Magneto-optic dynamics in a ferromagnetic nematic liquid crystal

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.

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.

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.

A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent

We present the macroscopic dynamics of polar nematic liquid crystals in a two-fluid context. We investigate the case of a nonchiral as well as of a chiral solvent. In addition, we analyze how the incorporation of a strain field for polar nematic gels and elastomers in a solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the polar subsystem and the solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from the other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in polar nematics to heat currents and in polar cholesterics to temporal changes of the polarization. In polar cholesterics, shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in polar nematic gels uniaxial stresses or strains generate temporal variations of the velocity difference.

Tailored nematic and magnetization profiles on two-dimensional polygons

We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We study the stable states in terms of stable critical points of an appropriately defined free energy, with a nemato-magnetic coupling energy. We numerically study the interplay between the shape of the regular polygon, the size of the polygon, and the strength of the nemato-magnetic coupling for the multistability of this prototype system. Our notable results include (1) the coexistence of stable states with domain walls and stable interior and boundary defects, (2) the suppression of multistability for positive nemato-magnetic coupling, and (3) the enhancement of multistability for negative nemato-magnetic coupling.

Domain growth in ferronematics: slaved coarsening, emergent morphologies and growth laws

Ferronematics (FNs) are suspensions of magnetic nanoparticles in nematic liquid crystals (NLCs). They have attracted much experimental attention, and are of great interest both scientifically and technologically. There are very few theoretical studies of FNs, even in equilibrium. In this paper, we study the non-equilibrium phenomenon of domain growth after a thermal quench (or coarsening) in this coupled system. Our modeling is based on coupled time-dependent Ginzburg-Landau (TDGL) equations for two order parameters: the LC tensor order parameter Q, and the magnetization M. We consider both shallow and deep quenches from a high-temperature disordered phase. The system coarsens by the collision and annihilation of topological defects. We focus on slaved coarsening, where a disordered Q (or M) field is driven to coarsen by an ordered M (or Q) field. We present detailed results for the morphologies and growth laws, which exhibit unusual features purely due to the magneto-nematic coupling. To the best of our knowledge, this is the first study of non-equilibrium phenomena in FNs.

Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers

We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Magnetic hybrid materials in liquid crystals

The integration of nanoparticles with magnetic, ferroelectric or semiconducting properties into liquid crystals (LCs) has attracted great interest both for fundamental investigations and for technological applications. Here, an overview of hybrid materials based on magnetic nanoparticles (MNPs) and thermotropic LCs is given. After a general introduction to thermotropic LCs and LC-MNP hybrid materials, various preparation methods established by us are presented. The synthesis of shape-(an)isotropic MNPs, their functionalization by tailored (pro)mesogenic ligands with linear or dendritic structures and their integration into LC hosts are discussed. The characterization of the MNPs, (pro)mesogenic ligands and resulting MNP-LC hybrid materials is described to show the influence of MNP functionalization on the MNP-LC interactions including aspects such as colloidal stability and structuring in the LC host. Overall, we show that the physical properties of the hybrid material are significantly influenced not only by the MNPs (i.e., their size, shape and composition) but also by their surface properties (i.e., the structure of the (pro)mesogenic ligands).

Magnetically Tunable Liquid Crystal-Based Optical Diffraction Gratings

We present a theoretical analysis of optical diffractive properties of magnetically tunable optical transmission gratings composed of periodically assembled layers of a polymer and a ferromagnetic liquid crystal (LC). The orientational structure of the LC layers as a function of an applied magnetic field is calculated by minimization of the Landau-de Gennes free energy for ferromagnetic LCs, which is performed numerically and also analytically by using the one-constant approximation and the approximations of the high and the low magnetic fields. Optical diffractive properties of the associated diffraction structure are calculated numerically in the framework of rigorous coupled-wave analysis (RCWA). The presented methodology provides a basis for designing new types of diffractive optical element based on ferromagnetic LCs and simulating their operation governed by the in-plane magnetic field.

Macroscopic two-fluid effects in magnetorheological fluids

We investigate macroscopic two-fluid effects in magnetorheological fluids generalizing a one-fluid model studied before. In the bulk of the paper we use a model in which the carrier fluid, with density ρ_{1}, moves with velocity v_{1}, while the magnetic component (density ρ_{2}) and, therefore, the magnetization and the magnetic-field-induced relaxing strain field move with velocity v_{2}. In the framework of macroscopic dynamics we find, in particular, reversible dynamic and dissipative cross-coupling terms between the magnetization and the velocity difference. Experiments to detect some of these cross-coupling terms are suggested. We also compare the results of the two-fluid model presented here with two-fluid models available for electrorheological fluids. In two appendices we discuss the simplifying assumptions made to arrive at the model used in this paper and we also outline how to detect potential deviations from this model.

Magnetically controllable random laser in ferromagnetic nematic liquid crystals

This paper first reports random laser action in dye-doped ferromagnetic nematic liquid crystals, which act as a randomly distributed cavity. The random laser intensity of the ferromagnetic nematic liquid crystals can be controlled by a weak magnetic field (∼1 mT). Moreover, the magnetic switching of random laser is attributed to the direction and polarization dependent emission of light in the ferromagnetic nematic liquid crystals in an external magnetic field.

Molecular theory of a ferromagnetic nematic liquid crystal

We employ a version of classical density functional theory to study the phase behavior of a simple model liquid crystal in an external field. The uniaxially symmetric molecules have a spherically symmetric core with superimposed orientation-dependent attractions. The interaction between the cores consists of a hard-sphere repulsion plus an isotropic square-well attraction. The anisotropic part of the interaction potential allows for the formation of a uniaxially symmetric nematic phase. The orientation of the molecules couples to an external polar field. The external field is capable of rotating the nematic director n[over ̂] in the x-z plane. The field is also capable of changing the topology of the phase diagram in that it suppresses the phase coexistence between an isotropic liquid and a nematic phase observed in the absence of the field. We study the transition from an unpolar to a polar nematic phase in terms of the orientation-distribution function (odf), nematic and polar order parameters, and components of n[over ̂]. If represented suitably the odf allows us to study orientational changes during the switching process between nonpolar and polar nematic phases. We also give a simple argument that explains why nematic order is lost whereas polar order persists up to the gas-liquid critical point along the coexistence curve. We also discuss the relevance of our theory for future experimental studies.

Study of optical rotation generated by the twisted nematic liquid crystal film: based on circular birefringence effect

The optical behavior of twisted nematic liquid crystals (TNLCs) is revealed through an angular scanning technique. Experimental results show that the optical rotation and degree of polarization of transmitted light are dependent on the polarization direction of incident light. The optical rotation is reciprocal, i.e., the polarization direction of incident and transmitted light can reciprocate when optical rotation is π/2. In some cases, the optical rotation is zero. The orientation of alignment layers in the TN cell can be determined from the behavior of optical rotation, which agrees with the measurement by an atomic force microscope. The experimental results are explained with the model of circularly polarized light based on the circular birefringence effect. Linearly polarized incident light is the superposition of right- and left-handed circularly polarized light. The propagation velocity of circularly polarized light in the LC is relevant to the polarization direction of incident light, so that the refractive indices of left- and right-handed circularly polarized light, n_- and n₊, or circular birefringence Δn(=n_--n₊) are not constants. As a result, when a linearly polarized light with the wavelength λ propagates through a TN cell with the cell gap l, the polarization direction of transmitted light is rotated to an angle Δθ. The optical rotation Δθ(=π(n_--n₊)l/λ) is dependent on the polarization direction of incident light, whereas the averaged refractive index ⟨n⟩(=(n_-+n₊)/2) can be independent of that. The incident light is partially linearly polarized light in our experiments, so that the degree of polarization of transmitted light varies with the polarization direction of incident light because the optical rotatory rates for the primary and secondary light beams are different.

Manipulation enhancement of terahertz liquid crystal phase shifter magnetically induced by ferromagnetic nanoparticles

Ferromagnetic liquid crystals (FLCs), the suspensions of magnetic nanoparticles dispersed at different concentrations in liquid crystals (LCs), and their special magnetically induced birefringence characteristics have been investigated in the terahertz regime, mainly focusing on the interaction between magnetic cluster chains and LC molecules. We experimentally demonstrated the surface anchoring effect of the magnetic cluster chains on LC molecules in a mm-thick LC cell under an extremely weak external magnetic field (EMF), leading to a uniform anchoring arrangement of the LC molecules over the entire LC cell. Unlike pure 5CB LCs, the phase shift range of the FLCs at 1.45 THz up to π (no to ne or ne to no) can be achieved over the whole tunable range by simply changing the magnitude of the EMF without changing its direction, and the optical axis of LC molecules can be controlled to rotate by 90°, thereby realizing a tunable THz wave plate. This work provides a new way in the development of THz magneto-optic devices and phase devices.

A ferronematic slab in external magnetic fields

The behavior of a uniformly magnetized ferronematic slab is investigated numerically in a situation in which an external magnetic field is applied parallel and antiparallel, respectively, to its initial magnetization direction. The employed numerical method allows one to determine hysteresis curves from which a critical magnetic field strength (i.e., the one at which the ferronematic sample becomes distorted) as a function of the system parameters can be inferred. Two possible mechanisms of switching the magnetization by applying a magnetic field in the antiparallel direction are observed and characterized in terms of the coupling constant between the magnetization and the nematic director and in terms of the coupling strength of the nematic liquid crystal and the walls of the slab. Suitably prepared walls allow one to combine both switching mechanisms in one setup, such that one can construct a cell, the magnetization of which can be reversibly switched off.

Director reorientation dynamics of ferromagnetic nematic liquid crystals

Successful realization of ferromagnetic nematic liquid crystals has opened up the possibility to experimentally study a completely new set of fundamental physical phenomena. In this contribution we present a detailed investigation of some aspects of the static response and the complex dynamics of ferromagnetic liquid crystals under the application of an external magnetic field. Experimental results are then compared with a macroscopic model. Dynamics of the director were measured by optical methods and analyzed in terms of a theoretical macroscopic model. A dissipative cross-coupling coefficient describing the dynamic coupling between the two system order parameters, the magnetization and the nematic director, is needed to explain the results. In this contribution we examine the dependency of this coefficient on material parameters and the saturation magnetization and the liquid crystal host. Despite the complexity of the system, the theoretical description allows for a proper interpretation of the results and is connected to several microscopic aspects of the colloidal suspension.

Effects of flow on the dynamics of a ferromagnetic nematic liquid crystal

We investigate the effects of flow on the dynamics of ferromagnetic nematic liquid crystals. As a model, we study the coupled dynamics of the magnetization, M, the director field, n, associated with the liquid crystalline orientational order, and the velocity field, v. We evaluate how simple shear flow in a ferromagnetic nematic is modified in the presence of small external magnetic fields, and we make experimentally testable predictions for the resulting effective shear viscosity: an increase by a factor of 2 in a magnetic field of about 20 mT. Flow alignment, a characteristic feature of classical uniaxial nematic liquid crystals, is analyzed for ferromagnetic nematics for the two cases of magnetization in or perpendicular to the shear plane. In the former case, we find that small in-plane magnetic fields are sufficient to suppress tumbling and thus that the boundary between flow alignment and tumbling can be controlled easily. In the latter case, we furthermore find a possibility of flow alignment in a regime for which one obtains tumbling for the pure nematic component. We derive the analogs of the three Miesowicz viscosities well-known from usual nematic liquid crystals, corresponding to nine different configurations. Combinations of these can be used to determine several dynamic coefficients experimentally.