Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

Abstract

Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed "preimages") of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. The field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.

Two-dimensional skyrmion bags in liquid crystals and ferromagnets

“…1 in a 2D plane is minimised until an energy minimum and a stable configuration is found. Details of numerical modeling are described elsewhere [31]. We follow, for the unit magnetisation n(x) = M (x)/|M (x)|, the magnetic skyrmion model of [23] using the energy density Eq.…”

Nature‐Inspired Emerging Chiral Liquid Crystal Nanostructures: From Molecular Self‐Assembly to DNA Mesophase and Nanocolloids

“…Interestingly, they found that the interaction of two chiral colloids depends on whether they are like‐handed or oppositely handed, and the sign of the interaction was dependent on the direction in which colloids approach relative to the far‐field orientation of LCs. More recently, they further demonstrated that the interactions of the colloidal nanoparticles could be electrically and magnetically modulated by dispersing chiral ferromagnetic nanoparticle into achiral LCs . It is worth noting that liquid crystalline BPs can function as 3D soft templates, in which the intrinsic 3D disclination networks could direct the promising self‐assembly of colloidal particles or polymers into 3D functional nanostructures .…”

Three-dimensional crystals of adaptive knots

“…For a given linear polarization of the beam, each 3PEF-PM image yielded a preimage of a single point on ] 2 /ℤ 2 or preimages of a pair of diametrically opposite points on ] 2 for vector ! (#) field, due to the nonpolar response of molecules in LC to the excitation (23,(35)(36)(37). For a vectorized director field (i.e., a director field smoothly decorated by vectors), the preimages can be assigned by comparing the experimental preimages to preimages obtained in numerical modeling.…”