Toroid moments in electrodynamics and solid-state physics

Dubovik, V.M.; Тугушев, В. В.

doi:10.1016/0370-1573(90)90042-z

Cited by 504 publications

(524 citation statements)

References 25 publications

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“…In both phases, hypertoroidization coexists with a homogeneous axial toroidal moment. A giant step in the field of ferroelectricity occurred with the discovery of toroidal ordering [1] of polarization [2]. Indeed the possibility to create new dipole configurations based on this special arrangement of polar order in the form of vortices has opened exciting possibilities for the downscaling of electronic devices such as ferroelectric random access memories [3].…”

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confidence: 99%

Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization

et al. 2014

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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 striking newpolarization patterns (phase IV) due to azimuthal variations of the hypertoroidal moment. In both phases, hypertoroidization coexists with a homogeneous axial toroidal moment

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confidence: 99%

Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization

et al. 2014

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“…While this relation is very important for low-energy real-photon processes, it is not suitable at higher momentum transfer. Following the ideas outlined in [4,14], one can build a variant of Siegert's theorem at arbitrary momentum q. Thus the r.m.e.…”

Section: Toroidal Multipolesmentioning

confidence: 99%

“…This approximation is equivalent to neglecting the transition charge moments Q λ and the average 2n-power radii of the charge distribution r 2n λ defined in [4,14,19]. We have represented graphically the differential cross-sections for the RR and IF models in both cases, the exact (29) and approximate (30), for the quadrupole ( fig.3a) and hexadecupole ( fig.3b) transitions induced by the scattered electron.…”

Section: Observation Of Toroidal Quadrupole Transitions In Electron Smentioning

confidence: 99%

Toroidal quadrupole transitions associated with collective rotational-vibrational motions of the nucleus

Mișicu¹

1995

J. Phys. G: Nucl. Part. Phys.

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Toroidal quadrupole transitions associated to collective rotational-vibrational motions of the nucleus Abstract. In the frame of the collective model one computes the longitudinal, transverse and toroidal multipoles corresponding to the excitations of low-lying levels in the ground state band of several even-even nuclei by inelastic electron scattering (e, e ′ ). In connection with this transitions a new quantity, which accounts for the deviations from the Siegert theorem, is introduced in the frame of the Riemann Rotational Model with non-vanishing vorticity. Inelastic differential cross-sections calculated at backscattering angles shows the dominancy of toroidal form-factors over a broad range of momentum transfer

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“…theory where the Goldstone bosons, and not the phonons, will couple the electrons of the Cooper pairs. Models of the electron-hole pairing involving toroidal moments have been already studied in the case of excitonic-insulators [13]. Let us mention that the Goldstone bosons will interact between themselves via their electric and magnetic moments, i.e., via segnetomagnon modes.…”

Section: -Conclusionmentioning

confidence: 99%

“…In case of static multipolar electric moments, this latter can be expanded up to a constant factor as [12,13] ξ…”

Section: -Preliminariesmentioning

confidence: 99%

Broken relativistic symmetry groups, toroidal moments and superconductivity in magnetoelectric crystals

Rubin

1993

Il Nuovo Cimento D

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A connection between creation of toroidal moments and breaking of the relativistic crystalline group associated to a given crystal, is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, Goldstone bosons, also associated to toroidal moments, are created and, as a consequence, corresponding toroidal phases in crystals. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.Key Words: toroidal moments, relativistic crystalline symmetries, symmetry breaking, anyons.PACS 1990: 05.30.L -Anyons and parastatistics. 61.50.E -Crystal symmetry, models and space groups, crystalline systems and classes. .80 -Magnetomechanical and magnetoelectric effects, magnetostriction. * E-mail: jacques.rubin@inln.cnrs.fr -IntroductionThe aim of this paper is to present a possible link between magnetoelectric effects and toroidal moments via the concept of relativistic crystalline groups [1,2,3,4,5] and to see how this link can be applied to derive a possible origin of superconductivity in electric and magnetic crystals. These crystals are characterized by their magnetic groups which are subgroups of the Shubnikov group O(3)1 ′ . Among the 122 magnetic groups, only 106 are compatible with the existence of a linear or quadratic magnetoelectric effect [6]. Let us recall that, in these groups, the time inversion 1 ′ appears in addition to or in combination with orthogonal transformations of the Euclidean space.In the present paper, we will consider relativistic symmetry group theory in crystals. Therefore, we need an extension from the Shubnikov group O(3)1 ′ to the group O(1, 3) in the Minkowski space. More particularly, our attention will be devoted to transformations of O(1, 3) leaving invariant polarization and magnetization vectors and generating a subgroup of the relativistic point group associated to the magnetic group G of a given crystal, namely the normalizerThis subgroup may not be identified to the magnetic group if G leaves invariant a particular non-zero velocity vector, i.e., if G ′ and G ⊆ G ′ are isotropy groups of O(1, 3). If such a vec-1 tor exists and G ′ = G, one strictly speaks about the relativistic crystalline symmetry G ′ . We can represent, as in figure 1, the list of the magnetic groups for which one can have in a crystal a spontaneous magnetization, a spontaneous polarization or an invariant non-zero velocity vector [15]. Thus, as it can be seen in the figure 1, only 31 magnetic groups are compatible with the existence of a relativistic crystalline symmetry (see the groups contained into the lowest circle). The invariant non-zero velocity vectors can be linked with toroidal moments from the point of view of magnetic symmetries as it has been already shown in previous papers [7,...

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Toroid moments in electrodynamics and solid-state physics

Cited by 504 publications

References 25 publications

Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization

Axial hypertoroidal moment in a ferroelectric nanotorus: A way to switch local polarization

Toroidal quadrupole transitions associated with collective rotational-vibrational motions of the nucleus

Broken relativistic symmetry groups, toroidal moments and superconductivity in magnetoelectric crystals

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