Antiferroelectric materials feature a peculiar response to applied electric fields, characterized by a structural transition between non-polar and polar states. Controllable structural changes are always interesting and potentially useful; in the case of antiferroelectrics, their field-driven transition allows to store high energy densities in them. Hugo Aramberri and I have spent several years thinking how to increase this stored energy density, either by optimizing known antiferroelectrics or by trying to discover new ones. While interesting, our results were hardly the expected ones: we ended up doubting the strict antiferroelectric nature of the model compound in the field (see Aramberri et al., npj Computational Materials 7, 196 (2021)) and did not manage to predict any viable alternative. As a last resort, we decided to consider artificial antiferroelectrics made of well-known ferroelectric compounds subject to suitable electrostatic constraints. We knew about the multidomain polar structures that ferroelectric layers usually display when sandwiched between dielectrics, where up- and down-polarization regions spontaneously appear to minimize spurious electric fields and the attendant energy cost of polarizing the dielectrics. It occurred to us that such multidomain structures look like an antiferroelectric (antipolar) phase, and that they can surely be transformed into a monodomain (polar) state under a field. Thus, we tackled a high-throughput computational investigation of hundreds of ferroelectric-dielectric superlattices, optimizing various design variables (layer thickness, dielectric response, ...) to get the best energy-storage behavior. The results exceeded our expectations, as we found that these artificial antiferroelecric-like materials compete with the best known compounds and, more importantly, can be tailored to display optimal properties under specific operation conditions. A happy ending to our struggles! You can read more about it in Aramberri et al., Science Advances 8, eabn4880 (2022).

A few years ago, we learned that hafnia (HfO₂) -- a dielectric compound well-known to the electronics industry -- can be prepared in a ferroelectric phase with spontaneous and switchable electric polarization. At first, work on ferroelectric hafnia was essentially restricted to engineers interested in memories and field-effect transistors. Eventually, the ferroelectrics community got to study this new family member; and fortunately so, as it is revealing itself as a source of very novel behaviors. A big first surprise was that hafnia's ferroelectric order is more robust in smaller (nanometric) samples, at variance with all other known ferroelectrics. Further, this material presents no trace of soft modes, thus deviating from the standard model for ferroelectric behavior amply represented in the perovskite oxide family. We thus knew that, when working with this compound, we should reset our minds and avoid assumptions coming from previous experience with other materials. This fresh approach proved useful when we started work on hafnia's piezoelectric response, as we found a non-standard behavior whereby a (longitudinal) compression yields a stronger polarization, instead of weakening it. Our findings quickly moved from the non-standard to the first-ever category, as we discovered that the sign of the piezoresponse could be reversed by tuning the relative strengths of the chemical bonds in the polar state (which can be done by imposing suitable elastic boundary conditions -- epitaxial strains -- to the material). To learn more, have a look at Dutta et al., Nature Communications 12, 7301 (2021), a hopefully pedagogical article where we compare HfO₂ to well-known piezoelectric perovskite PbTiO₃. And stay tuned, because it seems we are in for a long ride of surprises with hafnia!

Two years ago, Hugo Aramberri and I set up to discover new antiferroelectric materials using a high-throughput computational approach. Antiferroelectrics are close relatives of ferroelectrics, but with local dielectric dipoles (which result from the relative displacement of cations and anions) being antialigned (and thus canceling out) instead of aligned (which would result in a net macroscopic polarization). In particular, we looked at the family of perovskite oxides, which includes quite a few ferroelectrics (e.g., BaTiO₃, PbTiO₃) but very few antiferroelectrics (e.g., PbZrO₃). Would we be able to discover previously unnoticed antiferroelectric perovskites and, in passing, figure out the reasons for the ferro over antiferro prevalence? As it often happens, this journey took us to an unexpected destination, as the best (only) new antiferroelectric candidate we were able to identify (CsVO₃) turned out to yield a non-perovksite structure when we investigated its ground state. Indeed, we then discovered that this compound (as well as RbVO₃ and the better studied KVO₃) display a lattice sometimes called pyroxene-like due to its similarities with the very abundant and well-know pyroxene minerals. Most interestingly, pyroxene structures feature MO₄ tetrahedra (where M can be something like Si or a metal atom) that are asymmetric by construction, thus presenting a permanent electric dipole. In normal conditions, such dipoles are antialigned, but we predicted that it is possible to apply an electric field to make them parallel and access a ferroelectric-like state. Hence, KVO₃ and the other vanadates we looked at are antiferroelectric; and, most importantly, we have good reasons to believe that essentially all pyroxenes are antiferroelectric candidates! (Check out the details in Aramberri and Íñiguez, Comm. Mats. 1, 52 (2020).) Hence, antiferroelectrics -- relatively rare and unique materials that are promising for e.g. energy applications -- might be hiding all around, and we might be able to discover many more by looking at some very old minerals in a new light!

Magnetic skyrmions are mesmerizing spin structures of unique topology and particle-like properties. Can there be an electric analogue, with electric dipoles instead of spins? Scientists have been pondering this question for a few years, and some interesting theoretical proposals have appeared. However, the strategies suggested so far to stabilize skyrmion-like electric states are difficult to implement experimentally and by-construction preclude some of the most desirable properties of skyrmions, e.g. their mobility. The situation has turned around this year. In a second-principles investigation led by M.A.P. Gonçalves (LIST), and with collaborators J. Junquera and P. García-Fernández (Cantabria), we have shown it is possible to harness the non-trivial structure of the ferroelectric domain walls of PbTiO₃ to create skyrmion bubbles by simply writing column-like nano-domains in an homogeneously polarized matrix [Gonçalves et al., Science Advances 5, eaau7023 (2019)]. Further, we find that these bubbles undergo topological and isotopological transitions when subject to external fields or heating, offering us a great deal of control. But that's not all: Most importantly, together with collaborators in Berkeley, Penn State and Cornell, we have been able to prove experimentally that such skyrmion bubbles can be stabilized at ambient conditions in PbTiO₃-based heterostructures! [Das et al., Nature 568, 368 (2019)] While many challenges lay ahead (how to move the bubble domains, and thus the skyrmions, in a controlled way; how to switch their chirality), these works constitute a major breakthrough towards the obtention and manipulation of topological structures in strong ferroelectric materials, and effectively inaugurate a field that promises to be as exciting as it gets.

There is a keen interest in engineering the lattice thermal conductivity of materials, either to reduce it (as required to obtain good thermoelectric properties) or to enhance it (e.g. for efficient cooling down in electronics, or to maximize heat transfer in caloric applications). More visionary is the possibility that such a control, could it be exerted in a dynamic way, would allow to use heat currents in the same way we use electronic ones today, to do electronics with phonons (aka phononics). Some years ago, Riccardo Rurali (ICMAB-CSIC) and I thought that such a dynamic control of the lattice thermal conductivity could be achieved in ferroelectrics, as in these materials one can use electric fields to write and erase obstacles to the propagating phonons. Indeed, our scatterers would be the so-called domain walls, that is, the boundaries that separate regions with equivalent, but differently oriented, electric polarizations. Our second-principles simulations proved that the concept works, with a twist: we found that ferroelectric domain walls may act as highly-selective phonon filters!, rather than as simple resistors [Royo et al., Phys. Rev. Mats. 1, 051402 (2017); Seijas-Bellido et al., Phys. Rev. B 96, 140101 (2017)]. Further, we also realized that, in highly-polarizable compounds like ferroelectrics and incipient ferroelectrics, the response of the lattice to applied electric fields can be as strong as to cause dramatic changes in the lattice thermal conductivity, an effect we call electrophononic. Interestingly, the strongest electrophononic effects yield a (much) reduced conductivity and rely on an universal mechanism, namely, the field-induced symmetry breaking and attendant increase of three-phonon scattering processes. This effect, which we have predicted to occur in PbTiO₃ [Torres et al., Phys. Rev. Lett. 123, 185901 (2019); Seijas-Bellido et al., Phys. Rev. B 97, 184306 (2018)] and SrTiO₃ [Torres et al., Phys. Rev. Mats. 3, 044404 (2019)], suggests a specific and promising route to obtain a thermal transistor. In addition to the great fun and learning it is bringing us, this multi-year work suggests that ferroelectric and related materials might prove unique and useful for future applications involving heat management.

Perovskite oxides share the same generic chemical formula (ABO₃) and basic structure: a lattice or corner-sharing rather-regular oxygen octahedra, with A and B cations located at the inter-octahedral spaces and octahedral interiors, respectively. Despite these structural similarities, subtle changes in perovskite composition may yield drastically different physical properties; further, even a given compound can present a wide variety of behaviors depending on the external conditions (e.g., temperature) or applied fields (e.g., electric, elastic). This richness is the result of a feature that makes perovskites rather unique: the large number of degrees of freedom (structural and electronic, including magnetic ones) competing for attention in these compounds. Among those, there is a structural order parameter that is all but omnipresent in perovskites, and which strongly influences all others: the quasi-rigid concerted rotations (or tilts) of the oxygen octahedra, typically in long-range patterns displaying perfectly in-phase or antiphase spatial modulations. Because of their central importance to the physics of these oxides, understanding the driving forces that favor different tilt orders, and how to control them, has been recognized as a critical issue, albeit one that is much complicated by the fact that a detailed experimental characterization of the network of octahedra (oxygens being nearly invisible to most diffraction and microscopy techniques) is very challenging. Recently, in a series of theoretical papers with Hongjun Xiang (Fudan), Laurent Bellaiche (Arkansas) and other colleagues, we have contributed to the on-going efforts to shed some light on these matters, explaining the mechanisms that favor some tilt polymorphs over others [Chen et al., Phys. Rev. B 97, 024113 (2018)], elucidating their behavior under pressure [Xiang et al., Phys. Rev. B 96, 054102 (2017)], or revealing surprising aspects of their interaction with ferroelectricity [Gu et al., Phys. Rev. Lett. 120, 197602 (2018)]. Beyond their specific merits and impact in the field of perovskites, these works illustrate the usefulness of simulation to understand critical structural aspects of functional materials.

Can a metal present a polar distortion that breaks the inversion symmetry of the lattice? (In spite of the fact that the usual driving force for polarity are Coulomb dipole-dipole interactions that all but vanish in metals.) If so, would we be able to switch such a polar distortion with an external bias? (Despite the fact that metals are not supposed to sustain voltage drops.) The interest in these questions is many-fold, from fundamental to applied; indeed, it is always good to understand what's possible and what's not, plus non-centrosymmetric (polar) metals are rare creatures, potentially useful in various contexts. With A. Filippetti, V. Fiorentini (Cagliari) and others, we have studied these problems and stumbled upon a few surprises in the way. We have found that the answer to the first question is an affirmative one; as a matter of fact, we have identified a previously unnoticed, seemingly-universal "meta-screening" effect that favors polar order in metallized ferroelectrics. As for the second question, we are now convinced that, in well-chosen conditions, it is possible to apply an external electric field to a metal and switch its polar distortion, which yields a genuine ferroelectric metal! As a result, we think we have access to a new and fairly exciting family of materials that are likely to surprise us with additional unexpected behaviors. You can read more in Zhao et al., Phys. Rev. B 97, 054107 (2018) and Filippetti et al., Nat. Comm. 7, 11211 (2016).

Spins and phonons talk, and their conversation may have consequences, ranging from superconductivity and metal-insulator transitions to magnetoelectricity. Even strongly discontinuous structural transformations, as those occurring in steels, are significantly influenced by the magnetic contribution to the free energy of competing polymorphs. Thus, we had long wondered about spin-phonon (SP) effects in the structural phase diagram of multiferroic perovskite oxides, which are magnetic and display a wealth of crystallographic transformations. However, when C. Cazorla (New South Wales) and I investigated BiFeO₃, the compound we thought most likely to test positive for SP, the result was rather disappointing: SP couplings are not small, but are similar for different BiFeO₃ polymorphs, having no significant effect in the structural transitions [Phys. Rev. B 88, 214430 (2013)]. Nevertheless, this work led us to understand the requirements to obtain the SP effects we were after, and thus to investigate a second multiferroic, BiCoO₃. The results exceeded our expectations greatly this time, as we found that the SP couplings drastically modify BiCoO₃'s temperature-pressure phase diagram. In particular, in a wide pressure range they render an unprecedented double-reentrant transition sequence from a high-temperature paraelectric phase, to a ferroelectric phase, then to a different paraelectric state, and finally to a different ferroelectric phase at low temperatures. You can read this story at Cazorla et al., Sci. Adv. 3, e1700288 (2017), where you can also learn about the theoretical approach we devised to account for the effect of spin fluctuations as we move across differently (dis)ordered magnetic phases.

Anti-ferroelectric (AFE) materials receive much attention today, discussions often starting with their very definition. (Important) subtleties aside, these insulators present a peculiar response to applied electric fields, featuring an often-sharp field-induced transition to a strongly polarized state. Interestingly, this property makes it possible to charge them with large energy densities and, in principle, discharge them quickly, obtaining a fast energy release that is useful in pulsed-power applications. Beyond the fundamental interest to understand the AFE response of specific compounds, the key for the optimization of these materials is to control their hysteresis loop, so as to maximize the stored energy and release efficiency. Recently, with Arkansas' Bin Xu and Laurent Bellaiche, we realized that there is a family of paraelectric/ferroelectric compounds -- namely, solid solutions based on BiFeO₃ -- that offers incredible flexibility to optimize their AFE response to electric fields... even if such materials had (almost) never been thought of as AFEs before! Indeed, we obtain incredible figures of merit from atomistic simulations, and also propose a simple model to understand AFE performance in terms of a few key parameters. You can find the full story in Xu et al., Nat. Comm. 8, 15682 (2017).

In some magnetic materials, complex arrangements of the spins (e.g., forming cycloids or spirals) break the symmetry of the lattice in ways that are compatible with the occurrence of a spontaneous electric polarization. These so-called "type II" multiferroics -- whose most famous representative may be perovskite oxide TbMnO₃ -- are interesting because their polarization, while usually very small, is strongly coupled to the magnetic structure, which results in giant magnetoelectric effects. Interestingly, in the typical "type II" multiferroics, only one spin sublattice (e.g., the Mn spins in TbMnO₃) is involved in the magnetoelectric effects, and complex magnetic orders are required to break spatial inversion symmetry. However, with H.J. Zhao, L. Bellaiche and other collaborators, we have shown that, provided our compound has two active spin sublattices, very simple spin orders can induce the desired symmetry breaking. Indeed, we have studied model material GdFeO₃ -- which is representative of all ABO₃ perovskites in which both A and B cations are magnetic -- to reveal a number of surprising effects. For example, we show that ordering both spin lattices in simple (very common) collinear arrangements produces a magnetically-driven pizoelectricity! Further, this piezoelectric phase becomes polar upon cell distortions that occur naturally in most perovkiste oxides. For more, look at Zhao et al., Nat. Comms. 8, 14025 (2017), where we reveal these effects and their governing rules, and predict specific strategies to engineer and enhance them.

In inhomogeneous ferroelectric media, different regions respond differently to an applied electric field. The more responsive regions develop relatively large polarizations and similarly large depolarizing fields, to the extent that such fields can actually exceed (and be against) the external field that caused the material's reaction in the first place. Such reactive regions display negative dielectric permittivity and capacitance, and the voltage drop through them is opposite to the applied bias. As a result, the more inert regions are subject to a tension that is actually larger than the applied bias, and we thus obtain a voltage amplification! Collaborators at UC London (Zubko) and Geneva (Triscone) have managed to harness and characterize such a striking effect in superlattices formed by PbTiO₃ (a ferroelectric in a highly-responsive frustrated state) and SrTiO₃ (which plays the role of relatively stiff dielectric). We have used atomistic simulation to confirm and explain the experimental observations, revealing the key role of that domain wall movement plays in the anomalous response of PbTiO₃. To know the details of these surprising results, which could be a first step towards the development of low-consumption electronic devices, have a look at Zubko et al., Nature 534, 524 (2016). Our work also led us to discover an incredible "domain melting" state in which domain wall motion is spontaneously activated; you can see a movie here (search for "at a glance", "videos").

It is an old mantra: magnetoelectric multiferroic materials will allow us to control the magnetization direction and sign by means of electric fields, which will permit the development of switchable low-power magnetic devices. Yet, in spite of the wealth of magnetoelectric couplings discovered over the past decade, this promise remains largely unfulfilled. The main roadblock is our inability to control (in a deterministic way, shall we say) the final magnetic state obtained upon electric switching, as it is typically the case that several magnetic outcomes (which may present e.g. magnetizations of opposite sign) are equally possible. Fortunately, this difficulty can be overcome by engineering the path of the ferroelectric switching, so that the final magnetic state is well determined. This is what our simulations suggest was achieved by the group of R. Ramesh and collaborators [Nature 516, 370 (2014)], who were able to obtain reproducible magnetization reversal at room temperature in BiFeO₃. Further, together with Laurent Bellaiche, Philppe Ghosez and others, we have been able to predict that a similar path control, and magnetization switch, can be achieved in the so-called hybrid improper ferroelectrics [see e.g. Phys. Rev. B 88, 060102(R) (2013) and Adv. Func. Mats. 25, 3626 (2015)], which suggest that this strategy may be a general and viable one!

In ferroelastic and ferroelectric materials, different regions may distort in equivalent, but differently oriented, ways, forming multi-domain configurations. Sometimes such configurations make it possible to accommodate elastic and electric constraints the material is subject to; conversely, by tuning such constraints, domains can be controlled. The boundaries between domains, i.e. the domain walls, are peculiar regions, characterized by a structural mismatch that often yields unusual high-energy atomic arrangements. Our collaborators Noheda et al. have recently discovered that chemical substitution may be an effective way to release the stress at the walls, rendering long-range-ordered structures that constitute genuine two-dimensional crystals! It thus seems possible to use domain walls as chemical reactors, as they offer environmental conditions not achievable otherwise, to obtain atomic configurations never seen in extended systems. The possibilities to create original self-assembled nano-structures, maybe with novel and useful properties, seem endless! Read more in Farokhipoor et al., Nature 515, 379 (2014).

Ferroelectric domain walls are unique nanostructures whose distinct and useful properties (conductive, magnetic, optical) have made them a focal point of attention. Further, ferroelectric walls can be experimentally moved, created and erased in a well controlled manner, which may eventually permit the development of switchable and tunable nano-devices. Understanding the origin of the surprising behaviors displayed by these walls poses a major challenge for theorists and experimentalists alike. Thanks to our recently developed methods for large-scale lattice-dynamical simulations, we can now tackle such a challenge and provide a realistic characterization, at the atomic level, of ferroelectric domain walls in the most interesting materials. Our first application already revealed an astonishing effect: We discovered a temperature-driven ferroelectric phase transition confined within the ferroelectric domain walls of prototypic material PbTiO₃! This striking phenomenon gathers some of the most appealing ingredients of the physics of phase transitions (low dimensionality, strong fluctuations, anomalous dynamics) and surely heralds further exciting discoveries. Read more in Wojdeł and Íñiguez, Phys. Rev. Lett. 112, 247603 (2014).

Ferroelectric and piezoelectric oxides constitute a very active research area within our group. Much of our recent activity has focused on the development of a new family of model potentials, with parameters computed from first principles, that make it possible to simulate the lattice-dynamical properties of these (and any) compounds at finite temperatures. We mimic the traditional approach to the investigation of vibrational spectra: We start from a suitably chosen reference configuration of the material and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a text-book approach has plenty of advantages (generality, simplicity, systematic refinement), and the first potentials thus produced are already leading to very interesting results (e.g., a huge competition between structural instabilities in PbTiO₃). Read more in Wojdeł et al., Journal of Physics: Condensed Matter 25, 305401 (2013).

Last year, one of our favorite and also most dreaded materials, room-temperature multiferroic BiFeO₃ (BFO), continued to challenge our imagination with beautiful and unexpected behaviors. In a study of the ferroelectric domain walls (FE DWs) of the bulk compound, we found out that the DW energy is not determined by the type of discontinuity of the electric polarization; rather, it is the change of a supposedly secondary distortion (involving the concerted rotation of the O₆ octahedra in the perovskite latiice) what controls it. As it turns out, these secondary modes are not secondary at all! Further, we also discovered that the lowest-energy DWs present an atomic structure that is essentially identical to other metastable phases of the compound. Hence, BFO's DWs display a novel form of polytypism! These polytypic arrangements can extend throughout the bulk of the material to form novel structures that one might call nano-twinned. With L. Bellaiche and other colleagues, we predicted that such nano-twinned phases are stable in various regions of BFO's phase diagram, i.e., at high temperatures, under pressure, etc. To close the year, we discovered that magnetic frustration occurs in the so-called super-tetragonal phase of the compound, which can be grown on strongly compressive substrates. In addtion to the surprise of finding such an effect in a simple lattice that does not present any peculiar (e.g., triangular) bonding topology, we showed that the degree of frustration can be continuously tuned by appropriately chosing the substrate. Read more in Physical Review Letters 109, 247202 (2012); Physical Review B 87, 024102 (2013); and Advanced Functional Materials 23, 234 (2013).

Artificially layered structures of complex oxides sometimes display unexpected new functionalities. Collaborators Gibert et al. from the University of Geneva (Switzerland) have demonstrated experimentally how interfacial interactions can induce a complex magnetic structure in a non-magnetic material, as revealed by the observation of exchange bias in superlattices composed of (111)-oriented layers of paramagnetic LaNiO₃ and ferromagnetic (in thin film form) LaMnO₃. Our simulations suggest that a strongly damped spin-density wave develops inside the LaNiO₃ layers, and hint at possible intrinsic mechanisms for the exchange bias. Read more in Gibert et al., Nature Materials 11, 195 (2012).

Bismuth ferrite (BiFeO₃ or BFO) is one of the best studied materials of the day. This perovskite oxide presents both ferroelectric and magnetic orders at room temperature, which makes it one of the few real candidates for device applications based on magnetoelectric couplings. But BFO is already fascinating from the point of view of its structural properties, as it displays a large variety of phases under different conditions (of temperature, pressure, epitaxial strain, at skin layers, etc.) and there are indications that it may be possible to induce transformations between some of those phases by application of electric fields. Recently we have been able to prove from first principles that BFO's structural richness is an intrinsic property of the compound and manifests itself in a huge number of local (meta)stable minima of the energy that are quasi-degenerate with the ground state. Moreover, our simulations indicate that, if reversible switching between some of BFO's phases were achieved, we would obtain large functional responses of various kinds, including electric, piezoelectric, and magnetoelectric ones. Read more in the series of papers with Oswaldo Diéguez and others, including experimental collaborators Infante et al.: Physical Review Letters 107, 057601 (2011); ibid. 107, 237601 (2011); Physical Review B 83, 094105 (2011).

Magnetoelectric materials are insulators whose magnetic properties can be controlled by application of external electric fields. This possibility opens the door to many interesting applications, such as the development of magnetic memories that would be writeable by means of electric fields, thus solving Joule-heating problems that currently complicate the miniaturization of MRAMs. We have introduced a method for first-principles calculations of magnetoelectric effects. Thanks to this technique, it is now possible for the first-principles theory to make a significant contribution to the experimental search for new materials that display robust magnetoelectric properties at room temperature. Indeed, we have been able to prove that inducing structural softness in regular magnetoelectrics — i.e., tuning the materials to make their structure strongly reactive to applied fields — makes it possible to obtain very large magnetoelectric effects. Read more in the series of papers with Jacek C. Wojdeł: Physical Review Letters 105, 037208 (2010); ibid 103, 267205 (2009); ibid 101, 117201 (2008).

Developing safe and efficient methods for storing hydrogen at ambient conditions is critical for the progress of fuel-cell technologies. Current efforts focus on obtaining hydrogen-binding interactions in the range that is appropriate for applications, namely, about 0.5 eV. First-principles methods enable a detailed analysis of the H₂ binding interactions, and are thus ideally suited for the search of novel solid state systems for hydrogen storage. Our latest work focused on graphites intercalated with light metal atoms, and suggest that alkaline-earths, like Be or Mg, could lead to useful storage properties. Read more in the series of papers with Taner Yildirim and others, about metal-assisted carbons for hydrogen storage [J. Phys.: Condens. Matt 20, 285212 (2008); Phys. Rev. B 72, 153403 (2005)] and solid state storage [J. Phys.: Condens. Matt. 19, 176007 (2007); Appl. Phys. Lett. 86, 103109 (2005); Phys. Rev. B 70, 060101 (2004)].