Energy surface and minimum energy paths for Fréedericksz transitions in bistable cholesteric liquid crystals

Ivanov, Aleksei V.; Bessarab, Pavel F.; Aksenova, E. V.; Romanov, V. P.; Uzdin, V. M.

doi:10.1103/physreve.93.042708

Cited by 7 publications

(5 citation statements)

References 33 publications

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“…In Fig. 2 (a) and (b), we plot the interaction energy as a function of the distance r between the centers of horizontal and vertical skyrmions calculated for different values of the applied magnetic field using minimal energy path method 38,39 (see the Supplemental Material on different methods of interaction energy calculation). Such Lennard-Jones type potential profiles show that the attractive interskyrmion coupling is characterized by a low potential barrier and a rather deep potential well establishing the equilibrium separation of skyrmions in the bound biskyrmion state.…”

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confidence: 99%

Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

et al. 2019

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We report the discovery and direct visualization of skyrmion clusters with mutually-orthogonal orientations of constituent isolated skyrmions in chiral liquid crystals and ferromagnets. We show that the nascent conical state underlies attracting inter-skyrmion potential, whereas an encompassing homogeneous state leads to the repulsive skyrmion-skyrmion interaction. The crossover between different regimes of skyrmion interaction could be identified upon changing layer thickness and/or the surface anchoring. We develop a phenomenological theory describing two types of skyrmions and the underlying mechanisms of their interaction. We show that isolated horizontal skyrmions with the same polarity may approach a vertical isolated skyrmion from both sides and thus constitute two energetically-different configurations which are also observed experimentally. In an extreme regime of mutual attraction, the skyrmions wind around each other forming compact superstructures with undulations. We also indicate that our numerical simulations on skyrmion clusters are valid in a parameter range corresponding to the A-phase region of cubic helimagnets.

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confidence: 99%

Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

et al. 2019

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“…Leaving aside technical details about the numerical procedure described in Refs. [40,41], we just briefly comment on the geodesic nudged elastic band (GNEB) method to find MEPs between local minima on the curved manifolds [34]. This approach involves taking an initial guess of a path between the two minima of the free energy surface and systematically bringing that to the nearest MEP.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In Ref. [40,41] the approach based on MEPs was applied to explore field-induced distortions of the free energy landscape in CLC cells subjected to external (magnetic or electric) fields. These distortions are known to lead to a variety of field-induced orientational effects such as the Fréedericksz and unwinding transitions.…”

Section: Introductionmentioning

confidence: 99%

Hysteresis and Freedericksz thresholds for twisted states in chiral nematic liquid crystals: Minimum-energy path approach

Tenishchev¹,

Tambovtcev²,

Kiselev³

et al. 2020

Preprint

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We study minimum-energy pathways (MEPs) between the branches of metastable helical structures in chiral nematic liquid crystals (CNLCs) subjected to the electric field applied across the cell. By performing stability analysis we have found that, for the branches with non-vanishing half-turn number, the threshold (critical) voltage of the Fréedericksz transition is an increasing function of the free twisting wave number. The curves for the threshold voltage depend on the elastic anisotropy and determine the zero-field critical free twisting number where the director out-of-plane fluctuations destabilize the CNLC helix. For each MEP passing through a first order saddle point we have computed the energy barrier as the energy difference between the saddle-point and the initial structures at different values of the applied field. In our calculations, where the initial approximation for a MEP at the next step was determined by the MEP obtained at the previous step, the electric field dependence of the energy barrier is found to exhibit the hysteresis. This is the hysteresis of electrically driven transition of the saddle-point configuration between the planar and the tilted structures involving out-of-plane director deformations. It turned out that, by contrast to the second-order Fréedericksz transition, this transition is first order and we have studied how it depends on the zenithal anchoring energy strength.

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“…As in Ref. [56], we have used the geodesic nudged elastic band (GNEB) method to find MEPs between local minima on the curved manifolds [55]. This approach involves taking an initial guess of a path between the two minima and systematically bringing that to the nearest MEP.…”

Section: A Minimum Energy Pathsmentioning

confidence: 99%

“…The purpose of this paper is to explore global properties of the free energy landscape related to transitions between CLC states which are local minima (minimizers) of the free energy. The free energy pathways connecting pairs of metastable helical states appear as basic elements of a natural mathematical language dealing with the relevant geometry of the landscape viewed as a multidimensional free energy surface [54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals

Tenishchev¹,

Kiselev²,

Ivanov³

et al. 2019

Phys. Rev. E

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We apply the minimum energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures; and (b) the anchoring breaking approximation that involves the structures with profound out-of-plane director deviations. It is shown that, at sufficiently low voltages, the unwinding transition is solely governed by the director slippage mechanism with the planar saddle point structures. When the applied voltage exceeds its critical value below the threshold of the Fréedericksz transition, the additional scenario through the anchoring breaking transitions is found to come into play. For these transitions, the saddle point structure is characterized by out-of-plane deformations localized near the bounding surface. The energy barriers for different paths of transitions are computed as a function of the voltage and the anchoring energy strengths. * tenischev.

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Energy surface and minimum energy paths for Fréedericksz transitions in bistable cholesteric liquid crystals

Cited by 7 publications

References 33 publications

Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

Hysteresis and Freedericksz thresholds for twisted states in chiral nematic liquid crystals: Minimum-energy path approach

Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals

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