin, Cooper, Grinberg and Rappe ^{19 ,} Reference Sepliarsky, Asthagiri, Phillpot, Stachiotti and Migoni ^{20 ]} and effective Hamiltonians^[ Reference Zhong, Vanderbilt and Rabe ^{21 ,} Reference Bellaiche, Garcia and Vanderbilt ^{22 ]}), and mesoscale Landau-based thermodynamic models (i.e., numerical phase-field^[ Reference Chen ^{23 ,} Reference Li, Hu, Liu and Chen ^{24 ]} and Ginzburg–Landau–Devonshire (GLD) models^[ Reference Pertsev, Kukhar, Kohlstedt and Waser ^{25 ,} Reference Koukhar, Pertsev and Waser ^{26 ]}) that can be used to both predict and understand multifunctional phenomena. These TMC approaches have, however, been relatively limited to a few specific material systems and conditions (i.e., compositional, temperature, strain, etc.) due to both limitations in computing capacity and a lack of availability of phenomenological constants and parameters. In the last decade, and particularly since the launch of the Materials Genome Initiative,^[ Reference Ward ^{27 ]} there has been a massive push to utilize predictive high-throughput (HT) electronic-structure calculations based on DFT and the tools of data science to discover new materials with targeted properties, which stands ready to revolutionize how we design and discover new ferroic materials.^[ Reference Curtarolo, Hart, Nardelli, Mingo, Sanvito and Levy ^{9 ,} Reference Ceder and Persson ^{28 –} Reference Jain, Shin and Persson ^{30 ]} The associated development of curated databases^[ Reference Curtarolo, Hart, Nardelli, Mingo, Sanvito and Levy ^{9 ,} Reference Saal, Kirklin, Aykol, Meredig and Wolverton ^{31 – 35 ]} and open-source software^[ Reference Curtarolo, Setyawan, Wang, Xue, Yang, Taylor, Nelson, Hart, Sanvito, Buongiorno-Nardelli, Mingo and Levy ^{33 ,} Reference Pizzi, Cepellotti, Sabatini, Marzari and Kozinsky ^{34 ,} Reference Ong, Richards, Jain, Hautier, Kocher, Cholia, Gunter, Chevrier, Persson and Ceder ^{36 ]} for automated property calculations has enabled consideration of tens of thousands of compounds in the search for new materials and property combinations. These efforts have provided a predictive framework for computing a wide range of material properties including: phase stability,^[ Reference Chen ^{23 ]} electronic and crystal structure,^[ Reference Fischer, Tibbetts, Morgan and Ceder ^{37 ]} elastic moduli,^[ Reference De Jong, Chen, Angsten, Jain, Notestine, Gamst, Sluiter, Ande, van der Zwaag and Plata ^{38 ]} thermal conductivity,^[ Reference Toher, Plata, Levy, De Jong, Asta, Nardelli and Curtarolo ^{39 ,} Reference Yang, Xi, Qiu, Wu, Shi, Chen, Yang, Zhang, Uher and Singh ^{40 ]} dielectric and piezoelectric response,^[ Reference de Jong, Chen, Geerlings, Asta and Persson ^{41 ]} polarization, and much more. Furthermore, it is now possible to automate DFT-based computational workflows such that large amounts of data on material properties can be obtained. Similar approaches have already been applied in the search for: improved catalysts,^[ Reference Greeley, Stephens, Bondarenko, Johansson, Hansen, Jaramillo, Rossmeisl, Chorkendorff and Norskov ^{42 ]} new electrode materials for batteries,^[ Reference Ceder and Persson ^{28 ]} new intermetallic compounds,^[ Reference Hart, Blum, Walorski and Zunger ^{43 ]} topological insulators,^[ Reference Yang, Setyawan, Wang, Nardelli and Curtarolo ^{44 ]} and thermoelectric materials.^[ Reference Xiang ^{45 ]} Despite this progress, relatively little work has focused on HT discovery of new polar/ferroelectric systems,^[ Reference Benedek and Fennie ^{46 ]} but such TMC approaches are poised to be implemented in this regard.

In this direction, researchers have demonstrated a database predicting the piezoelectric tensors of 919 different materials [Fig. 2(b)].^[ Reference de Jong, Chen, Geerlings, Asta and Persson ^{41 ]} This work suggests a number of novel, Pb-free compounds that are candidates to have high piezoelectric response. Further development of these approaches and screening of multifunctional materials could lead to the discovery of materials with interesting and novel polar phases, strain-induced polar phases, and regions of strain-induced phase instabilities; all of which could provide for enhanced materials performance. These HT TMC approaches can also be adapted to predict phenomenological constants from first principles,^[ Reference Jain, Ong, Hautier, Chen, Richards, Dacek, Cholia, Gunter, Skinner, Ceder and Persson ^{32 ]} allowing prediction of temperature- and field-dependent susceptibilities over large length- and time-scales. Computational data collected can also be easily collated to populate online materials databases such as the Materials Project,^[ Reference Jain, Ong, Hautier, Chen, Richards, Dacek, Cholia, Gunter, Skinner, Ceder and Persson ^{32 ]} AFLOWlib,^[ Reference Curtarolo, Setyawan, Wang, Xue, Yang, Taylor, Nelson, Hart, Sanvito, Buongiorno-Nardelli, Mingo and Levy ^{33 ]} and Open Quantum Materials Database (OQMD).^[ Reference Saal, Kirklin, Aykol, Meredig and Wolverton ^{31 ]} Such databases can be combined with experimental data which can then be mined using statistical approaches and predictive machine learning algorithms; providing needed direction for additional (potentially resource intensive) computational exploration and further experimental materials development.

It should be noted, that such data analytics concepts are not limited to computational materials discovery alone and experimental methods are becoming increasingly data intensive, commonly generating large multidimensional datasets (>3 dimensions). Such “big data” experiments are common in (time-resolved) synchrotron- and neutron-based diffraction and imaging,^[ Reference Wang, Xu, Yang, Luo, Sun, Zhao, Zheng, Dong, Zhou, Ren, Gao and Cao ^{47 ]} scanning-probe microscopy,^[ Reference Jesse, Maksymovych and Kalinin ^{48 ,} Reference Jesse, Chi, Belianinov, Beekman, Kalinin, Borisevich and Lupini ^{49 ]} and (scanning) transmission electron microscopy.^[ Reference Jesse, Chi, Belianinov, Beekman, Kalinin, Borisevich and Lupini ^{49 –} Reference Ozdol, Gammer, Jin, Ercius, Ophus, Ciston and Minor ^{51 ]} These multidimensional datasets can be particularly powerful as they can provide dynamic spectroscopy of materials enabling the direct observation of material responses under external perturbations (at practically relevant timescales). The large datasets that are produced are generally not suitable for brute force analysis as the pertinent features occur over a dimensionality difficult to comprehend. For example, a relatively simple band-excitation piezoresponse force microscopy (BE-PFM) switching spectroscopy experiment, a scanning-probe-based technique capable of imaging local piezoelectric switching, generates four-dimensional (4D) datasets (space [64 × 64] × frequency [64] × voltage [128]) typically >256 MB in size.^[ Reference Jesse, Maksymovych and Kalinin ^{48 ]} Detailed analysis of such multidimensional datasets (beyond 3D) is most effectively analyzed using data analytics such as multivariate statistical analysis to reduce data dimensionality, allowing the visualization and extraction of scientifically relevant information. In this regard, there is an expansive set of statistical tools including principal component analysis, Bayesian de-mixing, independent component analysis (ICA), clustering algorithms, neural networks, etc.^[ Reference Kalinin, Sumpter and Archibald ^{8 ,} Reference Belianinov, Vasudevan, Strelcov, Steed, Yang, Tselev, Jesse, Biegalski, Shipman and Symons ^{52 ]} that can be adapted to analyze these datasets.

Such approaches have recently been applied to ferroic materials in the study of local relaxation behavior in ferroelectric relaxors (1 − x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ (PMN–xPT).^[ Reference Vasudevan, Zhang, Okatan, Jesse, Kalinin and Bassiri-Gharb ^{53 ]} In this example, relaxation in the piezoresponse was measured using BE-PFM as a function of time (in the remanent state) following a DC bias of varying magnitude [Fig. 3(a)]; and thus the final dataset is 4D A = (x, y, V, t). Through the use of ICA the amplitude of the piezoresponse can be represented as the sum of “n” number of independent components (representing a response) multiplied by a mixing coefficient at each point [Figs. 3(b)–3(e)]. ICA of this dataset, assuming two independent components, revealed two primary modes of response whose relative character varies spatially. The first component S ₁(t) can be well fit by an exponential function, the expected relaxation response. The second component S ₂(t) showed a slower somewhat larger response indicative of mesoscopic disorder. Using these approaches, it was determined that the mesoscopic heterogeneities in PMN–0.28PT are correlated to differing volume fractions of rhombohedral and tetragonal phases under the tip.

Figure 3. (a) Sample-averaged (all 2500 points), off-field piezoresponse relaxation amplitude on PMN-0.28PT. Independent component analysis (b) c₁ mixing coefficient map, (c) graph of independent component s ₁, (d) c₂ mixing coefficient map, (e) graph of component s ₂ (Reprinted from [Reference Somnath, Belianinov, Kalinin and Jesse54], with the permission of AIP Publishing).

While there has been a tremendous growth in the implementation of multivariate statistical analysis in the experimental study of multifunctional materials, this is not yet standard practice. Most experimental researchers are unaware of the language, scope, and methodologies of big-data analytics and, in turn, do not effectively mine or even collect all of the data they could. For instance, during data collection most experimental equipment pre-processes data, storing only the data deemed to be of the highest value. As big-data approaches become more integrated into the scientific approach, experimental systems will need to be redesigned or reprogrammed to acquire a fuller set of data (for an example, see g-mode scanning probe studies^[ Reference Somnath, Belianinov, Kalinin and Jesse ^{54 ]}). This, as a result, will facilitate the growth of curated experimental databases, which can be rapidly mined using supercomputer-based statistical analyses and machine learning techniques redefining the scope and insight gleaned from experimental characterization. Looking forward, we can expect to see increased collaboration between computational data scientists and experimentalists. As the potential impact of these big-data analysis techniques become more mainstream we can expect the development of complex networks where computational results and raw data from full data-acquisition experiments are fed directly into curated databases accessible to the global research community. These databases will enable the materials genome to be mapped and the data to be mined without constraints of experimental/computational resource availability. This “networked” approach has the potential to reshape the scientific and technological landscape revolutionizing the efficiency of scientific discovery, but will require that researchers establish and implement expectations for participation, data access protocols and rules regarding access, and ownership of intellectual property.

Reshaping ferroic physics—exploring exotic and emergent polarization states

Researchers have explored an enormous phase space of materials by leveraging their ability to manipulate chemistry and elastic boundary conditions (i.e., epitaxial strain, film thickness, geometry, etc.) to engineer the crystal and domain structure, and ultimately, the response and susceptibility of multifunctional materials. Using these conventional strain-based approaches it has been possible to manipulate the properties of multifunctional materials including inducing room temperature ferroelectricity in paraelectric SrTiO₃,^[ Reference Biegalski, Jia, Schlom, Trolier-McKinstry, Streiffer, Sherman, Uecker and Reiche ^{55 ,} Reference Haeni, Irvin, Chang, Uecker, Reiche, Li, Choudhury, Tian, Hawley, Craigo, Tagantsev, Pan, Streiffer, Chen, Kirchoefer, Levy and Schlom ^{56 ]} enhancing ferroelectric transition temperatures and remnant polarization in BaTiO₃,^[ Reference Choi, Biegalski, Li, Sharan, Schubert, Uecker, Reiche, Chen, Pan, Gopalan, Chen, Schlom and Eom ^{57 ]} and creating the novel multiferroic EuTiO₃ which is neither ferroelectric nor ferromagnetic in the bulk.^[ Reference Lee, Fang, Vlahos, Ke, Jung, Kourkoutis, Kim, Ryan, Heeg, Roeckerath, Goian, Bernhagen, Uecker, Hammel, Rabe, Kamba, Schubert, Freeland, Muller, Fennie, Schiffer, Gopalan, Johnston-Halperin and Schlom ^{58 ]} Recently advances in control of interface chemistry and in situ monitoring/control of growth processes has enabled the manipulation of these materials at the sub-unit-cell level.^[ Reference Martin, Chu and Ramesh ^{59 ]} In turn, it is possible to create tailored interfaces and superlattices that are nearly “atomically sharp” (minimal chemical intermixing) as well as designer chemical gradients. This ability to manipulate the chemistry, strain and strain gradients, and the electrostatic boundary conditions of multifunctional material allows for the design of nano-/meso-scale polar structures with unique susceptibilities and response.

For example, there has been growing interest in generating inhomogeneous polarization states (or polarization gradients) in multifunctional materials. Such inhomogeneous polarization states are interesting as they provide a way to break symmetry, generate a preferred poling direction,^[ Reference Agar, Damodaran, Velarde, Pandya, Mangalam and Martin ^{60 ,} Reference Mangalam, Agar, Damodaran, Karthik and Martin ^{61 ]} broaden ferroelectric transition temperatures,^[ Reference El-Naggar, Dayal, Goodwin and Bhattacharya ^{62 ,} Reference Cole, Ngo, Hirsch, Demaree, Zhong and Alpay ^{63 ]} decouple typically coupled order parameters,^[ Reference Mangalam, Agar, Damodaran, Karthik and Martin ^{61 ,} Reference Catalan, Sinnamon and Gregg ^{64 ]} give rise to exotic space charge arrangements,^[ Reference Cross ^{65 ,} Reference Chu, Jang, Sung, Shin, Lee, Song, Lee, Woo, Kim, Choi, Koo, Kim, Oh, Jo and Yang ^{66 ]} among other effects, enabling the optimization of materials responses^[ Reference Mangalam, Agar, Damodaran, Karthik and Martin ^{61 ,} Reference Majdoub, Sharma and Cagin ^{67 ]} and even giving rise to novel functionalities.^[ Reference Bhaskar, Banerjee, Abdollahi, Solanas, Rijnders and Catalan ^{68 ]} While there are many routes to achieve inhomogeneous polarization gradients, the most common approach leverages the flexoelectric effect [Fig. 4(a)], the linear coupling of a strain gradient ∂ε _ij /∂x _k to the polarization (P _i ), an interaction mediated by a fourth-rank flexoelectric tensor (μ _ijkl ).^[ Reference Indenbom, Loginov and Osipov ^{69 ]} From a materials engineering standpoint there are now many effective routes to generate large strain gradients (on the order of 10⁵–10⁶ m⁻¹), including: controlled strain relaxation,^[ Reference Lee, Jeon, Yoon, Shin, Lee, Song, Bu, Kim, Chung, Yoon and Noh ^{70 ]} ferroelastic domain walls,^[ Reference Catalan, Lubk, Vlooswijk, Snoeck, Magen, Janssens, Rispens, Rijnders, Blank and Noheda ^{71 ,} Reference Jia, Urban, Alexe, Hesse and Vrejoiu ^{72 ]} through compositional grading,^[ Reference Agar, Damodaran, Velarde, Pandya, Mangalam and Martin ^{60 ,} Reference Mangalam, Agar, Damodaran, Karthik and Martin ^{61 ,} Reference Agar, Damodaran, Okatan, Kacher, Gammer, Vasudevan, Pandya, Dedon, Mangalam, Velarde, Jesse, Balke, Minor, Kalinin and Martin ^{73 ,} Reference Mangalam, Karthik, Damodaran, Agar and Martin ^{74 ]} and by creating nanoscale free-standing structures.^[ Reference Bhaskar, Banerjee, Abdollahi, Wang, Schlom, Rijnders and Catalan ^{75 ]} For example, to achieve strain gradients using compositional gradients, an epitaxially strained film is grown wherein the chemistry is changed such that the bulk lattice parameter(s) of the film evolves with the thickness [Fig. 4(b)]. Using this approach large strain gradients of the order of 10⁵ m⁻¹ have been achieved in compositionally-graded PbZr_1−x Ti _x O₃ resulting in shifted ferroelectric hysteresis loops (i.e., built-in potentials), highly suppressed dielectric susceptibilities, and enhanced pyroelectric figures of merit.^[ Reference Agar, Damodaran, Velarde, Pandya, Mangalam and Martin ^{60 ,} Reference Mangalam, Agar, Damodaran, Karthik and Martin ^{61 ,} Reference Mangalam, Karthik, Damodaran, Agar and Martin ^{74 ]} Additionally, it has been found that these chemical and strain gradients can modify the morphology and response of ferroelastic domains; making them appear more needle-like rather than parallelepiped-like [Fig. 4(c)].^[ Reference Agar, Damodaran, Okatan, Kacher, Gammer, Vasudevan, Pandya, Dedon, Mangalam, Velarde, Jesse, Balke, Minor, Kalinin and Martin ^{73 ]} Subsequent studies of electric-field induced switching identified that these needle-like ferroelastic domains are highly mobile expanding (or contracting) from the free surface depending on the direction of the applied bias.^[ Reference Agar, Damodaran, Okatan, Kacher, Gammer, Vasudevan, Pandya, Dedon, Mangalam, Velarde, Jesse, Balke, Minor, Kalinin and Martin ^{73 ]} This unusual field-dependent response renders these domains highly mobile in the out-of-plane direction yet spatially localized in the plane; prompting them to be called “springy” in nature.^[ Reference Dörr ^{76 ]} Such work highlights the ability to utilize strain gradients to finely control the structure, response, and properties of ferroelastic domains. These new modalities of domain engineering provide a nearly limitless space to engineer domain wall functionalities facilitating the fabrication of a range of proposed domain wall-based devices.

Figure 4. (a) Schematic illustration indicating the fundamental principles of flexoelectricity. (b) Phase diagram and lattice parameter evolution in PbZr_1−x Ti _x O₃ system showing how compositional gradients with large strain gradients can be fabricated (Reprinted with permission from Ref. [Reference Agar, Damodaran, Velarde, Pandya, Mangalam and Martin60]. Copyright 2015 American Chemical Society). (c) Cross-sectional nanobeam diffraction strain mapping out-of-plane strain image of needle-like ferroelastic domains in compositionally-graded heterostructures. Strain values indicated are in reference to the GdScO₃ pseudocubic lattice parameter (Reprinted with permission from Ref. [Reference Agar, Damodaran, Okatan, Kacher, Gammer, Vasudevan, Pandya, Dedon, Mangalam, Velarde, Jesse, Balke, Minor, Kalinin and Martin73], Copyright 2016 Nature Publishing Group). (d) Top, schematic drawing of flexoelectric actuator consisting of SrTiO₃ sandwiched between to SrRuO₃ electrodes. Bottom left, optical image of an array of fabricated nanocantilevers. Bottom Right, image of nanocantilever colored to indicate the out-of-plane deflection (Reprinted with permission from Ref. [Reference Bhaskar, Banerjee, Abdollahi, Wang, Schlom, Rijnders and Catalan75], Copyright 2016 Nature Publishing Group).

To provide greater flexibility in the design of strain/polarization gradients, researchers have created free-standing heterostructures wherein the strain/polarization gradients can be tuned “on-demand”.^[ Reference Bhaskar, Banerjee, Abdollahi, Wang, Schlom, Rijnders and Catalan ^{75 ,} Reference Baek, Park, Kim, Aksyuk, Das, Bu, Felker, Lettieri, Vaithyanathan, Bharadwaja, Bassiri-Gharb, Chen, Sun, Folkman, Jang, Kreft, Streiffer, Ramesh, Pan, Trolier-McKinstry, Schlom, Rzchowski, Blick and Eom ^{77 ]} Such, NEMS/MEMS permit the generation of large dynamic strain gradients wherein flexoelectricity is a dominant feature. One recent example using this concept was the fabrication of all-oxide nanocantilevers composed of SrTiO₃ sandwiched between two SrRuO₃ electrodes on SrTiO₃-buffered Si [Fig. 4(d)].^[ Reference Bhaskar, Banerjee, Abdollahi, Wang, Schlom, Rijnders and Catalan ^{75 ]} This study demonstrated that SrTiO₃-based free-standing devices fabricated using state-of-the-art techniques with large flexoelectric effects can outperform the best piezoelectric electromechanical actuators.^[ Reference Bhaskar, Banerjee, Abdollahi, Wang, Schlom, Rijnders and Catalan ^{75 ]} These foundational studies are just the tip of the iceberg. It will be exciting to see these concepts become mature technologies.

Despite these recent successes there are still many open questions regarding the understanding and utilization of strain/polarization gradients and flexoelectricity. The principal area of contention relates to the magnitude of the flexoelectric coefficient which experiments find to be orders of magnitude larger than theoretical predictions.^[ Reference Biancoli, Fancher, Jones and Damjanovic ^{78 ]} The recent implementation of advanced nanoscale transmission electron microscopy techniques coupled with “big data” analytics are on the brink of being able to reconcile this discrepancy^[ Reference Agar, Damodaran, Okatan, Kacher, Gammer, Vasudevan, Pandya, Dedon, Mangalam, Velarde, Jesse, Balke, Minor, Kalinin and Martin ^{73 ,} Reference Cao, Li, Chen and Kalinin ^{79 ]} as they can now directly measure strain gradients in materials and this new understanding will, in turn, likely usher in a new era of strain gradient-based polarization engineering.

Leveraging the ability to generate inhomogeneous strain and polarization gradients, researchers have also sought routes to generate topological structures in polar materials. While simple planar topological defects, such as those formed by domains have been utilized to stabilize new phases and structures^[ Reference Farokhipoor, Magén, Venkatesan, Íñiguez, Daumont, Rubi, Snoeck, Mostovoy, De Graaf, Müller, Döblinger, Scheu and Noheda ^{80 ]} that can act as nanoscale functional elements,^[ Reference Seidel ^{81 ,} Reference Seidel, Vasudevan and Valanoor ^{82 ]} there is both fundamental^[ Reference Choudhury, Walizer, Lisenkov and Bellaiche ^{83 ,} Reference Nahas, Prokhorenko and Bellaiche ^{84 ]} and technological^[ Reference Seidel, Vasudevan and Valanoor ^{82 ]} interest in designing more complex topological states in multifunctional materials such as vortices, waves, merons, skyrmions, etc. [Figs. 5(a)–5(e)]^[ Reference Hong, Catalan, Fang, Artacho and Scott ^{85 ,} Reference Nahas, Prokhorenko, Louis, Gui, Kornev and Bellaiche ^{86 ]} and exploring their formation, susceptibilities, and phase transition characteristics.^[ Reference Prosandeev, Ponomareva, Kornev, Naumov and Bellaiche ^{87 ]} Using computational approaches, a wide range of novel orders, structures, and effects have been predicted including axial peizotoroidic, electric toroidal susceptibility, pyrotoroidic, etc.^[ Reference Prosandeev, Ponomareva, Naumov, Kornev and Bellaiche ^{88 ]} The highly coupled order parameters in these topological structures could facilitate new device concepts for random access memory (RAM), nanoscale transducers, sensors, switches, motors, etc.^[ Reference Prosandeev, Ponomareva, Kornev, Naumov and Bellaiche ^{87 ]} In particular, it has been proposed that vortex structures could give rise to a multifold increase in storage capacity for non-volatile ferroelectric RAM.^[ Reference Naumov, Bellaiche and Fu ^{89 ]} Despite considerable theoretical and modeling work,^[ Reference Chen, Zheng, Wang and Liu ^{90 –} Reference Baudry, Sene, Luk'yanchuk, Lahoche and Scott ^{92 ]} it was only in the last year that such novel topologies of polarization were experimentally realized. For example, smoothly varying polar vortices, were created and observed in superlattices of paraelectric SrTiO₃ and ferroelectric PbTiO₃ [Figs. 5(f)–5(i)].^[ Reference Yadav, Nelson, Hsu, Hong, Clarkson, Schlepüetz, Damodaran, Shafer, Arenholz, Dedon, Chen, Vishwanath, Minor, Chen, Scott, Martin and Ramesh ^{93 ]} These vortex structures are thought to be stabilized by a competition of gradient, electrostatic, and elastic energies. Initial studies have suggested that these vortex states can be transformed into a uniform polarization state providing a potential pathway for controllability and, ultimately, functionality.^[ Reference Naumov and Fu ^{94 ]}

Figure 5. 2D projections of proposed/realized topological structures based on ferroelectric polarization wherein the order parameter is represented by the direction of the arrows for (a) a radial skyrmion, (b–c) vortex structures, (d) a chiral skyrmion, and (e) a four-quadrant closure structure (Reprinted with permission from Ref. [Reference Seidel, Vasudevan and Valanoor82]). (f) Observation of vortex/anti-vortex structures in intermediate periodicity (PbTiO₃)₁₀/(SrTiO₃)₁₀ superlattices realized using cross-sectional, atomic-scale imaging via scanning transmission electron microscopy (the overlaid polarization vector maps represent the local polar distortion). (g) A magnified image of a single vortex/anti-vortex pair where the polarization state within such vortex pairs can be visualized. (h) Phase-field simulations of the same superlattice structure also predicting the vortex pairs. (i) The curl of polarization (∇ × P) for a vortex pair, extracted from the data in (g). The data is plotted with a red/blue color scale where no-vorticity (curl  =  0) is white, clockwise (negative) is blue and anticlockwise (positive) is red. (Reprinted with permission from Ref. [Reference Yadav, Nelson, Hsu, Hong, Clarkson, Schlepüetz, Damodaran, Shafer, Arenholz, Dedon, Chen, Vishwanath, Minor, Chen, Scott, Martin and Ramesh93], Copyright 2016 Nature Publishing Group).

With experiments now catching-up with theoretical and modeling approaches, there are expansive opportunities to explore new systems and create new topologies; and it will be exciting to see how future studies can control, manipulate, and utilize these topological states. Future work will likely leverage multi-scale modeling approaches to deterministically control polarization field textures (i.e., type, scaling, winding number, etc.).^[ Reference Hong, Catalan, Fang, Artacho and Scott ^{85 ,} Reference Nahas, Prokhorenko, Louis, Gui, Kornev and Bellaiche ^{86 ]} Furthermore, it is possible that topological polarization states can be induced in intrinsically multiferroic materials (such as BiFeO₃), such that the ferroelectric polarization which is coupled to antiferromagnetic and canted moments^[ Reference Heron, Bosse, He, Gao, Trassin, Ye, Clarkson, Wang, Liu, Salahuddin, Ralph, Schlom, Iniguez, Huey and Ramesh ^{95 ]} can induce topological states in the magnetic sublattice. Such multiferroic topological states could provide a powerful and versatile pathway to achieve large susceptibilities and novel functionalities. Finally, due to the complexity of these topological polarization states an extension of common characterization protocols will be required to understand their structure and response under applied fields. This will motivate the development and implementation of advanced electron microscopy, resonant x-ray scattering, spatially-resolved optical techniques, as well as polarized light temperature-dependent studies of susceptibilities in exotic structures (e.g., electric toroidic and pyrotorodic).

All told, the community stands poised to reshape ferroelectric physics or order by manipulating chemistry and electrical and elastic boundary conditions at the nanoscale. The combination of detailed computational simulation, advances in growth and fabrication techniques, and deeper understanding of polarization physics are now enabling researchers to directly mold polarization states “on demand,” making the design of novel and technologically relevant nanoscale functional elements possible.

Addressing global challenges—ferroics in energy and the environment

Little needs to be said to emphasize the growing importance and immediate impact that cutting-edge research and development needs to have on matters of extreme societal import including energy and the environment. In this section, we highlight the potential role for ferroic materials in this regard.

One area of interest that is poised for major impact in the coming years is the study of ferroelectric photovoltaics.^[ Reference Yuan, Xiao, Yang and Huang ^{96 –} Reference Butler, Frost and Walsh ^{98 ]} The bulk photovoltaic effect (or photogalvanic effect) is observed in non-centrosymmetric materials exhibiting a polarization without the need for junction-based structures. Recent years have seen marked advances in our understanding of these effects wherein theoretical approaches have highlighted how excitation of quantum wave packets in non-centrosymmetric materials can lead to the formation of “shift currents” or the excitation of carriers from one band to another while moving from the initial real space location.^[ Reference Young, Zheng and Rappe ^{99 –} Reference Young and Rappe ^{101 ]} A second effect, the anomalous or ballistic photovoltaic effect, describes how, unlike in conventional photovoltaics where the photovoltage is limited by the band gap of the material, in systems with a spontaneous polarization, photovoltages can be orders of magnitude higher than the band gap. The ballistic contribution to the bulk photovoltaic effect is now thought to arise from asymmetric scattering from phonons and lattice defects. In polydomain ferroelectrics, an additional opportunity arises wherein the domain walls can act as charge separators. In ferroelectric and multiferroic materials, a high density of domain walls can amplify the anomalous photovoltaic effect.^[ Reference Yang, Martin, Byrnes, Conry, Basu, Paran, Reichertz, Ihlefeld, Adamo, Melville, Chu, Yang, Musfeldt, Schlom, Ager and Ramesh ^{102 –} Reference Seidel, Fu, Yang, Alarcón-Lladó, Wu, Ramesh and Ager ^{106 ]} Subsequent research has worked to better understand these bulk photovoltaic and domain-wall-based mechanisms.^[ Reference Yan, Chen, Lu and Spanier ^{107 ,} Reference Bhatnagar, Chaudhuri, Kim, Hesse and Alexe ^{108 ]} This area is primed for future development as researchers determine how to create devices with the optimum geometries required to extract useful function from these systems. Particularly there is interest in how to enhance photoexcited carrier concentrations and motilities as well as determining the role of electron correlations in photo transport. In turn, efficiencies and applicability will be improved. In this regard, one of the most promising developments in recent years has been the design of a new class of low band gap polar materials, including [KNbO₃]_1−x [BaNi_1/2Nb_1/2O_3−δ ] _x which can be tuned to have a band gap from 1.1 to 3.8 eV and (with x = 0.1 and a band gap of 1.39 eV) have produced photocurrent densities ~50 times larger than classic ferroelectric photovoltaics!^[ Reference Grinberg, West, Torres, Gou, Stein, Wu, Chen, Gallo, Akbashev, Davies, Spanier and Rappe ^{109 ]}

Another area of impact for ferroic materials is in the development of cooling technologies. Refrigeration accounts for nearly 10% of commercial energy use^[ Reference Michaels ^{110 ]}; however, within the past few decades, refrigeration technologies have remained essentially unchanged. Multifunctional materials which allow the mutual convertibility of work from an external perturbation (i.e., mechanical, magnetic, and/or elastic) and heat (or entropy) represent a potentially important class of materials to realize solid state refrigeration without the need for gaseous refrigerants.^[ Reference Lang ^{111 ]} For instance, if one was to take an expanded spring and release the tension, move a piece of nickel away from a magnet, or remove an electric field from a paraelectric crystal these materials would absorb heat (entropy) from the environment thereby cooling it. In turn, there is significant interest in cooling via application of magnetic fields (magnetocaloric), electric fields (electrocaloric), and/or mechanical stress (elastocaloric). While most of the caloric effects (elastocaloric and magnetocaloric) have predominantly been studied in polymers, intermetallics, and alloys, electrocaloric effects which require a material with a spontaneous polarization are limited to pyroelectric, ferroelectric, or multiferroic materials.

The recent reemergence of interest in the electrocaloric effect, in particular, has been driven by demonstrations in thin-film devices wherein small voltages (<5 V) can drive potentially large electrocaloric responses [Fig. 6(a)]. Large effects generally occur when designing materials in the vicinity of phases transition,^[ Reference Moya, Kar-Narayan and Mathur ^{112 ]} typically achieved using strain or variations in chemical composition. Using this approach, large electrocaloric effects (comparable with the thermoelectric effect) have been reported in PbZr_0.95Ti_0.05O₃ (ΔT = 12 K, ΔE = 481 kV/cm),^[ Reference Mischenko, Zhang, Scott, Whatmore and Mathur ^{113 ]} relaxor ferroelectrics such as (1 − x)PbMg _y Nb_1−y O₃–(x)PbTiO₃ (PMN–PT) (ΔT = 5–9 K, ΔE = 720–985 kV/cm),^[ Reference Mischenko, Zhang, Whatmore, Scott and Mathur ^{114 ]} and SrBi₂Ta₂O₉ (ΔT = 4.93 K, ΔE = 600 kV/cm).^[ Reference Chen, Ren, Wu, Yang and Liu ^{115 ]} Concern remains, however, as to how to accurately measure these effects, particularly in films where the temperature changes and thermal mass is small. Generally, indirect routes where the polarization is measured as a function of temperature is used to estimate the electrocaloric temperature change via a Maxwell relation (which allows for estimation of an adiabatic temperature or isothermal entropy change) are preferred because of their simplicity. Despite their widespread utilization, these indirect approaches neglect secondary effects such as elastocaloric effects that can be large in thin films, and thus tend to overestimate the electrocaloric temperature change. In recent years, efforts have led to the development of techniques capable of measuring the electrocaloric response directly via infrared imaging,^[ Reference Guo, Gao, Yu, Santhanam, Fedder, McGaughey and Yao ^{116 ]} microfabricated device structures [Fig. 6(b)],^[ Reference Bhatia, Damodaran, Cho, Martin and King ^{117 ]} laser thermoreflectance-based measurements,^[ Reference Tong, Karthik, Mangalam, Martin and Cahill ^{118 ,} Reference Tong, Karthik, Martin and Cahill ^{119 ]} and differential scanning calorimetry.^[ Reference Goupil, Berenov, Axelsson, Valant and Alford ^{120 ]}

Figure 6. (a) Schematic diagram indicating the change in polarization that gives rise to electrocaloric and pyroelectric effects (Ref. [Reference Lang111]). (b) Schematic drawing of microfabricated device capable of measuring pyroelectric/electrocaloric response at high frequency. The device consists of a BaTiO₃ thin-film capacitor with electrical access to top and bottom electrodes. A gold strip placed above the pyroelectric capacitor serves as the resistive heater. A high resistivity SiO₂ layer, sandwiched between the top electrode and heater strip, electrically insulates the pyroelectric film and minimizes interference from the heating voltage (Reprinted from Ref. [Reference Bhatia, Damodaran, Cho, Martin and King117], with the permission of AIP Publishing.). (c) Intrinsic and extrinsic magnetocaloric effect of La_0.7Ca_0.3MnO₃/BaTiO₃ heterostructures. Graph shows film entropy change ΔS(T) at selected fields. There is evidence of a strong extrinsic magnetocaloric response near the BaTiO₃ rhombohedral to orthorhombic transition. A small magnetocaloric effect is observed at the T_c of La_0.7Ca_0.3MnO₃ (Reprinted with permission from Ref. [Reference Moya, Hueso, Maccherozzi, Tovstolytkin, Podyalovskii, Ducati, Phillips, Ghidini, Hovorka, Berger, Vickers, Defay, Dhesi and Mathur124], Copyright 2016 Nature Publishing Group).

Leveraging such measurements, new insights into the physics of these systems are being unraveled. Of particular interest are coupled terms and resulting multicaloric responses (e.g., piezoelectrocaloric, elastocaloric, magnetoelectrocaloric, etc.). For example, in PbZr_0.2Ti_0.8O₃ thin films, direct electrocaloric measurements revealed a ~50% reduction in the electrocaloric entropy change due to elastocaloric effects arising from substrate clamping.^[ Reference Tong, Karthik, Mangalam, Martin and Cahill ^{118 ,} Reference Karthik and Martin ^{121 ]} Based on first principles studies of PbTiO₃, it was predicted that the multicaloric effect could far exceed either the electrocaloric or elastocaloric effects.^[ Reference Lisenkov, Mani, Chang, Almand and Ponomareva ^{122 ]} In turn, future heterostructure design concepts must be chosen to leverage (or at least consider) these secondary effects. In a similar vein, researchers have sought routes to engineering multicaloric responses using magnetoelectric coupling in multiferroic materials/heterostructures where application of either electric or magnetic fields can couple to both ferroic order parameters (ferroelectric and ferromagnetic). Initial work in this regard has focused on magnetoelectric heterostructures designed to exhibit strongly coupled ferroic order. For example, indirect estimates of such effects have been reported for Ni₄₄Co_5.2Mn_36.7In_14.1 ribbon and PMN–PT composites^[ Reference Gong, Wang, Cao, Liu, Liu and Du ^{123 ]}. Recently this concept was exploited in an all-oxide heterostructure of La_0.7Ca_0.3MnO₃ on BaTiO₃ substrates wherein it was shown that giant reversible magnetocaloric effects can be driven by interfacial strain resulting from the rhombohedral-to-tetragonal phase transition in BaTiO₃ at ~200 K. It was determined that the giant entropic change observed (|ΔS/μ ₀ΔH|~9 J/K/kg/T) was due to strain induced changes in ferromagnetic/paramagnetic volume fractions [Fig. 6(c)].^[ Reference Moya, Hueso, Maccherozzi, Tovstolytkin, Podyalovskii, Ducati, Phillips, Ghidini, Hovorka, Berger, Vickers, Defay, Dhesi and Mathur ^{124 ]} With a similar directive, recently it was demonstrated that the irreversible nature of the giant magnetocaloric effect in FeRh can be overcome by a dual-stimulus magnetic–electric refrigeration cycle enabling large electrocaloric effects to be achieved over ~100 K temperature range inclusive of room temperature.^[ Reference Liu, Phillips, Mattana, Bibes, Barthélémy and Dkhil ^{125 ]} These exciting results motivate the exploration of new composite geometries and material, which could be used to optimize the magnitude and operational range (i.e., temperature, magnetic field, etc.) where large magnetoelectrocaloric effects can be achieved.

Looking forward, work on calorics has a rather clear, but not straightforward goal: create the biggest temperature changes with the least applied fields across the widest temperature range possible. To achieve these goals, novel heterostructure concepts are needed. For example, work on compositionally-graded ferroelectrics has already shown that the presence of a built-in field can suppress the dielectric permittivity while having minimal effect on the pyroelectric response, in turn, enhancing the pyroelectric and the electrocaloric figures of merit.^[ Reference Mangalam, Agar, Damodaran, Karthik and Martin ^{61 ]} Likewise, such compositionally-graded ferroelectrics may also exhibit large responses over wider temperature ranges than homogeneous materials. Alternatively, exotic highly-ordered ferroelectric phases such as polar vortices in oxide superlattices^[ Reference Yadav, Nelson, Hsu, Hong, Clarkson, Schlepüetz, Damodaran, Shafer, Arenholz, Dedon, Chen, Vishwanath, Minor, Chen, Scott, Martin and Ramesh ^{93 ]} could give rise to novel caloric effects, namely the toroidocaloric effect,^[ Reference Castán, Planes and Saxena ^{126 ]} analogous to those observed in magnetic-vortex structures such as LiCo(PO₄)₃ and Ba₂CoGe₂O₇. While the jury is still out on what the most effective material and/or device structure is to maximize caloric responses in multifunctional materials these exciting recent developments hold promise that these effects previously deemed just a scientific curiosity will be developed into integrated and functional devices.

A low-power future—ferroics for novel energy efficient devices

Driven by the already large and growing market for mobile, battery-powered devices and the rapidly emerging “Internet-of-Things (IOT),” a new bottleneck in terms of speed and power consumption now dominates. As electronics approach the critical lengthscale of sub-10 nm, Moore's Law,^[ Reference Moore ^{127 ]} which so far has set the pace for transistor scaling, is nearing its “demise.”^[ Reference Markoff ^{128 ]} As a consequence, there is quite a bit of interest in alternative approaches to information processing, such as quantum or neuromorphic computing. The possibility for multiple analog states in a ferroelectric hysteresis loop makes it likely that ferroelectrics will play a key role in neuromorphic computing.^[ Reference Mead ^{129 ]} In parallel, ferroics are already playing a critical role in enhancing conventional digital electronics. A particularly emergent example is the use of the negative capacitance time domain regime of ferroelectric switching^[ Reference Khan, Chatterjee, Wang, Drapcho, You, Serrao, Bakaul, Ramesh and Salahuddin ^{130 ]} and the potential to leverage nanodomain structures to produce negative capacitance over a large temperature range.^[ Reference Zubko, Wojdeł, Hadjimichael, Fernandez-Pena, Sené, Luk'yanchuk, Triscone and Íñiguez ^{131 ]} Such approaches will enable us to, at least temporarily, overcome the 60 mV/decade limit that is current in CMOS transistors.

On the memory front, it would be extremely desirable to significantly lower the energy consumption/bit of information stored. Current memory technologies operate approximately in the few picoJoule/bit regime of energy consumption.^[ Reference Dean ^{132 ]} Approaching the fundamental “Landauer limit” (kT[ln 2]) poses several fundamental and materials challenges.^[ Reference Landauer ^{133 ]} As an intermediate step, the goal is to create logic and memory that can operate with an energy consumption of the order of attojoules per logic or memory operation. This requires a reinvention of the materials and architectures of logic and memory. Multifunctional materials with their multiple susceptibilities represent a versatile platform to design future microelectronic devices with the potential of attojoule operation.

Toward this objective, there is considerable interest in designing composite structures which couple multifunctional materials such that they manipulate the functional properties of one another. Coupling of functionalities can be mediated by the lattice (which is typically the case as in piezoelectrics), or through coupling of spin (exchange coupling), charge (field effects), and/or orbital effects. Within this framework, there has been a significant amount of interest in electric-field control of both the direction and state of magnetism.^[ Reference Chu, Martin, Holcomb, Gajek, Han, He, Balke, Yang, Lee, Hu, Zhan, Yang, Fraile-Rodríguez, Scholl, Wang and Ramesh ^{134 ]} Typically, these device concepts rely on generating an acoustic pulse or strain in one component of the composite structure which is elastically coupled in such a way that it can generate a measureable change in response in another material. In this regard, many device concepts have been explored including piezoelectronic transistors which operate by using a piezoelectric layer to drive a metal-insulator transition in a piezoresistive material [Fig. 7(a)],^[ Reference Newns, Elmegreen, Liu and Martyna ^{135 ,} Reference Solomon, Bryce, Kuroda, Keech, Shetty, Shaw, Copel, Hung, Schrott, Armstrong, Gordon, Reuter, Theis, Haensch, Rossnagel, Miyazoe, Elmegreen, Liu, Trolier-McKinstry, Martyna and Newns ^{136 ]} magnetic or ferroelectric tunnel junctions where the polarization direction alters the tunneling electroresistance enabling the formation of non-volatile memories with large on/off ratios [Fig. 7(b)],^[ Reference Tsymbal and Kohlstedt ^{137 –} Reference Garcia and Bibes ^{140 ]} (potentially) field effect transistors with negative capacitance that could allow for ultra-low-power electronic devices,^[ Reference Khan, Chatterjee, Wang, Drapcho, You, Serrao, Bakaul, Ramesh and Salahuddin ^{130 ,} Reference Khan, Bhowmik, Yu, Kim, Pan, Ramesh and Salahuddin ^{141 ]} and others. In an alternative approach, the presence of a ferroelectric polarization can manipulate the carrier density, and in turn, the electronic properties of 2D materials (e.g., graphene) enabling the design of robust field-effect transistors.^[ Reference Baeumer, Rogers, Xu, Martin and Shim ^{142 –} Reference Baeumer, Saldana-Greco, Martirez, Rappe, Shim and Martin ^{145 ]} The considerable excitement about these device concepts has recently lead to the study of ferroelectric/FeRh heterostructures as a new way to harness these effects [Fig. 7(c)].^[ Reference Cherifi, Ivanovskaya, Phillips, Zobelli, Infante, Jacquet, Garcia, Fusil, Briddon, Guiblin, Mougin, Ünal, Kronast, Valencia, Dkhil, Barthélémy and Bibes ^{146 –} Reference Phillips, Cherifi, Ivanovskaya, Zobelli, Infante, Jacquet, Guiblin, Ãœnal, Kronast, Dkhil, Barthélémy, Bibes and Valencia ^{149 ]} Heterostructures based on FeRh are particularly promising compared with strongly correlated complex oxides (e.g., cuprates and doped maganites) due to the giant electroresistance which can be achieved at near ambient temperatures. FeRh exhibits a temperature-dependent, first-order phase transition from antiferromagnetic (low temperature) to ferromagnetic (high temperature) at ~100 °C which is characterized by a ~1% volumetric expansion.^[ Reference Marti, Fina, Frontera, Liu, Wadley, He, Paull, Clarkson, Kudrnovsky, Turek, Kunes, Yi, Chu, Nelson, You, Arenholz, Salahuddin, Fontcuberta, Jungwirth and Ramesh ^{150 ]} By growing epitaxial films of FeRh on single crystals of BaTiO₃ it was shown that magnetoelectric coupling coefficients of the order of ~10⁻⁵ s/m can be achieved; the largest reported for any multiferroic heterostructure and providing potential for use in electric-field-driven magnetic and resistive memory devices [Fig. 7(d)].^[ Reference Cherifi, Ivanovskaya, Phillips, Zobelli, Infante, Jacquet, Garcia, Fusil, Briddon, Guiblin, Mougin, Ünal, Kronast, Valencia, Dkhil, Barthélémy and Bibes ^{146 ]} Direct evidence of this strain-induced magnetic phase transition was observed using magnetic force microscopy [Figs. 7(e) and 7(f)].^[ Reference Liu, Li, Gai, Clarkson, Hsu, Wong, Fan, Lin, Rouleau, Ward, Lee, Sefat, Christen and Ramesh ^{147 ]} Ultimately, to achieve low-power device operation requires low-voltage operation. Future studies will likely focus on how to create similar devices with thin film piezoelectric/ferroelectric layers capable of significantly reducing the operational voltage.

Figure 7. (a) Piezoelectronic resistor concept with fulling intergraded transductive stack consisting of a piezoresistive element on top of a piezoelectric element confined by a high Young's modulus (HYM) yoke. The three metal contacts (gray) are called gate, common, and sense. The large piezoelectric/piezoresistive cross-sectional area ~25:1 serves to amplify the stress in the piezoresistive layer relative to the piezoelectric layer (Reprinted with permission from Ref. [Reference Solomon, Bryce, Kuroda, Keech, Shetty, Shaw, Copel, Hung, Schrott, Armstrong, Gordon, Reuter, Theis, Haensch, Rossnagel, Miyazoe, Elmegreen, Liu, Trolier-McKinstry, Martyna and Newns136]. Copyright 2015 American Chemical Society). (b) Schematic of a ferroelectric tunnel junction consisting of an ultra-thin ferroelectric layer sandwiched between two metal layers. Readout is performed by passing a small current across the ferroelectric layer, which does not change the polarization state. Due to the tunneling electroresistance effect the current depends of the direction of the polarization (Reprinted with permission from Ref. [Reference Tsymbal and Gruverman139], Copyright 2016 Nature Publishing Group). (c) Schematic of electric-field-induced magnetic phase transition in multiferroic heterostructures consisting of an epitaxial FeRh layer and a perovskite ferroelectric substrate (such as BaTiO₃ and PMN-PT, image courtesy of Dr. X. Renshaw Wang, NTU, Singapore). (d) Variation of the magnetization in FeRh/BaTiO₃ heterostructure with the applied voltage at 385 K, after heating under an external voltage of +21 V. The symmetric dependence of magnetization indicates that the voltage-induced strain effect from the ferroelectric BaTiO₃ dominates the magnetoeletric response. The inset shows the voltage dependence of the out-of-plane parameter of FeRh at 390 K (Reprinted with permission from Ref. [Reference Cherifi, Ivanovskaya, Phillips, Zobelli, Infante, Jacquet, Garcia, Fusil, Briddon, Guiblin, Mougin, Ünal, Kronast, Valencia, Dkhil, Barthélémy and Bibes146], Copyright 2016 Nature Publishing Group). (e) MFM phase images (8 × 8 μm²) of an FeRh/BTO heterostructure collected after heating up to 376 K with zero E. (f) MFM image of the same region after application of E = −1 kV/cm to the BTO substrate (at 376 K). The false color stands for the phase shift Δφ, which reflects the strength and orientation of out-of-plane magnetic moment (orange color represents up moment and blue color down). Green color Δφ ~ 0 corresponds to negligible moment (Reprinted with permission from Ref. [Reference Liu, Li, Gai, Clarkson, Hsu, Wong, Fan, Lin, Rouleau, Ward, Lee, Sefat, Christen and Ramesh147]).

While these proof-of-concept studies are exciting there are many scientific and engineering challenges that need to be addressed. From a materials physics perspective, perhaps the top priority is to identify the fundamental limits of cross-coupling. Additionally, and equally important, is determining the limitations on dynamics of various coupling phenomena (i.e., switching speed). From a materials synthesis perspective, one of the most difficult challenges in creating these heterostructure devices is finding ways to strongly couple (at the atomic level) dissimilar materials which could have incompatible chemical structure and reactivity, large lattice mismatch, incompatible surface energies, and/or deposition conditions.^[ Reference Liu, Biegalski, Hsu, Shang, Marker, Liu, Li, Fan, Meyer, Wong, Nichols, Chen, You, Chen, Wang, Wang, Ward, Gai, Lee, Sefat, Lauter, Liu and Christen ^{151 ]} Future studies will surely explore how to tailor the interfaces to increase coupling between these layers. Furthermore, creating heterostructure devices generally requires the patterning of multifunctional oxide materials. Currently the most common routes involve multistep processes using focused ion beam,^[ Reference Solomon, Bryce, Kuroda, Keech, Shetty, Shaw, Copel, Hung, Schrott, Armstrong, Gordon, Reuter, Theis, Haensch, Rossnagel, Miyazoe, Elmegreen, Liu, Trolier-McKinstry, Martyna and Newns ^{136 ,} Reference Ganpule, Stanishevsky, Su, Aggarwal, Melngailis, Williams and Ramesh ^{152 ]} or sacrificial oxide hardmask processes^[ Reference Karthik, Damodaran and Martin ^{153 ]}; however, selective wet-chemical etching would be preferable. One potential route to achieve increased selectivity in wet-chemical etching processes could involve the adaption of metal-assisted chemical etching to complex oxides.^[ Reference Li ^{154 ]} Regardless of the route, the gargantuan impact of composite structures of multifunctional materials will drive a significant research effort and advancement within the next decade.

Beyond just using ferroic materials as elements in a composite structure, there is also growing interest in utilizing the innate potential for collective, long-range interactions in ferroic materials to enable novel low-energy devices. The idea here is that controllable excitation of low-energy perturbations of the elementary building blocks of these materials could enable long-range and deterministic changes in the ensemble system. Such collective behavior is pervasive in nature, and has been observed in biological (e.g., clustering of migratory animals),^[ Reference Cavagna, Cimarelli, Giardina, Parisi, Santagati, Stefanini and Viale ^{155 ]} chemical (e.g., self-assembly of colloidal Janus particles),^[ Reference Yan, Chaudhary, Bae, Lewis and Granick ^{156 ]} and physical (e.g., superconductivity, magnetism, and martensitic transformations) systems. In ferroics, collective behavior has been observed in magnets which result in novel spin states such as skyrmions^[ Reference Mochizuki ^{157 ]} and artificial spin ice structures.^[ Reference Nisoli, Moessner and Schiffer ^{158 ]} As an example, recent work has revealed the collective dynamics of magnetic moment reversal in artificial spin ice systems that give rise to avalanches with the appearance of 1D Dirac strings as a natural degree of freedom [Figs. 8(a)–8(c)].^[ Reference Mengotti, Heyderman, Rodriguez, Nolting, Huegli and Braun ^{159 ,} Reference Ladak, Read, Perkins, Cohen and Branford ^{160 ]}

Figure 8. XMCD images showing direct observation of field reversal in a fully polarized honeycomb lattice. This processes proceeds by creation and propagation of avalanches of pairs of opposite magnetic charges separated by a Dirac string. Evolution shown as a function of applied field (a) <82%, (b) 92% and (c) 99% of the coercive field Hc (Reprinted with permission from Ref. [Reference Mengotti, Heyderman, Rodriguez, Nolting, Huegli and Braun159], Copyright 2016 Nature Publishing Group). (d–f) Maps of the piezoelectric nonlinearity in PZT films of different thickness (Reprinted with permission from Ref. [Reference Vasudevan, Marincel, Jesse, Kim, Kumar, Kalinin and Trolier-McKinstry163]). (g) The highly ordered nanotwinned domain structure with high density ferroelastic domain walls in (111)-oriented PbZr_0.2Ti_0.8O₃ thin films (Reprinted with permission from Ref. [Reference Xu, Liu, Grinberg, Karthik, Damodaran, Rappe and Martin169], Copyright 2016 Nature Publishing Group).

While collective phenomena are clearly at play on the atomic scale in magnetic systems there has been budding interest in exploiting mesoscale collective phenomena in ferroelectrics. In ferroelectrics, collective phenomenon can occur when domain walls move in a correlated manner. Such collective domain wall motion reduces the travel distance of the domain walls enabling fast switching and, potentially, low-power operation for devices. Recent studies have observed the alignment of ferroelastic and ferroelectric domains across multiple grain boundaries as a result of both long-range substrate clamping and short-range inter-granular coupling.^[ Reference Ivry, Chu, Scott and Durkan ^{161 ]} Due to the collective nature of these domain walls, avalanche-like correlated domain wall motion can occur upon application of an external electric field impacting both the nonlinear dielectric properties in low-field, sub-switching Rayleigh regimes and switching properties in high-field regimes [Figs. 8(d)–8(g)].^[ Reference Gruverman, Auciello and Tokumoto ^{162 –} Reference Ivry, Scott, Salje and Durkan ^{167 ]} While the length scale of collective phenomena in polycrystalline ferroelectrics is rather small (as compared with magnetic systems) due to the presence of grain boundaries, these limitations can be skirted in ferroelectric single crystals or epitaxial thin films. In turn, there has been a dedicated effort to generate highly ordered ferroelastic domain structures to exploit collective phenomenon. One particularly promising example was demonstrated in (111)-oriented PbZr_1−x Ti _x O₃ films which exhibit a highly ordered, nanotwinned domain structure with dense ferroelastic domain walls, wherein the strong elastic coupling between nanotwinned domains should result in collective motion of domain wall twins [Fig. 7(h)].^[ Reference Xu, Karthik, Damodaran and Martin ^{168 ,} Reference Xu, Liu, Grinberg, Karthik, Damodaran, Rappe and Martin ^{169 ]} Alternatively, dense ordered ferroelastic domain structures capable of exhibiting collective phenomenon can be obtained by manipulating the geometry, dimension, and elastic boundary conditions of ferroelectric structures.^[ Reference Schilling, Bowman, Catalan, Scott and Gregg ^{170 ]} This approach has been successfully demonstrated in magnetic comb structures where domain walls can be driven at high velocities,^[ Reference Lewis, Petit, O'Brien, Fernandez-Pacheco, Sampaio, Jausovec, Zeng, Read and Cowburn ^{171 ]} but has only been minimally exploited in ferroelectrics.

All told, while ferroic-based, low-powered devices are in the infancy of their development they hold significant promise due to the large number of highly coupled susceptibilities which can be exploited. By carefully interweaving the interactions between dissimilar materials with differing responses and susceptibilities there are near limitless bounds on the device architectures. There are many important questions, however, that need to be addressed including exploring the potential physical limitations of device relevant parameters such as stable minimum feature size, minimum coercive field, energy dissipation, switching speed, etc. Nevertheless, with the correct design schemes one could envision creating ferroic-based, low-power “beyond binary” logic and memory devices that could truly revolutionize our computational and data storage capabilities.