On the molecular origins of the ferroelectric splay nematic phase

Interface-Engineered Polar Topological Domains in Ferroelectric Nematic Liquid Crystals

Polar topological domains, distinguished by their inherent topological protection and diverse optoelectronic functionalities, have recently attracted significant interest across scientific disciplines. However, the realization of these structures in inorganic materials is often impeded by crystal symmetry constraints. In this context, ferroelectric nematic liquid crystals, characterized by spontaneous polarization and flexible polarization orientation, provide an exceptional platform for the development of polar topological domains. Despite their potential, a considerable challenge lies in identifying a straightforward yet versatile approach for engineering polar topological domains within liquid crystals. Here, this study presents an interfacial engineering strategy that effectively stabilizes a range of polar topological domains in ferroelectric nematic liquid crystals, including vortex, centrifugal vortex, and center-divergent configurations, by synergistically modulating the surface tension and interfacial tension. Utilizing a combination of experimental characterization and simulation, the role of anchoring energy is systematically investigated in the molecular alignment of liquid crystals and facilitates transitions between diverse topological structures. This research not only extends the horizons for constructing and manipulating polar topological domains but also enhances their prospective applications in topological photonics.

Research on Quantum Materials and Quantum Technology at RIKEN

RIKEN covers fundamental research on physics, chemistry, biology, life and medical science, information and mathematical science, and engineering. Here, we outline research activities on quantum materials and quantum technology that include topological and correlated materials, spintronics, nanoscale materials and structures, atomic and quantum optics, and quantum computing.

Antiferroelectric Order in Nematic Liquids: Flexoelectricity Versus Electrostatics

The recent discovery of ferroelectric nematic liquid crystalline phases marks a major breakthrough in soft matter research. An intermediate phase, often observed between the nonpolar and the ferroelectric nematic phase, shows a distinct antiferroelectric response to electric fields. However, its structure and formation mechanisms remain debated, with flexoelectric and electrostatics effects proposed as competing mechanisms. By controlling the magnitude of electrostatic forces through ion addition in two representative ferroelectric nematic materials, it is shown that the primary mechanism for the emergence of antiferroelectric order is the flexoelectric coupling between electric polarization and splay deformation of the nematic director. The addition of ions significantly expands the temperature range over which the antiferroelectric phase is observed, with this range increasing with increasing ion concentration. Polarizing optical microscopy studies and second harmonic generation (SHG) microscopy reveal the splayed structure modulated in 2D, while SHG interferometry confirms its antiferroelectric character. The model previously used to describe pretransitional behavior is extended by incorporating the electrostatic contribution of ions. The model shows qualitative agreement with the experiments, accurately reproducing the phase diagram and temperature-dependent evolution of the modulation period of the observed structure.

Ferroelectric Nematic Liquid Crystals Showing High Birefringence

High birefringence nematic liquid crystals are particularly demanded for adaptive optics applications in the infrared spectrum because it enable a thinner cell gap for achieving fast response time and improved diffraction efficiency. The emerging ferroelectric nematic liquid crystals have attracted widespread interest in soft matter due to their unique combination of ferroelectricity and fluidity. However, the birefringence, which is one of the most important optical parameters in electro-optic devices, is not large enough (<0.25) in most ferroelectric nematic materials. Here, a polar liquid crystal molecule library containing more than 60 molecules with a highly rigid and fluorinated nature is developed. The introduction of triple bonds constructs a long π-electron conjugated mesogen skeleton, significantly improving the birefringence of polar liquid crystal phases. The birefringence and dispersion properties are systematically studied, demonstrating a strong dependence on chemical structures and the type of polar phases. Furthermore, through multi-component mixing, polar liquid crystal mixtures with ultra-wide temperature range and excellent stability at or near room temperature are obtained. They possess much higher birefringence than the existing ferroelectric liquid crystal materials. The unique combination of high birefringence and fluidic ferroelectricity is expected to promote the application of polar liquid crystals in electro-optic technologies.

Macroscopic dynamics of the antiferroelectric smectic Z A phase and its magnetic analog Z M

We analyze the macroscopic dynamics of antiferroelectric smectic Z A and antiferromagnetic smectic Z M liquid crystals. The smectic Z A phase is characterized by antiferroelectric order in one direction in the planes of the smectic layers giving rise to an orthogonal biaxial overall symmetry without polar direction. Thus in sufficiently thick (bulk) samples without externally applied electric fields, globally D 2 h symmetry results. Therefore, the macroscopic dynamics of the smectic Z A is isomorphic to that of the McMillan phase and one can take over the corresponding results in the field-free limit. This also applies to the defect structure in the sense that one can expect the appearance of half-integer defects as they have also been observed for the McMillan phase. Based on the fact that ferromagnetic nematic liquid crystals are known for about a decade, it seems natural to investigate the antiferromagnetic analog of the smectic Z A phase, which we denote as Z M in the present paper. In this phase, one also has an in-plane preferred direction, which is, however, not like a director in an ordinary nematic, but odd under time reversal. It can be characterized by a staggered magnetization, N , just as in a solid antiferromagnet like MnO. As additional macroscopic variables when compared to a usual non-polar smectic A phase, we have the in-plane staggered magnetization and the magnetization M . As a consequence, we find that spin waves (frequently called anti-magnons in solids) become possible. Therefore, we have for the antiferromagnetic smectic phase, Z M , three pairs of propagating modes: first and 'second' sound as in usual smectic A phases and one pair of spin waves. The coupling between 'second' sound and spin waves is also analyzed leading to the possibility to excite spin waves by dynamic layer compressions and, vice versa, to generate 'second' sound by temporally varying magnetic fields. We note, however, that without additional mechanical or magnetic deformations, the coupling between spin waves on the one hand and first and second sound on the other is a higher order effect in the wave vector q . We also analyze the question of antiferroelectricity and antiferromagnetism for nematic liquid crystals.

Impact of charge distribution on the stability of ferroelectric nematic liquid crystals

This study explores the influence of charge distribution and molecular shape on the stability of ferroelectric nematic liquid crystalline phases through atomistic simulations of DIO molecules. We demonstrate the role of dipole-dipole interactions and molecular shape in achieving polar ordering by simulating charged and chargeless topologies, and analysing positional and orientational pair-distribution functions. The charged DIO molecules exhibit head-to-tail and side-by-side parallel alignments conducive to long-range polar order, whereas the chargeless molecules show no polar ordering. The 2D x-y cross-section of the correlation pair-distribution function shows that lateral local dipoles in the molecular structure are critical for the formation of the ferroelectric phase, highlighting the importance of charge asymmetry and electrostatic interactions in stabilizing long-range polar order.

Systematic Fluorination Is a Powerful Design Strategy toward Fluid Molecular Ferroelectrics

Ferroelectric nematic (NF) liquid crystals combine liquid-like fluidity and orientational order of conventional nematics with macroscopic electric polarization comparable in magnitude to solid-state ferroelectric materials. Here, we present a systematic study of twenty-seven homologous materials with various fluorination patterns, giving new insight into the molecular origins of spontaneous polar ordering in fluid ferroelectric nematics. Beyond our initial expectations, we find the highest stability of the NF phase to be in materials with specific fluorination patterns rather than the maximal fluorination, which might be expected based on simple models. We find a delicate balance between polar and apolar nematics, which is entirely dictated by the substitution of the fluorine atoms. Aided by electronic structure calculations, we show this to have its origins in the radial distribution of charge across the molecular surface, with molecules possessing a more oscillatory distribution of electrons across their surfaces and possessing a higher propensity to form polar nematic phases. This work provides a new set of ground rules and design principles that can inform the synthesis of future ferroelectric nematogens.

Polar Order in a Fluid Like Ferroelectric with a Tilted Lamellar Structure - Observation of a Polar Smectic C (SmCP) Phase

The discovery of fluid states of matter with spontaneous bulk polar order is appreciated as a major discovery in the fields of soft matter and liquid crystals. Typically, this manifests as polar order superimposed atop conventional phase structures and is thus far limited to orthogonal phase types. Here we report a family of materials which exhibit a previously unseen state of matter which we conclude is a polar smectic C phase, and so we term it SmCP. The spontaneous polarisation of the SmCP phase is over two orders of magnitude larger than that found in conventional ferroelectric SmC phase of chiral materials used in some LCD devices. Fully atomistic molecular dynamics simulations faithfully and spontaneously reproduce the proposed structure and associated bulk properties; comparison of experimental and simulated X-ray scattering patterns shows excellent agreement. The materials disclosed here have significantly smaller dipole moments than typical polar liquid crystals such as RM734 which suggests the role of molecular electrical polarity in generating polar order is perhaps overstated, a view supported by consideration of other molecular systems.

Low field electrocaloric effect at isotropic-ferroelectric nematic phase transition

Electrocaloric effects (ECE) in solid state materials, such as ferroelectric ceramics and ferroelectric polymers, have a great impact in developing cooling systems. Herein, we describe the ECE of a newly synthesized ferroelectric nematic liquid crystal compound at the isotropic-ferroelectric nematic (I-NF) phase transition. While the Joule heat completely suppressed the ECE in a DC field, in an AC field with E < 1.2 V μm-1 and f ≥ 40 Hz, an increase in optical transmittance was observed, which in comparison with a zero-field transmittance versus temperature plot indicated a shift in the transition temperature. These findings implied that one can induce the desired phase transition using an electric field via ECE with an EC responsivity of ∼1.7 × 10-6 km V-1. Notably, the required electric field was two orders of magnitude smaller than the typical fields for other EC materials. EC effects observed under such low fields is a unique property of ferroelectric nematic liquid crystals. Furthermore, the specific EC energy could be increased considerably by reducing the ionic content, thus suppressing the Joule heat.

Freely suspended nematic and smectic films and free-standing smectic filaments in the ferroelectric nematic realm

We show that stable, freely suspended liquid crystal films can be made from the ferroelectric nematic (NF) phase and from the recently discovered polar, lamellar SmZA and SmAF phases. The NF films display two-dimensional, smectic-like parabolic focal conic textures comprising director/polarization bend that are a manifestation of the electrostatic suppression of director splay in the film plane. In the SmZA and SmAF phases, the smectic layers orient preferentially normal to the film surfaces, a condition never found in typical thermotropic or lyotropic lamellar LC phases, with the SmZA films exhibiting focal-conic fan textures mimicking the appearance of typical smectics in glass cells when the layers are oriented normal to the plates, and the SmAF films showing a texture of plaquettes of uniform in-plane orientation where both bend and splay are suppressed, separated by grain boundaries. The SmAF phase can also be drawn into thin filaments, in which X-ray scattering reveals that the smectic layer planes are normal to the filament axis. Remarkably, the filaments are mechanically stable even if they break, forming free-standing, fluid filaments supported only at one end. The unique architectures of these films and filaments are stabilized by the electrostatic self-interaction of the liquid crystal polarization field, which enables the formation of confined, fluid structures that are fundamentally different from those of their counterparts made using previously known liquid crystal phases.

Broadband Spin and Orbital Momentum Modulator Using Self-Assembled Nanostructures

The structural symmetry of solids plays an important role in defining their linear and nonlinear optical properties. The quest for versatile, cost-effective, large-scale, and defect-free approaches and materials platforms for tailoring structural and optical properties on demand is underway since decades. A self-assembled spherulite material comprised of synthesized molecules with large dipole moments aligned azimuthally, forming a vortex polarity with spontaneously broken symmetry, is experimentally demonstrated. This unique self-assembled structure enables new linear and nonlinear light-matter interactions, including generating optical vortex beams with complex spin states and on-demand topological charges at the fundamental, doubled, and tripled frequencies. This work will likely enable numerous applications in areas such as high-dimensional quantum information processing with large capacity and high security, spatiotemporal optical vortices, and a novel optical manipulation and trapping platform.

Emergent Ferroelectric Nematic and Heliconical Ferroelectric Nematic States in an Achiral "Straight" Polar Rod Mesogen

Ferroelectric nematic liquid crystals (NFLCs) are distinguished by their remarkable polarization characteristics and diverse physical phenomena, sparking significant interest and excitement within the scientific community. To date, over 150 NFLC molecules are developed; however, there are no reports regarding straight linear polar molecules with a parallel alignment of the permanent dipole moment and the molecular axis. The straight polar mesogen nBOE exhibits an enantiotropic NF phase with a wide temperature window (up to 100 K) despite having a longer alkyl chain (up to n = 6) than the critical alkyl chain length of conventional models. Interestingly, nBOE with a medium-length alkyl chain displays an exotic phase sequence of NF-HCNF-SmXF during the elimination of positional displacement among adjacent molecules. Furthermore, the reflective color modulation of the HCNFLC over the entire VIS-NIR spectral regime by ultralow E-field (up to 0.14 V µm-1) is demonstrated.

Order-disorder behavior in the ferroelectric nematic phase investigated via Raman spectroscopy

Polar-ordered fluids are of interest both fundamentally and from an application standpoint. The recently discovered ferroelectric nematic phase is an example of a polar-ordered fluid, and while there has been extensive research interest in these materials, some of the fundamental properties are yet to be fully understood. Here, we report the order parameters of one of the first known materials that exhibit a ferroelectric nematic phase, RM734, determined via Raman spectroscopy. Raman spectroscopy been used extensively to determined order parameters in liquid crystals systems but also to probe ferroelectric behavior in solid ferroelectric systems and is therefore a powerful technique to study the ferroelectric nematic phase. A reduction and subsequent recovery of order parameters (Δ〈P_{2}〉≈0.1, Δ〈P_{4}〉≈0.06) is observed near the onset of the N to N_{F} transition, a feature that is confirmed via complementary birefringence measurements. This dip in order parameters has been attributed to splay fluctuations, which occur at the onset of the N_{F} transition; here we suggest a different explanation. A broadening of the full-width half-maxima (FWHM), of the order of 1 cm^{-1}, of the selected Raman peak is observed near the N to N_{F} phase transition, which we relate to either a change in reorientational dynamics or the onset of polar order. The N_{F} transition is analyzed using standard solid ferroelectric frameworks. An energetic barrier associated with the para- to ferroelectric transition is found to be of the order of 2.5±0.6kJ/mol, which is comparable to solid ferroelectric materials.

Tunable Intracavity Coherent Up-Conversion with Giant Nonlinearity in a Polar Fluidic Medium

The study has demonstrated a novel microcavity-based flexible photon up-conversion system using second harmonic generation (SHG) from a polar nematic fluidic medium doped with a laser dye. The idea is based on coherent light generation via stimulated emission (lasing) and simultaneous frequency doubling inside a microcavity. The polar nematic fluid equips very high even-order optical nonlinearity due to its polar symmetry and large dipole moment along the molecular long axis. At the same time, its inherent fluidic nature allows to easily functionalize the media just by doping, in the present case, with an emissive laser dye. The demonstrated system exhibits a giant nonlinear optical response to input light, while enabling spectral narrowing and multiple-signal output of up-converted light, which is not attainable through the simple SH-conversion of input light. Furthermore, the susceptibility of the liquid crystal offers dynamic modulation capabilities by an external stimulus, such as signal switching by the application of electric field or wavelength tuning through temperature variation. Such a brand-new type of simple coherent flexible up-conversion system must be promising as a new principle for easily accessible and down-scalable wavelength conversion devices.

Electrically activated ferroelectric nematic microrobots

Ferroelectric nematic liquid crystals are fluids exhibiting spontaneous electric polarization, which is coupled to their long range orientational order. Due to their inherent property of making bound and surface charges, the free surface of ferroelectric nematics becomes unstable in electric fields. Here we show that ferroelectric liquid bridges between two electrode plates undergo distinct interfacial instabilities. In a specific range of frequency and voltage, the ferroelectric fluid bridges move as active interacting particles resembling living organisms like swarming insects, microbes or microrobots. The motion is accompanied by sound emission, as a consequence of piezoelectricity and electrostriction. Statistical analysis of the active particles reveals that the movement can be controlled by the applied voltage, which implies the possible application of the system in new types of microfluidic devices.

Bulk photovoltaic effect in ferroelectric nematic liquid crystals

The bulk photovoltaic (BPV) effect in ferroelectric liquid crystals is of increasing scientific interest owing to its great potential for light-energy conversion. The ferroelectric nematic phase exhibits a huge spontaneous polarization that can be aligned to a preferred direction. In this Letter, we investigate the tensorial properties of the BPV effect in the planarly aligned ferroelectric nematic phase of the liquid crystalline material RM734. A steady-state short-circuit photocurrent of ~160 pA and an open-circuit photovoltage of ~50 mV were observed in a cell with a thickness of 5.5 µm under the illumination of ultraviolet light without any bias voltage. Based on the photocurrent measurements in different electrode configurations, the non-zero elements of the BPV tensor were obtained. The BPV effect is attributed to the combination of the spontaneous polarization and the asymmetric distribution of photoinduced charge carriers. This study not only provides an understanding of the bulk PV mechanism in soft ferroelectrics but also promises a wide range of unprecedented, to the best of our knowledge, benefits for light harvesting to engineer marketable photovoltaic devices.

Liquid crystals from curved colloidal rods: waves, twists and more

The curvature of elongated microscopic building blocks plays a crucial role on their self-assembly into orientationally ordered phases. While rod-like molecules form a handful of liquid crystal (LC) phases, curved or banana-shaped molecules show more than fifty phases, with fascinating physical properties, such as chirality or polarity. Despite the fundamental and technological importance of these so-called 'banana-shaped liquid crystals', little is known about their microscopic details at the single-molecule level. Curved colloidal liquid crystals-liquid crystals formed by curved colloidal rods-are excellent model systems to optically resolve the structure and dynamics of curved building blocks within these condensed phases. Recent advances in the synthesis of curved rod-like particles have unlocked the potential for studying-at the single-particle level-the intimate relationship between shape and phase symmetry, and even confirmed the stability of elusive LC phases. Further developments in this nascent field promise exciting findings, such as the first observation of the colloidal twist-bend nematic phase or the fabrication of functional materials with curvature-dependent properties. In this Report on Progress, we will highlight recent advances in the synthesis and assembly of curved colloidal liquid crystals and discuss the upcoming challenges and opportunities of this field.

Constraining the value of the dielectric constant of the ferroelectric nematic phase

Ferroelectric nematic liquid crystals are currently being subject to a plethora of investigations since they are of great fundamental interest and could potentially foster promising applications. However, many basic aspects are still poorly understood, among which the problem of the dielectric constant stands out. Ferroelectric nematics have previously been reported to exhibit giant dielectric constants whose value depends on the thickness of the measurement cell, claims that have recently been shown to be the result of an incorrect interpretation of the experimental data. The intrinsic permittivity of these materials has not been determined yet. In this work, we tackle this problem by modeling the dielectric response of the liquid crystal filled cell through an equivalent circuit proposed by Clark et al. [Phys. Rev. Res. 6, 013195 (2024)2643-156410.1103/PhysRevResearch.6.013195] accounting for polarization reorientation and the effect of insulating interfacial layers. We arrive at the conclusion that the perpendicular component of the permittivity ɛ_{⊥} is of the order of 10 in the prototypical ferroelectric nematogen DIO, while the parallel component ɛ_{∥} is of the order of 150. In this way, the dielectric tensor of DIO has been fully determined.

Dielectric Properties of a Ferroelectric Nematic Material: Quantitative Test of the Polarization-Capacitance Goldstone Mode

The recently discovered ferroelectric nematic (N_{F}) liquid crystals (LC) have been reported to show an extraordinarily large value of the real part of the dielectric constant (ϵ^{'}>10^{3}) at low frequencies. However, it was argued by Clark et al. in Phys. Rev. Res. 6, 013195 (2024)PPRHAI2643-156410.1103/PhysRevResearch.6.013195 that what was measured was the capacitance of the insulating layer at LC or electrode surface and not that of the liquid crystal. Here we describe the results of dielectric spectroscopy measurements of an N_{F} material in cells with variable thickness of the insulating layers. Our measurements quantitatively verify the model by Clark et al. Additionally, our measurements in cells with bare conducting indium tin oxide surface provide a crude estimate of ϵ_{⊥}∼10^{2} in the N_{F} phase.

The effect of particle geometry and initial configuration on the phase behavior of twisted convex n-prisms

We study the phase behavior of twisted convex n-prisms with n = 3 and 4, via Monte Carlo simulations. Biaxial phases, in untwisted prisms, can be induced by choosing specific geometries of the prisms. However, due to the convexity of the twisted particles, a strong twisting disables the formation of biaxial phases and stabilizes uniaxial nematic and smectic phases. Using the increased volume of the twisted convex particles, we define an effective aspect ratio of the twisted prisms and find a homogeneous phase behavior across the geometry of the prisms' cross-section and even across different shapes of the cross-section. In this representation biaxial phases are found for large aspect ratios, while the low aspect ratio behavior can be compared to the hard cylinder phase diagram. For 3-prisms with a small base angle, we show the influence of the initial configuration; a polar initial configuration results in a (polar) splay nematic phase, whereas a non-polar initial configuration results in a biaxial phase.

Revealing the antipolar order in the antiferroelectric SmZA phase by means of circular alignment

Many ferroelectric nematic liquid crystals, like one of the archetype materials, DIO, do not have a direct paraelectric N to ferroelectric NF phase transition, but exhibit yet another phase between N and NF. This phase has recently been proposed to be antiferroelectric, with a layered structure of alternating polarization normal to the average director and is sometimes referred to as Smectic ZA (SmZA). We have examined the SmZA phase in circularly rubbed (CR) cells, known to discriminate between the polar NF and the non-polar N phase from the configuration of disclination lines formed. We find that the ground state of SmZA has the same disclination configuration as the non-polar N phase, demonstrating that the SmZA phase is also non-polar, i.e., it has no net ferroelectric polarization. At the same time, the SmZA texture generally has a grainy appearance, which we suggest is partly a result of the frustration related to layered order combined with the imposed twist in CR cells. We discuss possible orientations of the smectic layers, depending on the alignment conditions. While a horizontal SmZA layer structure is always compatible with surface-induced twist, a vertical layer structure would tend to break up in a twisted bookshelf structure to match non-parallel alignment directions at the two surfaces.

Macroscopic dynamics of ferromagnetic smectic-A

We derive the macroscopic dynamic equations for ferromagnetic smectic-A liquid crystals for which the spontaneous magnetization is parallel to the layer normal of the layering. As additional macroscopic variables when compared to simple fluids, we have the layer displacement u, familiar from smectic liquid crystals, and the magnetization density M. We find a number of reversible and dissipative cross-coupling terms to the additional macroscopic variables and discuss possible experiments to detect them. Among other effects, we point out that the velocity of first sound becomes anisotropic due to the influence of the modulus of the magnetization, while the magnitude of the velocity of second sound is modified. As for the static behavior, we find cross-coupling terms between the magnitude of the magnetization, on the one hand, and layer compression as well as osmotic pressure, on the other hand. In addition, we point out that as a dissipative effect, temperature gradients can induce gradients in the magnetization parallel to the layer normal, mediated by layer compressions.

The Emergence of a Polar Nematic Phase: A Chemist's Insight into the Ferroelectric Nematic Phase

The discovery of a new polar nematic phase; the ferroelectric nematic, has generated a great deal of excitement in the field of liquid crystals. To date there have been around 150 materials reported exhibiting the ferroelectric nematic phase, in general, following three key archetypal structures with these compounds known as RM734, DIO and UUQU-4N. In this review, the relationship between the molecular structure and the stability of the ferroelectric nematic, NF, phase will be described from a chemist's perspective. This will look to highlight the wide variety of functionalities which have been incorporated into these archetypal structures and how these changes influence the transition temperatures of the mesophases present. The NF phase appears to be stabilised particularly by reducing the length of terminal alkyl chains present and adding fluorines laterally along the length of the molecular backbone. This review will look to introduce the background of the ferroelectric nematic phase before then showing the molecular structures of a range of materials which exhibit the phase, describing their structure-property relationships and therefore giving an up-to-date account of the literature for this fascinating new mesophase.

Exploring the Impact of Linkage Structure in Ferroelectric Nematic and Smectic Liquid Crystals

The liquid crystal molecule 3-fluoro-4-(3,4,5-trifluorophenyl)phenyl 2,6-difluoro-4-(trans-5-n-propyl-1,3-dioxane-2-yl)benzoate (DIO) has attracted considerable interest owing to its unique ferroelectric nematic phase and extraordinarily high dielectric constant. To expand the DIO series, novel analogs with 1,3-dioxane units converted to ester units (EST analogs) were synthesized, and their physical properties were characterized. The EST analogs exhibited ferroelectric phases similar to those of the corresponding DIO analogs. Interestingly, an EST analogue featuring a defluorinated benzoate unit exhibited a ferroelectric smectic A phase, despite its smaller longitudinal dipole moment of 6.9 D. This result diverges from the common knowledge that the formation of large longitudinal dipoles is traditionally effective in the emergence of ferroelectric phases. Unlike the DIO series, the EST analogs can be readily obtained without the formation of undesired geometric isomers, which is advantageous for practical applications. The results of this study provide valuable insights into the design of liquid-crystalline materials expressing ferroelectric phases.

Fluid fibers in true 3D ferroelectric liquids

We demonstrate an exceptional ability of a high-polarization 3D ferroelectric liquid to form freely suspended fluid fibers at room temperature. Unlike fluid threads in modulated smectics and columnar phases, where translational order is a prerequisite for forming liquid fibers, recently discovered ferroelectric nematic forms fibers with solely orientational molecular order. Additional stabilization mechanisms based on the polar nature of the mesophase are required for this. We propose a model for such a mechanism and show that these fibers demonstrate an exceptional nonlinear optical response and exhibit electric field-driven instabilities.

New examples of ferroelectric nematic materials showing evidence for the antiferroelectric smectic-Z phase

We present a new ferroelectric nematic material, 4-((4'-((trans)-5-ethyloxan-2-yl)-2',3,5,6'-tetrafluoro-[1,1'-biphenyl]-4-yl)difluoromethoxy)-2,6-difluorobenzonitrile (AUUQU-2-N) and its higher homologues, the molecular structures of which include fluorinated building blocks, an oxane ring, and a terminal cyano group, all contributing to a large molecular dipole moment of about 12.5 D. We observed that AUUQU-2-N has three distinct liquid crystal phases, two of which were found to be polar phases with a spontaneous electric polarization Ps of up to 6 µC cm-2. The highest temperature phase is a common enantiotropic nematic (N) exhibiting only field-induced polarization. The lowest-temperature, monotropic phase proved to be a new example of the ferroelectric nematic phase (NF), evidenced by a single-peak polarization reversal current response, a giant imaginary dielectric permittivity on the order of 103, and the absence of any smectic layer X-ray diffraction peaks. The ordinary nematic phase N and the ferroelectric nematic phase NF are separated by an antiferroelectric liquid crystal phase which has low permittivity and a polarization reversal current exhibiting a characteristic double-peak response. In the polarizing light microscope, this antiferroelectric phase shows characteristic zig-zag defects, evidence of a layered structure. These observations suggest that this is another example of the recently discovered smectic ZA (SmZA) phase, having smectic layers with the molecular director parallel to the layer planes. The diffraction peaks from the smectic layering have not been observed to date but detailed 2D X-ray studies indicate the presence of additional short-range structures including smectic C-type correlations in all three phases-N, SmZA and NF-which may shed new light on the understanding of polar and antipolar order in these phases.

Macroscopic dynamics of the ferroelectric smectic A F phase with C ∞ v symmetry

We present the macroscopic dynamics of ferroelectric smectic A, smecticA F , liquid crystals reported recently experimentally by three groups. In this fluid and orthogonal smectic phase, the macroscopic polarization,P , is parallel to the layer normal thus giving rise toC ∞ v overall symmetry for this phase in the spatially homogeneous limit. A combination of linear irreversible thermodynamics and symmetry arguments is used to derive the resulting dynamic equations applicable at sufficiently low frequencies and sufficiently long wavelengths. Compared to non-polar smectic A phases, we find a static cross-coupling between compression of the layering and bending of the layers, which does not lead to elastic forces, but to elastic stresses. In addition, it turns out that a reversible cross-coupling between flow and the magnitude of the polarization modifies the velocities of both, first and second sound. At the same time, the relaxation of the polarization gives rise to dissipative effects for second sound at the same order of the wavevector as for the sound velocity. We also analyze reversible cross-coupling terms between elongational flow and electric fields as well as temperature and concentration gradients, which lend themselves to experimental detection. Apparently this type of terms has never been considered before for smectic phases. The question how the linearP ⋅ E coupling in the energy alters the macroscopic response behavior when compared to usual non-polar smectic A phases is also addressed.

Mixing twist-bend and ferroelectric nematic liquid crystals

Twist-bend (N_{tb}) and ferroelectric (N_{F}) nematic liquid crystals exhibit several novel effects and new physical properties. Here, we report experimental studies on the phase diagram and some physical properties of binary mixtures of CB9CB and RM734 mesogens. Both N-N_{tb} and N-N_{F} phase transition temperatures and the corresponding enthalpies decrease significantly and, eventually, these transitions disappear at some intermediate compositions, stabilizing wide nematic phase (N). Temperature-dependent birefringence several degrees above the N-N_{tb} phase transition shows strong director tilt fluctuations. The critical range of the fluctuations increases with the nematic range and the critical exponent is consistent with the mean field. The spontaneous polarization of RM734 decreases drastically with the addition of CB9CB mesogen. The temperature dependence of the splay elastic constant of the mixtures' high-temperature nematic (N) phase strikingly differs from that of the pristine CB9CB and RM734 mesogens. The study shows that a small inclusion of either compound has a substantial effect on the phase diagram and physical properties.

Room-temperature ferroelectric nematic liquid crystal showing a large and diverging density

The ferroelectric nematic phase (NF) is a recently discovered phase of matter in which the orientational order of the conventional nematic liquid crystal state is augmented with polar order. Atomistic simulations suggest that the polar NF phase would be denser than conventional nematics owing to contributions from polar order. Using an oscillating U-tube densitometer, we obtain detailed temperature-dependent density values for a selection of conventional liquid crystals with excellent agreement with earlier reports. Having demonstrated the validity of our method, we then record density as a function of temperature for M5, a novel room-temperature ferroelectric nematic material. We present the first experimental density data for a NF material as well as density data for a nematic that has not previously been reported. We find that the room-temperature NF material shows a large (>1.3 g cm-3) density at all temperatures studied, notably including phases without polar order. An increase in density at phase transitions is observed. The magnitude of the increase for the intermediate-to-ferroelectric nematic (NX-NF) transition is an order of magnitude smaller than the isotropic-nematic (I-N) transition. We then probe potential consequences that may result from an elevated density through measurement of the refractive indices (no and ne). The navg of M5 is compared with 5CB and polar smectic liquid crystals. We observe how the highly polar nature of the system counteracts the effects of an increase in density. With knowledge of experimental density, we are able to derive an approximation that yields the polar order parameter, 〈P1〉, from polarisation measurements. Present results may be typical of ferroelectric nematic materials, potentially guiding material development, and is especially relevant for informing ongoing studies into this emerging class of materials.

Transformation of polar nematic phases in the presence of an electric field

Only a few years have passed since the discovery of polar nematics, and now they are becoming the most actively studied liquid-crystal materials. Despite numerous breakthrough findings made recently, a theoretical systematization is still lacking. In the present paper, we take a step toward systematization. The powerful technique of molecular-statistical physics has been applied to an assembly of polar molecules influenced by electric field. Three polar nematic phases were found to be stable at various conditions: the double-splay ferroelectric nematic N_{F}^{2D} (observed in the lower-temperature range in the absence of or at low electric field), the double-splay antiferroelectric nematic N_{AF} (observed at intermediate temperature in the absence of or at low electric field), and the single-splay ferroelectric nematic N_{F}^{1D} (observed at moderate electric field at any temperature below transition into paraelectric nematic N and in the higher-temperature range (also below N) at low electric field or without it. A paradoxical transition from N_{F}^{1D} to N induced by application of higher electric field has been found and explained. A transformation of the structure of polar nematic phases at the application of electric field has also been investigated by Monte Carlo simulations and experimentally by observation of polarizing optical microscope images. In particular, it has been realized that, at planar anchoring, N_{AF} in the presence of a moderate out-of-plane electric field exhibits twofold splay modulation: antiferroelectric in the plane of the substrate and ferroelectric in the plane normal to the substrate. Several additional subtransitions related to fitting the confined geometry of the cell by the structure of polar phases were detected.

Collective and non-collective molecular dynamics in a ferroelectric nematic liquid crystal studied by broadband dielectric spectroscopy

A great deal of effort has been recently devoted to the study of dielectric relaxation processes in ferroelectric nematic liquid crystals, yet their interpretation remains unclear. In this work, we present the results of broadband dielectric spectroscopy experiments of a prototypical ferroelectric nematogen in the frequency range 10 Hz-110 MHz at different electrode separations and under the application of DC bias fields. The results evidence a complex behavior in all phases due to the magnitude of polar correlations in these systems. The observed modes have been assigned to different relaxation mechanisms based on existing theoretical frameworks.

Enantiotropic ferroelectric nematic phase in a single compound

The ferroelectric nematic phase became the centre of interest of scientists because of its unique physical properties. The uniqueness of this particular phase results in its monotropic character in all known NF materials. Here we present the very first example of a compound with an enantiotropic ferroelectric nematic phase. Compound 3JK is complementary with already well known NF materials, i.e. RM734 and DIO and is characterized by moderately high dielectric anisotropy.

Splay-induced order in systems of hard tapers

The main objective of this work is to clarify the role that taper-shaped elongated molecules, i.e., molecules with one end wider than the other, can play in stabilizing orientational order. The focus is exclusively on entropy-driven self-organization induced by purely excluded volume interactions. Drawing an analogy to RM734 (4-[(4-nitrophenoxy)carbonyl]phenyl-2,4-dimethoxybenzoate), which is known to stabilize ferroelectric nematic (N_{F}) and nematic splay (N_{S}) phases, and assuming that molecular biaxiality is of secondary importance, we consider monodisperse systems composed of hard molecules. Each molecule is modeled using six collinear tangent spheres with linearly decreasing diameters. Through hard-particle, constant-pressure Monte Carlo simulations, we study the emergent phases as functions of the ratio between the smallest and largest diameters of the spheres (denoted as d) and the packing fraction (η). To analyze global and local molecular orderings, we examine molecular configurations in terms of nematic, smectic, and hexatic order parameters. Additionally, we investigate the radial pair distribution function, polarization correlation function, and the histogram of angles between molecular axes. The last characteristic is utilized to quantify local splay. The findings reveal that splay-induced deformations drive unusual long-range orientational order at relatively high packing fractions (η>0.5), corresponding to crystalline phases. When η<0.5, only short-range order is affected, and in addition to the isotropic liquid, only the standard nematic and smectic-A liquid crystalline phases are stabilized. However, for η>0.5, apart from the ordinary nonpolar hexagonal crystal, three additional frustrated crystalline polar blue phases with long-range splay modulation are observed: antiferroelectric splay crystal (Cr_{S}P_{A}), antiferroelectric double-splay crystal (Cr_{DS}P_{A}), and ferroelectric double-splay crystal (Cr_{DS}P_{F}). Finally, we employ Onsager-Parsons-Lee local density functional theory to investigate whether any sterically induced (anti)ferroelectric nematic or smectic-A type of ordering is possible for our system, at least in a metastable regime.

Second harmonic generation in anisotropic stratified media: a generalization of the Berreman method and its application to photonic materials

We have developed a numerical method for calculating the second-harmonic generation (SHG) generated by an anisotropic material whose optical properties present an arbitrary modulation in one dimension. The method is based on the Berreman 4 × 4 matrix formalism, which is generalized to include nonlinear optical phenomena. It can be used under oblique incidences of the input beam, and is valid even when the SHG frequency is close to photonic bands, where the usual slowly-varying-amplitude approximation breaks down. As an example of application, we have studied the SHG performance of ferroelectric and helielectric fluids. The obtained results indicate that the present procedure may contribute to improving the structural design and enlarging the variety of nonlinear optical materials for application in optical devices.

Molecular Shape, Electronic Factors, and the Ferroelectric Nematic Phase: Investigating the Impact of Structural Modifications

The synthesis and characterisation of two series of low molar mass mesogens, the (4-nitrophenyl) 2-alkoxy-4-(4-methoxybenzoyl)oxybenzoates (NT3.m) and the (3-fluoro-4-nitrophenyl) 2-alkoxy-4-(4-methoxybenzoyl)oxybenzoates (NT3F.m), are reported in order to investigate the effect of changing the position of a lateral alkoxy chain from the methoxy-substituted terminal ring to the central phenyl ring in these two series of materials based on RM734. All members of the NT3.m series exhibited a conventional nematic phase, N, which preceded the ferroelectric nematic phase, NF , whereas all the members of the NT3F.m series exhibited direct NF -I transitions except for NT3F.1 which also exhibited an N phase. These materials cannot be described as wedge-shaped, yet their values of the ferroelectric nematic-nematic transition temperature, TN F N ${{_{{\rm N}{_{{\rm F}}}{\rm N}}}}$ , exceed those of the corresponding materials with the lateral alkoxy chain located on the methoxy-substituted terminal ring. In part, this may be attributed to the effect that changing the position of the lateral alkoxy chain has on the electronic properties of these materials, specifically on the electron density associated with the methoxy-substituted terminal aromatic ring. The value of TNI decreased with the addition of a fluorine atom ortho to the nitro group in NT3F.1, however, the opposite behaviour was found when the transition temperatures of the NF phase were compared which are higher for the NT3F.m series. This may reflect a change in the polarity and polarizability of the NT3F.m series compared to the NT3.m series. Therefore, it is suggested that, rather than simply promoting a tapered shape, the role of the lateral chain in inhibiting anti-parallel associations and its effect on the electronic properties of the molecules are the key factors in driving the formation of the NF phase.

Fluorination Enables Dual Ferroelectricity in Both Solid- and Liquid-Crystal Phases

Ferroelectric materials are a special type of polar substances, including solids or liquid crystals. However, obtaining a material to be ferroelectric in both its solid crystal (SC) and liquid crystal (LC) phases is a great challenge. Moreover, although cholesteric LCs inherently possess the advantage of high fluidity, their ferroelectricity remains unknown. Here, through the reasonable H/F substitution on the fourth position of the phenyl group of the parent nonferroelectric dihydrocholesteryl benzoate, we designed ferroelectric dihydrocholesteryl 4-fluorobenzoate (4-F-BDC), which shows ferroelectricity in both SC and cholesteric LC phases. The fluorination induces a lower symmetric polar P1 space group and a new solid-to-solid phase transition in 4-F-BDC. Beneficial from fluorination, the SC and cholesteric LC phases of 4-F-BDC show clear ferroelectricity, as confirmed by well-shaped polarization-voltage hysteresis loops. The dual ferroelectricity in both SC and cholesteric LC phases of a single material was rarely found. This work offers a viable case for the exploration of the interplay between ferroelectric SC and LC phases and provides an efficient approach for designing ferroelectrics with dual ferroelectricity and cholesteric ferroelectric liquid crystals.

Theoretical models of modulated nematic phases

Novel modulated nematic phases, such as twist-bend nematics, splay-bend nematics and splay nematics, are an important subject of research in the field of liquid crystals. In this article fundamental information about the discovery, structure and properties of these phases is presented. Various theoretical models of elastic properties are compared, especially the proposed formulae for the free energy density of modulated nematic phases and the conditions for their stability. The emphasis is put on the variety of material parameters and variables in the mathematical description of the structures. The elastic models are classified according to a few criteria. Flexopolarisation is indicated as a main phenomenon responsible for the formation of modulated nematic phases. The elastic models are used for analysing the deformations of the twist-bend nematic structure in external fields. Dielectric, flexoelectric, ferroelectric and magnetic effects are considered. Two types of distortions are distinguished: microscopic (connected with the deformation of the director distribution) and macroscopic (related to the change of the optic axis direction). This review can be a starting point for further studies, for example computer simulations of modulated phases and design of liquid crystalline devices.

Alignment properties of a ferroelectric nematic liquid crystal on the rubbed substrates

The orientation characteristics of FNLC-919, a new material with a ferroelectric nematic phase at room temperature, were investigated. Its alignment characteristics varied greatly depending on the relative rubbing direction on both substrates of a liquid crystal cell. In a cell where the two substrates were rubbed in the same direction, they were arranged homogeneously along the rubbing direction without domains or defects in the ferroelectric nematic phase. In a cell where the two substrates were rubbed in the anti-parallel direction, the two domains were twisted in the opposite direction. We quantitatively obtained the twisted direction and angle by matching the experimental data and calculation results using Jones matrix calculations. From the electro-optical experiment, it was confirmed that the polarization direction was opposite to the rubbing direction. In addition, the wavelength and temperature dependence of birefringence was measured for FNLC-919. In a cell where the rubbing direction between two substrates was 90°, two domains of opposite directions were observed in the nematic phase. When it becomes a ferroelectric nematic phase on cooling, the twist is determined to be only in one direction. The twist direction and angle were quantitatively obtained in the nematic and ferroelectric nematic phases. It was twisted more in the ferroelectric nematic phase than in the nematic phase.

Spontaneous mirror symmetry breaking and chiral segregation in the achiral ferronematic compound DIO

An achiral compound, DIO, known to exhibit three nematic phases namely N, N_X and N_F, is studied by polarizing microscopy and electro-optics for different surface conditions in confinement. The high temperature N phase assigned initially as a conventional nematic phase, shows two additional unusual features: the optical activity and the linear electro-optic response related to the polar nature of this phase. An appearance of chiral domains is explained by the spontaneous symmetry breaking arising from the saddle-splay elasticity and followed by the formation of helical domains of the opposite chirality. This is the first example of helical segregation observed in calamitic non-chiral molecules in the nematic phase. As reported previously, the ferronematic N_F shows strong polar azimuthal surface interaction energy which stabilizes a homogeneous structure in planar aligned LC cells rubbed parallel and exhibits a twisted structure in cells with antiparallel buffing. The transmission spectra are simulated using Berreman's 4 × 4 matrix method. The observed agreement between the experimental and the simulated spectra quantitatively confirms the presence of twisted structures in antiparallel rubbed cells.

The smectic ZA phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic

We have structurally characterized the liquid crystal (LC) phase that can appear as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-y-old void in the taxonomy of smectic LCs and which we term the "smectic ZA," is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer with a 180 Å period. A Landau free energy, originally derived from the Ising model of ferromagnetic ordering of spins in the presence of dipole-dipole interactions, and applied to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-SmZA-ferroelectric nematic phase sequence.

Towards Nematic Phases in Ionic Liquid Crystals - A Simulation Study

Ionic liquid crystals (ILCs) are soft matter materials with broad liquid crystalline phases and intrinsic electric conductivity. They typically consist of a rod-shaped mesogenic ion and a smaller spherical counter-ion. Their mesomorphic properties can be easily tuned by exchanging the counter ion. ILCs show a strong tendency to form smectic A phases due to the segregation of ionic and the non-ionic molecular segments. Nematic phases are therefore extremely rare in ILCs and the question of why nematic phases are so exceptional in existing ILCs, and how nematic ILCs might be obtained in the future is of vital interest for both the fundamental understanding and the potential applications of ILCs. Here, we present the result of a simulation study, which highlights the crucial role of the location of the ionic charge on the rod-like mesogenic ions in the phase behaviour of ILCs. We find that shifting the charge from the ends towards the centre of the mesogenic ion destabilizes the liquid crystalline state and induces a change from smectic A to nematic phases.

Spontaneous electric-polarization topology in confined ferroelectric nematics

Topological textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first liquid-state ferroelectric that would carry many possibilities of spatially-distributed polarization fields. Contrary to traditional magnetic or crystalline systems, anisotropic liquid crystal interactions can compete with the polarization counterparts, thereby setting a challenge in understating their interplays and the resultant topologies. Here, we discover chiral polarization meron-like structures, which appear during the emergence and growth of quasi-2D ferroelectric nematic domains. The chirality can emerge spontaneously in polar textures and can be additionally biased by introducing chiral dopants. Such micrometre-scale polarization textures are the modified electric variants of the magnetic merons. Both experimental and an extended mean-field modelling reveal that the polarization strength plays a dedicated role in determining polarization topology, providing a guide for exploring diverse polar textures in strongly-polarized liquid crystals.

Polarisation-driven magneto-optical and nonlinear-optical behaviour of a room-temperature ferroelectric nematic phase

Nematics with a broken polar symmetry are one of the fascinating recent discoveries in the field of soft matter. High spontaneous polarisation and the fluidity of the ferroelectric nematic N_F phase make such materials attractive for future applications and interesting for fundamental research. Here, we explore the polar and mechanical properties of a room-temperature ferroelectric nematic and its behaviour in a magnetic field. We show that N_F is much less susceptible to the splay deformation than to the twist. The strong splay rigidity can be attributed to the electrostatic self-interaction of polarisation avoiding the polarisation splay.

Emerging Ferroelectric Uniaxial Lamellar (Smectic AF) Fluids for Bistable In-Plane Polarization Memory

The emerging matter category of liquid-matter ferroelectrics, i.e., ferroelectric nematics, demonstrates an unprecedented combination of fluidity and spontaneous polarization. However, unlike traditional ferroelectrics, the field-switched polarization at zero-field cannot be conserved, so the memory effect remains challenging. Here we report another new type of ferroelectric liquid crystal state, dubbed the ferroelectric smectic A phase, where the polarization is longitudinally coupled to the smectic quasi-layer order. With higher packing density, the phase exhibits higher values of refractive anisotropy and spontaneous polarization compared to the ferroelectric nematics. A delicate balance between the liquid crystal elasticity and flow viscosity enables both the switching and memory of the polarization field, thus opening the door toward realizing liquid-matter ferroelectric memory devices.

The effect of a lateral alkyloxy chain on the ferroelectric nematic phase

The synthesis and characterisation of two series of low molar mass liquid crystals, the 4-[(4-nitrophenoxy)carbonyl]phenyl 2-alkoxy-4-methoxybenzoates (series 5-m) and the 4-[(3-fluoro-4-nitrophenoxy)carbonyl]phenyl 2-alkoxy-4-methoxybenzoates (series 6-m) are reported in order to explore the effects of a lateral alkyloxy chain on the formation and stability of the recently discovered ferroelectric nematic phase. In both series m, the number of carbon atoms in the lateral chain, is varied from one to nine. The two series differ by the addition of a fluorine substituent in the 6-m series. 5-1 is the extensively studied ferroelectric nematogen RM734. All the members of the 5-m series exhibited both a conventional nematic, N, and ferroelectric nematic, N_F, phase, whereas all the members of the 6-m series exhibit a direct N_F-I transition with the exception of 6-1 that also exhibits a N phase. The replacement of a hydrogen atom by a fluorine atom reduces the nematic-isotropic transition temperature, T _NI, whereas the ferroelectric nematic-nematic, or isotropic, transition temperature, T _NFN/I, increases. This is interpreted in terms of the reduced structural anisotropy associated with the larger fluorine atom whereas the increase in the stability of the N_F phase reflects changes in polarity and polarizability. The dependence of T _NI and T _NFN/I on m in both series is similar, and these initially decrease on increasing m but converge to limiting values on further increasing m. This suggests that the lateral alkyloxy chain may adopt conformations in which it lies along the major axis of the mesogenic unit.

Fluid Layered Ferroelectrics with Global C∞v Symmetry

Ferroelectricity in fluid materials, which allows free rotation of molecules, is an unusual phenomenon raising cutting-edge questions in science. Conventional ferroelectric liquid crystals have been found in phases with low symmetry that permit the presence of spontaneous polarization. Recently, the discovery of ferroelectricity with high symmetry in the nematic phase has attracted considerable attention. However, the physical mechanism and molecular origin of ferroelectricity are poorly understood and a large domain of macroscopically oriented spontaneous polarization is difficult to fabricate in the ferroelectric nematic phase. This study reports new fluid layered ferroelectrics with the C_∞v symmetry in which nearly complete orientation of the spontaneous polarization remains stable under zero electric field without any orientation treatment. These ferroelectrics are obtained by simplifying the molecular structure of a compound with a known ferroelectric nematic phase, although the simplification reduced the dipole moment. The results provide useful insights into the mechanism of ferroelectricity due to dipole-dipole interactions in molecular assemblies. The new ferroelectric materials are promising for a wide range of applications as soft ferroelectrics.

Ferroelectric nematic liquid-crystalline phases

Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these phases, guided by their fundamental and applicative interest. In this Perspective, we give an overview of this emerging field by linking history and theoretical predictions to a general outlook of the development and properties of the materials exhibiting ferroelectric nematic phases. We will highlight the most relevant observations to date, e.g., giant dielectric permittivity values, polarization values an order of magnitude larger than in classical ferroelectric liquid crystals, and nonlinear optical coefficients comparable with several ferroelectric solid materials. Key observations of anchoring and electro-optic behavior will also be examined. The collected contributions lead to a final discussion on open challenges in materials development, theoretical description, experimental explorations, and possible applications of the ferroelectric phases.