scholarly journals Stripe Skyrmions and Skyrmion Crystals

2020 ◽  
Author(s):  
X. R. Wang ◽  
X. C. Hu ◽  
H. T. Wu
Keyword(s):  
Formation Energy ◽  
Ground States ◽  
Soliton Solutions ◽  
Magnetic Films ◽  
Interaction Coefficient ◽  
Nonlinear Sigma Model ◽  
Number Density ◽  
Stiffness Constant ◽  
Topological Quantum ◽  
Spin Texture

Abstract Skyrmions are important in topological quantum field theory for being soliton solutions of nonlinear sigma model and magnetics for their attractive applications in information technology. Either isolated skyrmions or skyrmion crystals may exist in a given chiral magnet, but not both at the same time. When skyrmion crystals, in which skyrmions often arrange themselves into triangular lattices, can be observed in a chiral magnet, stripy spin textures in various forms appear also and even mix with skyrmion crystals. People believe that skyrmions are circular objects and stripy spin textures have zero skyrmion number. Those stripy spin textures are called anything such as spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, ``siblings" of circular skyrmions in skyrmion crystals and ``cousins" of isolated circular skyrmions. Specifically, isolated skyrmions are excitations of chiral magnetic films whose ground states are ferromagnetic and skyrmion formation energy is positive. When the skyrmion formation energy is negative (relative to the single domain state), condensed skyrmions are the ground states and stripe skyrmions appear spontaneously. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion has a ramified stripe structure that maximizes the skyrmion wall length in order to lower system energy. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects due to the competition between negative formation energy and stripe-stripe or skyrmion-skyrmion repulsion. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.

scholarly journals Stripe skyrmions and skyrmion crystals

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
X. R. Wang ◽  
X. C. Hu ◽  
H. T. Wu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Information Technology ◽  
Ground States ◽  
Quantum Field ◽  
Number Density ◽  
Topological Solitons ◽  
Magnetic Skyrmions ◽  
Spin Texture

AbstractSkyrmions are important in quantum field theory and information technology for being topological solitons and for their attractive applications. Magnetic skyrmions are believed to be circular and stripy spin textures accompanied skyrmion crystals (SkXs) termed spiral/helical/cycloid orders have zero skyrmion number. Here we show that those stripy spin textures are skyrmions, siblings of circular skyrmions in SkXs and cousins of isolated circular skyrmions. Various irregular morphologies are the nature structures of skyrmions in the ground states. At the extreme of one skyrmion in the whole sample, the skyrmion is a ramified stripe. As the skyrmion number density increases, skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to circular objects. At a high skyrmion number density, SkXs are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open an avenue for manipulating skyrmions.

A Theory of Skyrmion Size in Skyrmion Crystals

2021 ◽  
Author(s):  
X. R. Wang ◽  
H. T. Wu ◽  
X. C. Hu ◽  
K. Y. Jing
Keyword(s):  
Magnetic Anisotropy ◽  
Room Temperature ◽  
Perpendicular Magnetic Anisotropy ◽  
Magnetic Films ◽  
Ferromagnetic Phase ◽  
Square Root ◽  
Number Density ◽  
Material Parameters ◽  
Stiffness Constant ◽  
Moriya Interaction

Abstract A magnetic skyrmion is a topological object that can exist as a solitary embedded in the vast ferromagnetic phase, or coexists with a group of its "siblings" in various stripy phases as well as skyrmion crystals (SkXs). Isolated skyrmions and skyrmions in an SkX are circular while a skyrmion in other phases is a stripe of various forms. Unexpectedly, the sizes of the three different class of skyrmions depend on material parameters differently. For chiral magnetic films with exchange stiffness constant A, the Dzyaloshinskii-Moriya interaction (DMI) strength D, and perpendicular magnetic anisotropy K, κ=π2D2⁄(16AK)=1 separates isolated skyrmions from condensed skyrmion states. In contrast to isolated skyrmions whose size increases with D⁄K and is insensitive to κ<<1 and stripe skyrmions whose width increases with A⁄D and is insensitive to κ>>1, the size of skyrmions in SkXs is inversely proportional to the square root of skyrmion number density and decreases with A⁄D. This finding has important implications in searching for stable smaller skyrmions at the room temperature.

scholarly journals DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Paul Eugenio ◽  
Ceren Dag
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Ground States ◽  
Bilayer Graphene ◽  
Chern Number ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Density Matrix Renormalization ◽  
Topological Quantum ◽  
Twisted Bilayer Graphene

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern=\pm1=±1), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry (\mathbb{Z}_2ℤ2). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle|++⋯+⟩ or all negative |{--\cdots-}\rangle|−−⋯−⟩. If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2)SU(2) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1ν=1 spin-\frac{1}{2}12 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

scholarly journals Comparative study of dust acoustic solitons in two-temperature ion homogeneous and inhomogeneous plasmas

2020 ◽  
Vol 14 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Rashmi Srivastava ◽  
Hitendra K. Malik ◽  
Devi Singh
Keyword(s):  
Solitary Waves ◽  
Inhomogeneous Plasma ◽  
Low Frequency ◽  
Soliton Solutions ◽  
Dusty Plasmas ◽  
Number Density ◽  
Dust Charge ◽  
Plasma Species ◽  
Dust Acoustic ◽  
Two Temperature

AbstractThe dust acoustic solitary waves are theoretically investigated in dusty plasmas for different cases of with and without density gradients. These low-frequency solitary waves are studied using appropriate Korteweg–de Vries equations obtained using relevant stretched coordinates. The soliton solutions in homogeneous plasma, weakly inhomogeneous plasma and strongly inhomogeneous plasma, are thoroughly investigated for studying the effect of different parameters like dust charge and density of all the plasma species on the soliton profiles. The combination of the dust charge with its number density changes the dynamics of the solitons and that is further affected by the number density of the hot ion with respect to the cold ions.

scholarly journals Quantum skyrmionics

2019 ◽  
Vol 33 (21) ◽  
pp. 1930005 ◽  
Author(s):  
Hector Ochoa ◽  
Yaroslav Tserkovnyak
Keyword(s):  
Quantum Interference ◽  
Driving Forces ◽  
Equations Of Motion ◽  
Quantum Hall ◽  
Magnetic Films ◽  
Thin Magnetic Films ◽  
Noncommutative Quantum Mechanics ◽  
Fast Development ◽  
Spin Texture ◽  
Chern Simons

Skyrmions are topological solitons that emerge in many physical contexts. In magnetism, they appear as textures of the spin-density field stabilized by different competing interactions and characterized by a topological charge that counts the number of times the order parameter wraps the sphere. They behave as classical objects when the spin texture varies slowly on the scale of the microscopic lattice of the magnet. However, the fast development of experimental tools to create and stabilize skyrmions in thin magnetic films has led to a rich variety of textures, sometimes of atomistic sizes. In this paper, we discuss, in a pedagogical manner, how to introduce quantum interference in the translational dynamics of skyrmion textures, starting from the micromagnetic equations of motion for a classical soliton. We study how the nontrivial topology of the spin texture manifests in the semiclassical regime, when the microscopic lattice potential is treated quantum-mechanically, but the external driving forces are taken as smooth classical perturbations. We highlight close relations to the fields of noncommutative quantum mechanics, Chern–Simons theories, and the quantum Hall effect.

scholarly journals Solitons of Some Nonlinear Sigma-Like Models

2020 ◽  
Author(s):  
V.E. Vekslerchik ◽  
Keyword(s):  
Sigma Model ◽  
Soliton Solutions ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Differential Identities ◽  
Yang Mills ◽  
Class Of Matrices

We present a set of differential identities for some class of matrices. These identities are used to derive the N-soliton solutions for the Pohlmeyer nonlinear sigma-model, two-dimensional self-dual Yang-Mills equations and some modification of the vector Calapso equation.

scholarly journals ON THE GAUGED NONCOMPACT SPIN SYSTEM

1998 ◽  
Vol 13 (32) ◽  
pp. 5503-5517
Author(s):  
SUNG-SOO KIM ◽  
PHILLIAL OH
Keyword(s):  
Spin System ◽  
Sigma Model ◽  
Soliton Solutions ◽  
Finite Energy ◽  
Nonlinear Sigma Model ◽  
Rotationally Symmetric ◽  
Background Charge ◽  
Chern Simons ◽  
Symmetric Soliton ◽  
Naive Model

We examine classical and quantum aspects of the planar noncompact spin system coupled with Chern–Simons gauge field in the presence of background charge. We first define our classical spin system as nonrelativistic nonlinear sigma model in which the order parameter spin takes value in the noncompact manifold ℳ= SU(1, 1)/U(1) . Although the naive model does not allow any finite energy self-dual solitons, it is shown that the gauged system admits static Bogomol'nyi solitons with finite energy whose rotationally symmetric soliton solutions are analyzed in detail. We also discuss the large spin limit in which the self-dual equation reduces to the well-known gauged nonlinear Schrödinger model or Abelian Higgs model, depending on the choice of the background charge term. Then, we perform quantization of the model. We find that the spin algebra satisfies anomalous commutation relations, and the system is a field theoretic realization of the anyons.

scholarly journals TOROIDAL SOLITON SOLUTIONS IN O(3)N NONLINEAR SIGMA MODEL

2004 ◽  
Vol 19 (34) ◽  
pp. 2569-2578 ◽  
Author(s):  
A. WERESZCZYŃSKI
Keyword(s):  
Sigma Model ◽  
Soliton Solutions ◽  
Minkowski Spacetime ◽  
Scalar Fields ◽  
Repulsive Interaction ◽  
Nonlinear Sigma Model ◽  
Nonlinear Coupling ◽  
Highly Nonlinear

A set of N three-component unit scalar fields in (3+1) Minkowski spacetime is investigated. The highly nonlinear coupling between them is chosen to omit the scaling instabilities. The multi-soliton static configurations with arbitrary Hopf numbers are found. Moreover, the generalized version of the Vakulenko–Kapitansky inequality is obtained. The possibility of attractive as well as repulsive interaction between hopfions is shown. A noninteracting limit is also discussed.

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