Charge order in LuFe2O4: an unlikely route to ferroelectricity

Insights into Strain Engineering: From Ferroelectrics to Related Functional Materials and Beyond

Ferroelectrics have become indispensable components in various application fields, including information processing, energy harvesting, and electromechanical conversion, owing to their unique ability to exhibit electrically or mechanically switchable polarization. The distinct polar noncentrosymmetric lattices of ferroelectrics make them highly responsive to specific crystal structures. Even slight changes in the lattice can alter the polarization configuration and response to external fields. In this regard, strain engineering has emerged as a prevalent regulation approach that not only offers a versatile platform for structural and performance optimization within ferroelectrics but also unlocks boundless potential in various functional materials. In this review, we systematically summarize the breakthroughs in ferroelectric-based functional materials achieved through strain engineering and progress in method development. We cover research activities ranging from fundamental attributes to wide-ranging applications and novel functionalities ranging from electromechanical transformation in sensors and actuators to tunable dielectric materials and information technologies, such as transistors and nonvolatile memories. Building upon these achievements, we also explore the endeavors to uncover the unprecedented properties through strain engineering in related chemical functionalities, such as ferromagnetism, multiferroicity, and photoelectricity. Finally, through discussions on the prospects and challenges associated with strain engineering in the materials, this review aims to stimulate the development of new methods for strain regulation and performance boosting in functional materials, transcending the boundaries of ferroelectrics.

Rational design, crystal structure, and frustrated magnetism of the Ge-containing YbFe2O4-type layered oxides In2Zn3-xCoxGeO8 (0 ≤ x ≤ 3)

YbFe₂O₄-type layered oxides have attracted tremendous interest because the unique crystal comprises two distinct geometrically frustrated triangular cation-sublattices. Herein, a series of YbFe₂O₄-type materials In₂Zn_3-xCo_xGeO₈ (0 ≤ x ≤ 3) were rationally designed and experimentally synthesized for the first time. The crystal structures of In₂Zn_3-xCo_xGeO₈ were investigated comprehensively by Rietveld refinements against high-resolution monochromatic Cu K_α1 XRD data. Zn²⁺, Co²⁺, and Ge⁴⁺ cations are distributed randomly on the [MO]₂ bilayer and possess a trigonal bipyramid (TBP) coordination geometry. Because Co²⁺ has an unpaired electron in the d_z2 orbital and a larger electronegativity than Zn²⁺, Co²⁺-to-Zn²⁺ equivalent substitution in In₂Zn_3-xCo_xGeO₈ results in more compact MO₅-TBPs, which is the origin of anisotropic lattice expansion and contraction along the a and c axes, respectively. The Co²⁺ moments in the [MO]₂ bilayer are strongly AFM coupled and geometrically frustrated, therefore resulting in a spin-glass magnetic transition at around T_g = 20 K for In₂ZnCo₂GeO₈, while a long-range AFM ordering is established for In₂Co₃GeO₈ with a Néel temperature of 53 K, attributed to the significantly enhanced AFM interactions and increased In³⁺/Co²⁺ anti-site disordering, as compared to those in In₂ZnCo₂GeO₈.

Spin-Lattice and Magnetoelectric Couplings Enhanced by Orbital Degrees of Freedom in Polar Multiferroic Semiconductors

Orbital degrees of freedom mediating an interaction between spin and lattice were predicted to raise strong magnetoelectric effect, i.e., to realize an efficient coupling between magnetic and ferroelectric orders. However, the effect of orbital fluctuations has been considered only in a few magnetoelectric materials, as orbital-degeneracy driven Jahn-Teller effect rarely couples to polarization. Here, we explore the spin-lattice coupling in multiferroic Swedenborgites with mixed valence and Jahn-Teller active transition metal ions on a stacked triangular and Kagome lattice using infrared and dielectric spectroscopy. On one hand, in CaBaM_{4}O_{7} (M=Co, Fe), we observe a strong magnetic-order-induced shift in the phonon frequencies and a corresponding large change in the dielectric response. Remarkably, as an unusual manifestation of the spin-phonon coupling, the spin fluctuations reduce the phonon lifetime by one order of magnitude at the magnetic phase transitions. On the other hand, lattice vibrations, dielectric response, and electric polarization show no variation at the Néel temperature of CaBaFe_{2}Co_{2}O_{7}, which is built up by orbital singlet ions. Our results provide a showcase for orbital degrees of freedom enhanced magnetoelectric coupling via the example of Swedenborgites.

Coexistence and Coupling of Multiple Charge Orderings and Spin States in Hexagonal Ferrite

The coupling between charge and spin orderings in strongly correlated systems plays a crucial role in fundamental physics and device applications. As a candidate of multiferroic materials, LuFe₂O₄ with a nominal Fe^2.5+ valence state has the potential for strong charge-spin interactions; however, these interactions have not been fully understood until now. Here, combining complementary characterization methods with theoretical calculations, two types of charge orderings with distinct magnetic properties are revealed. The ground states of LuFe₂O₄ are decided by the parallel/antiparallel coupling of both charge and spin orderings in the adjacent FeO double layers. Whereas the ferroelectric charge ordering remains ferrimagnetic below 230 K, the antiferroelectric ordering undergoes antiferromagnetic-ferrimagnetic-paramagnetic transitions from 2 K to room temperature. This study demonstrates the unique aspects of strong spin-charge coupling within LuFe₂O₄. Our results shed light on the coexistence and competing nature of orderings in quantum materials.

Low-Temperature Growth of AlN Films on Magnetostrictive Foils for High-Magnetoelectric-Response Thin-Film Composites

This study reports a strong ME effect in thin-film composites consisting of nickel, iron, or cobalt foils and 550 nm thick AlN films grown by PE-ALD at a (low) temperature of 250 °C and ensuring isotropic and highly conformal coating profiles. The AlN film quality and the interface between the film and the foils are meticulously investigated by means of high-resolution transmission electron microscopy and the adhesion test. An interface (transition) layer of partially amorphous Al_xO_y/AlO_xN_y with thicknesses of 10 and 20 nm, corresponding to the films grown on Ni, Fe, and Co foils, is revealed. The AlN film is found to be composed of a mixture of amorphous and nanocrystalline grains at the interface. However, its crystallinity is improved as the film grew and shows a highly preferred (002) orientation. High self-biased ME coefficients (α_ME at a zero-bias magnetic field) of 3.3, 2.7, and 3.1 V·cm^-1·Oe^-1 are achieved at an off-resonance frequency of 46 Hz in AlN/Ni thin-film composites with different Ni foil thicknesses of 7.5, 15, and 30 μm, respectively. In addition, magnetoelectric measurements have also been carried out in composites made of 550 nm thick films grown on 12.5 μm thick Fe and 15 μm thick Co foils. The maximum magnetoelectric coefficients of AlN/Fe and AlN/Co composites are 0.32 and 0.12 V·cm^-1·Oe^-1, measured at 46 Hz at a bias magnetic field (H_dc) of 6 and 200 Oe, respectively. The difference of magnetoelectric transducing responses of each composite is discussed according to interface analysis. We report a maximum delivered power density of 75 nW/cm³ for the AlN/Ni composite with a load resistance of 200 kΩ to address potential energy harvesting and electromagnetic sensor applications.

Direct evidence of electronic ferroelectricity in YbFe2O4 using neutron diffraction and nonlinear spectroscopy

We report the first observation of room temperature spontaneous electric polarization in an electronic ferroelectric material, a YbFe₂O₄ single crystal. The observation was based on second harmonic generation (SHG), a nonlinear optical process. Tensor analysis of the SHG signal revealed that this material has a polar charge superstructure with Cm symmetry. This result settles the long-term discussion on the uncertainty about electronic ferroelectric properties, including the charge order structure. We present a complete picture of the polar charge ordering of this material via consistent results from two different characterization methods. The SHG signal shows the same temperature dependence as the superlattice signal observed in neutron diffraction experiments. These results prove ferroelectric coupling to electron ordering in YbFe₂O₄, which results in electronic ferroelectricity which is enabled by the real space ordering of iron cations with different valences. The existence of electronic ferroelectricity holds promise for future electronics technologies where devices run a thousand times faster than frequency of the present CPU (a few gigahertz) embedded in smartphones, etc.

A short history of multiferroics

The realization that materials with coexisting magnetic and ferroelectric order open up efficient ways to control magnetism by electric fields unites scientists from different communities in the effort to explore the phenomenon of multiferroics. Following a tremendous development, the field has now gained some maturity. In this article, we give a succinct review of the history of this exciting class of materials and its evolution from “ferroelectromagnets” to “multiferroics” and beyond.

Site-specific spectroscopic measurement of spin and charge in (LuFeO3)m/(LuFe2O4)1 multiferroic superlattices

Interface materials offer a means to achieve electrical control of ferrimagnetism at room temperature as was recently demonstrated in (LuFeO3)m/(LuFe2O4)1 superlattices. A challenge to understanding the inner workings of these complex magnetoelectric multiferroics is the multitude of distinct Fe centres and their associated environments. This is because macroscopic techniques characterize average responses rather than the role of individual iron centres. Here, we combine optical absorption, magnetic circular dichroism and first-principles calculations to uncover the origin of high-temperature magnetism in these superlattices and the charge-ordering pattern in the m = 3 member. In a significant conceptual advance, interface spectra establish how Lu-layer distortion selectively enhances the Fe2+ →  Fe3+ charge-transfer contribution in the spin-up channel, strengthens the exchange interactions and increases the Curie temperature. Comparison of predicted and measured spectra also identifies a non-polar charge ordering arrangement in the LuFe2O4 layer. This site-specific spectroscopic approach opens the door to understanding engineered materials with multiple metal centres and strong entanglement.

Hexagonal rare-earth manganites and ferrites: a review of improper ferroelectricity, magnetoelectric coupling, and unusual domain walls

Hexagonal rare-earth manganites and ferrites are well-known improper ferroelectrics with low-temperature antiferromagnetism/weak ferromagnetism. In recent decades, new multi-functional device concepts and applications have provoked the exploration for multiferroics which simultaneously possess ferroelectric and magnetic orders. As a promising platform for multiferroicity, hexagonal manganites and ferrites are attracting great research interest among the fundamental scientific and technological communities. Moreover, the novel type of vortex-like ferroelectric domain walls are locked to the antiphase structural domain walls, providing an extra degree of freedom to tune the magnetoelectric coupling and other properties such as conductance. Here, we summarize the main experimental achievements and up-to-date theoretical understanding of the ferroelectric, magnetic, and magnetoelectric properties, as well as the intriguing domain patterns in hexagonal rare-earth manganites and ferrites. Recent work on non-stoichiometric compounds will also be briefly introduced.

Controllable Ferromagnetism in Super-tetragonal PbTiO3 through Strain Engineering

The coupling strain in nanoscale systems can achieve control of the physical properties in functional materials, such as ferromagnets, ferroelectrics, and superconductors. Here, we directly demonstrate the atomic-scale structure of super-tetragonal PbTiO₃ nanocomposite epitaxial thin films, including the extraordinary coupling of strain transition and the existence of the oxygen vacancies. Large strain gradients, both longitudinal and transverse (∼3 × 10⁷ m^-1), have been observed. The original non-magnetic ferroelectric composites notably evoke ferromagnetic properties, derived from the combination of Ti³⁺ and oxygen vacancies. The saturation ferromagnetic moment can be controlled by the strain of both the interphase and substrate, optimized to a high value of ∼55 emu/cc in 10-nm thick nanocomposite epitaxial thin films on the LaAlO₃ substrate. Strain engineering provides a route to explore multiferroic systems in conventional non-magnetic ferroelectric oxides and to create functional data storage devices from both ferroelectrics and ferromagnetics.

Intrinsic Ferroelectricity in Charge-Ordered Magnetite

Single crystalline magnetite Fe 3 O 4 was investigated at low temperatures in the charge ordered state by electric measurements and time-resolved diffraction with voltage applied in-situ. Dielectric spectroscopy indicates relaxor ferroelectric characteristics, with polarization switching observably only at sufficiently low temperatures and in a suitably chosen time-window. PUND measurements with a ms time scale indicate a switchable polarization of about 0 . 6 μ C / cm 2 . Significant switching occurs only above a threshold field of about 3 kV / mm , and it occurs with a time delay of about 20 μ s . The time-resolved diffraction experiment yields, for sufficiently high voltage pulses, a systematic variation by about 0 . 1 % of the intensity of the ( 2 , 2 ¯ , 10 ¯ ) Bragg reflection, which is attributed to structural switching of domains of the non-centrosymmetric C c structure to its inversion twins, providing proof of intrinsic ferroelectricity in charge ordered magnetite.

Co-emergence of magnetic order and structural fluctuations in magnetite

The nature of the Verwey transition occurring at T_V ≈ 125 K in magnetite (Fe₃O₄) has been an outstanding problem over many decades. A complex low temperature electronic order was recently discovered and associated structural fluctuations persisting above T_V are widely reported, but the origin of the underlying correlations and hence of the Verwey transition remains unclear. Here we show that local structural fluctuations in magnetite emerge below the Curie transition at T_C ≈ 850 K, through X-ray pair distribution function analysis. Around 80% of the low temperature correlations emerge in proportion to magnetization below T_C. This confirms that fluctuations in Fe-Fe bonding arising from magnetic order are the primary electronic instability and hence the origin of the Verwey transition. Such hidden instabilities may be important to other spin-polarised conductors and orbitally degenerate materials.

Charge-Lattice Coupling in Hole-Doped LuFe_{2}O_{4+δ}: The Origin of Second-Order Modulation

Understanding singularities in ordered structures, such as dislocations in lattice modulation and solitons in charge ordering, offers great opportunities to disentangle the interactions between the electronic degrees of freedom and the lattice. Specifically, a modulated structure has traditionally been expressed in the form of a discrete Fourier series with a constant phase and amplitude for each component. Here, we report atomic scale observation and analysis of a new modulation wave in hole-doped LuFe_{2}O_{4+δ} that requires significant modifications to the conventional modeling of ordered structures. This new modulation with an unusual quasiperiodic singularity can be accurately described only by introducing a well-defined secondary modulation vector in both the phase and amplitude parameter spaces. Correlated with density-functional-theory (DFT) calculations, our results reveal that those singularities originate from the discontinuity of lattice displacement induced by interstitial oxygen in the system. The approach of our work is applicable to a wide range of ordered systems, advancing our understanding of the nature of singularity and modulation.

Advances in magnetoelectric multiferroics

The manipulation of magnetic properties by an electric field in magnetoelectric multiferroic materials has driven significant research activity, with the goal of realizing their transformative technological potential. Here, we review progress in the fundamental understanding and design of new multiferroic materials, advances in characterization and modelling tools to describe them, and the exploration of devices and applications. Focusing on the translation of the many scientific breakthroughs into technological innovations, we identify the key open questions in the field where targeted research activities could have maximum impact in transitioning scientific discoveries into real applications.

Observation of momentum-resolved charge fluctuations proximate to the charge-order phase using resonant inelastic x-ray scattering

In strongly correlated electron systems, enhanced fluctuations in the proximity of the ordered states of electronic degrees of freedom often induce anomalous electronic properties such as unconventional superconductivity. While spin fluctuations in the energy-momentum space have been studied widely using inelastic neutron scattering, other degrees of freedom, i.e., charge and orbital, have hardly been explored thus far. Here, we use resonant inelastic x-ray scattering to observe charge fluctuations proximate to the charge-order phase in transition metal oxides. In the two-leg ladder of Sr_14−xCa_xCu₂₄O₄₁, charge fluctuations are enhanced at the propagation vector of the charge order (q_CO) when the order is melted by raising temperature or by doping holes. In contrast, charge fluctuations are observed not only at q_CO but also at other momenta in a geometrically frustrated triangular bilayer lattice of LuFe₂O₄. The observed charge fluctuations have a high energy (~1 eV), suggesting that the Coulomb repulsion between electrons plays an important role in the formation of the charge order.

Present status of the experimental aspect of RFe₂O₄ study

We give a brief review of the experimental research on a triangular mixed valence iron oxide RFe2O4 (R = Y, Dy, Ho, Er, Tm, Yb, Lu, Sc or In). Interest in this material has been increasing every year because of the fascinating but complicated interaction between spin, charge and the orbital state of iron ions in frustrated geometry. Reports collected in this review cover experimental research on crystallography, chemical analysis, bulk and thin film preparation, magnetic, dielectric, diffraction with neutrons, x-ray and electron, optical and x-ray absorption, Mössbauer spectroscopy and other methods that incorporate the use of modern scientific technology and knowledge. The report mainly focuses on experimental facts since 1990 on which an early review by Siratori has been published (Kimizuka et al 1990 Handbook on the Physics and Chemistry of Rare Earths vol 13, ed K A Gschneidner Jr and L Eyring (Amsterdam: North-Holland/Elsevier) pp 283-384).

Observation of direct magneto-dielectric behaviour in Lu3Fe5O12−δ above room-temperature

Oxygen vacancy created an intrinsic magneto-dielectric effect in Lu₃Fe₅O₁₂.

Orbital-ordering-driven multiferroicity and magnetoelectric coupling in GeV₄S₈

We report here the discovery of multiferroicity and large magnetoelectric coupling in the type I orbital order system GeV₄S₈. Our study demonstrates that this clustered compound displays a para-ferroelectric transition at 32 K. This transition originates from an orbital ordering which reorganizes the charge within the transition metal clusters. Below the antiferromagnetic transition at 17 K, the application of a magnetic field significantly affects the ferroelectric polarization, revealing thus a large magnetoelectric coupling. Our study suggests that the application of a magnetic field induces a metamagnetic transition which significantly affects the ferroelectric polarization thanks to an exchange striction phenomenon.

Electronic ferroelectricity induced by charge and orbital orderings

After the revival of the magnetoelectric effect which took place in the early 2000s, the interest in multiferroic materials displaying simultaneous presence of spontaneous long-range magnetic and dipolar order has motivated an exponential growth of research activity, from both the experimental and theoretical perspectives. Within this context, and relying also on the rigorous formulation of macroscopic polarization as provided by the Berry-phase approach, it has been possible to identify new microscopic mechanisms responsible for the appearance of ferroelectricity. In particular, it has been realized that electronic spin, charge and orbital degrees of freedom may be responsible for the breaking of the space-inversion symmetry, a necessary condition for the appearance of electric polarization, even in centrosymmetric crystal structures. In view of its immediate potential application in magnetoelectric-based devices, many efforts have been made to understand how magnetic orderings may lead to ferroelectric polarization, and to identify candidate materials. On the other hand, the role of charge and orbital degrees of freedom, which have received much less attention, has been predicted to be non-negligible in several cases. Here, we review recent theoretical advances in the field of so-called electronic ferroelectricity, focusing on the possible mechanisms by which charge- and/or orbital-ordering effects may cause the appearance of macroscopic polarization. Generally, a naive distinction can be drawn between materials displaying almost localized electrons and those characterized by a strong covalent character and delocalized electrons. As for the latter, an intuitive understanding of basic mechanisms is provided in the framework of tight-binding model Hamiltonians, which are used to shed light on unusual charge/orbital effects in half-doped manganites, whereas the case of magnetite will be thoroughly discussed in light of recent progress pointing to an electronic origin of its proposed ferroelectric and magnetoelectric properties.

Neutron scattering and μSR investigations of the low temperature state of LuCuGaO₄

LuCuGaO₄ has magnetic Cu(2+) and diamagnetic Ga(3+) ions distributed on a triangular bilayer and is suggested to undergo a spin glass transition at Tg ∼ 0.4 K. Using μSR (muon spin rotation) and neutron scattering measurements, we show that at low temperature the spins form a short range correlated state with spin fluctuations detectable over a wide range of timescales: at 0.05 K magnetic fluctuations can be detected in both the μSR time window and also extending beyond 7 meV in the inelastic neutron scattering response, indicating magnetic fluctuations spanning timescales between ∼10(-5) and ∼10(-10) s. The dynamical susceptibility scales according to the form χ″(ω)T(α), with α = 1, throughout the measured temperature range (0.05-50 K). These effects are associated with quantum fluctuations and some degree of structural disorder in ostensibly quite different materials, including certain heavy fermion alloys, kagome spin liquids, quantum spin glasses, and valence bond glasses. We therefore suggest that LuCuGaO₄ is an interesting model compound for the further examination of disorder and quantum magnetism.

Dielectric properties of charge-ordered LuFe(2)O(4) revisited: the apparent influence of contacts

We show results of broadband dielectric measurements on the charge ordered, proposed to be multiferroic material LuFe(2)O(4). The temperature and frequency dependence of the complex permittivity as investigated for temperatures above and below the charge-order transition near T(CO)≈320  K and for frequencies up to 1 GHz can be well described by a standard equivalent-circuit model considering Maxwell-Wagner-type contacts and hopping induced ac conductivity. No pronounced contribution of intrinsic dipolar polarization could be found, and thus the ferroelectric character of the charge order in LuFe(2)O(4) has to be questioned.