Abstract:International audienceGrowth of ferroelectric nanotori is reported and first-principles-based effective Hamiltonian simulations were performed on these new objects. They could reproduce the nonpolar (phase I) and homogeneously toroidized (phase II) states of an isolated nanotorus. Computation of an axial hypertoroidal moment leads to numerical observation of two new phases: (i) a homogeneously hypertoroidized one (phase III) that can be switched by a homogeneous electric field and (ii) another one with strikin… Show more
“…Thus, the polarizations form a helical polarization configuration in nature that is driven by the unique chirality of the nanospring shape. The characteristics of the continuous flow are consistent with those observed in preceding studies of ferroelectric nanowires 27 , nanorings 28 , and nano-metamaterials 21 , where the polarization pattern is significantly governed by the outer shape of the nanostructure. In addition, a recent experiment has observed a similar global magnetization helix in a magnetic nanospiral 29 .…”
Topological objects of nontrivial spin or dipolar field textures, such as skyrmions, merons, and vortices, interacting with applied external fields in ferroic materials are of great scientific interest as an intriguing playground of unique physical phenomena and novel technological paradigms. The quest for new topological configurations of such swirling field textures has primarily been done for magnets with Dzyaloshinskii-Moriya interactions, while the absence of such intrinsic chiral interactions among electric dipoles left ferroelectrics aside in this quest. Here, we demonstrate that a helical polarization coiled into another helix, namely a polar superhelix, can be extrinsically stabilized in ferroelectric nanosprings. The interplay between dipolar interactions confined in the chiral geometry and the complex strain field of mixed bending and twisting induces the superhelical configuration of electric polarization. The geometrical structure of the polar superhelix gives rise to electric chiralities at two different length scales and the coexistence of three order parameters, i.e., polarization, toroidization, and hypertoroidization, both of which can be manipulated by homogeneous electric and/or mechanical fields. Our work therefore provides a new geometrical configuration of swirling dipolar fields, which offers the possibility of multiple order-parameters, and electromechanically controllable dipolar chiralities and associated electro-optical responses.
“…Thus, the polarizations form a helical polarization configuration in nature that is driven by the unique chirality of the nanospring shape. The characteristics of the continuous flow are consistent with those observed in preceding studies of ferroelectric nanowires 27 , nanorings 28 , and nano-metamaterials 21 , where the polarization pattern is significantly governed by the outer shape of the nanostructure. In addition, a recent experiment has observed a similar global magnetization helix in a magnetic nanospiral 29 .…”
Topological objects of nontrivial spin or dipolar field textures, such as skyrmions, merons, and vortices, interacting with applied external fields in ferroic materials are of great scientific interest as an intriguing playground of unique physical phenomena and novel technological paradigms. The quest for new topological configurations of such swirling field textures has primarily been done for magnets with Dzyaloshinskii-Moriya interactions, while the absence of such intrinsic chiral interactions among electric dipoles left ferroelectrics aside in this quest. Here, we demonstrate that a helical polarization coiled into another helix, namely a polar superhelix, can be extrinsically stabilized in ferroelectric nanosprings. The interplay between dipolar interactions confined in the chiral geometry and the complex strain field of mixed bending and twisting induces the superhelical configuration of electric polarization. The geometrical structure of the polar superhelix gives rise to electric chiralities at two different length scales and the coexistence of three order parameters, i.e., polarization, toroidization, and hypertoroidization, both of which can be manipulated by homogeneous electric and/or mechanical fields. Our work therefore provides a new geometrical configuration of swirling dipolar fields, which offers the possibility of multiple order-parameters, and electromechanically controllable dipolar chiralities and associated electro-optical responses.
“…(PbTiO 3 ) n /(SrTiO 3 ) n heterostructures provide an intriguing opportunity to test for this possibility, since researchers have already demonstrated the formation of emergent polar topologies, such as chiral vortices 1,3 , ferroelectric chiral and achiral domain walls 10,11 or ferroelectric bubble domains 12 . Theoretical predictions suggest that there is considerable potential for obtaining bubble-shaped nanodomains 13 and skyrmion-like topological structures in ferroelectric materials driven by the interplay of elastic, electrostatic and gradient energies [14][15][16][17] . By recognizing the crucial role of lattice-mismatch strain, we demonstrate the formation of chiral, polar-skyrmion bubbles with a skyrmion number of +1 using a combination of real-space imaging, second-principles ab initio calculations and phase-field modelling.…”
“…A ring of static or dynamic magnetic moments results in the excitation of the polar toroidal moment or a magnetic toroidal moment ( Spaldin et al., 2008 ; Zimmermann et al., 2014 ; Fedotov et al., 2013 ; Fan et al., 2013 ). In contrast, axial toroidal moments are formed by a ring of electric dipolar moments ( Dubovik et al., 1986 ; Thorner et al., 2014 ). Figure 1 The formation of electric, magnetic, and toroidal dipolar moments (A) Electric dipolar moment is formed because of charge separation.…”
Summary
The vigorous research on low-loss photonic devices has brought significance to a new kind of electromagnetic excitation, known as toroidal resonances. Toroidal excitation, possessing high-quality factor and narrow linewidth of the resonances, has found profound applications in metamaterial (MM) devices. By the coupling of toroidal dipolar resonance to traditional electric/magnetic resonances, a metamaterial analogue of electromagnetically induced transparency effect (EIT) has been developed. Toroidal induced EIT has demonstrated intriguing properties including steep linear dispersion in transparency windows, often leading to elevated group refractive index in the material. This review summarizes the brief history and properties of the toroidal resonance, its identification in metamaterials, and their applications. Further, numerous theoretical and experimental demonstrations of single and multiband EIT effects in toroidal-dipole-based metamaterials and its applications are discussed. The study of toroidal-based EIT has numerous potential applications in the development of biomolecular sensing, slow light systems, switches, and refractive index sensing.
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