Chiral Magnets from String Theory

Abstract

Chiral magnets with the Dzyaloshinskii-Moriya (DM) interaction have received quite an intensive focus in condensed matter physics because of the presence of a chiral soliton lattice (CSL), an array of magnetic domain walls and anti-domain walls, and magnetic skyrmions. In this paper, we realize chiral magnets in type-IIA/B string theory by using the Hanany-Witten brane configuration (consisting of D3, D5 and NS5-branes) and the fractional D2 and D6 branes on the Eguchi-Hanson manifold. In the both cases, we put constant non-Abelian magnetic fluxes on flavor D-branes, turning them into magnetized D-branes. The $O(3)$ sigma model with an easy-axis or easy-plane potential and the DM interaction is realized on the worldvolume of the color D-branes. The ground state is the ferromagnetic (uniform) phase and the color D-brane is straight when the DM interaction is small compared with the scalar mass. However, when the DM interaction is larger, the uniform state is no longer stable and the ground state is inhomogeneous: the CSL phases and helimagnetic phase. In this case, the color D-brane is no longer straight but is snaky (zigzag) when the DM interaction is smaller (larger) than a critical value. A magnetic domain wall in the ferromagnetic phase is realized as a kinky D-brane. We further construct magnetic skyrmions in the ferromagnetic phase, realized as D1-branes (fractional D0-branes) in the former (latter) configuration. We see that the host D2-brane is bent around the position of a D0-brane as a magnetic skyrmion. Finally, we construct, in the ferromagnetic phase, domain-wall skyrmions, that is, composite states of a domain wall and skyrmions, and find that the domain wall is no longer flat in the vicinity of the skyrmion. Consequently, a kinky D2-brane worldvolume is pulled or pushed in the vicinity of the D0-brane depending on the sign of the skyrmion topological charge.

37 pages, 15 figures, v2: typos corrected, v3: references added, published version

References in corpus (38)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet
• Quantum Anomalies in Dense Matter
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Axial anomaly and magnetism of nuclear and quark matter
• Instantons in the Higgs Phase
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet GdRu2Si2
• Non-Abelian Walls in Supersymmetric Gauge Theories
• On the moduli space of semilocal strings and lumps
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Josephson vortices and the Atiyah-Manton construction
• Webs of Walls
• Intertwined order and holography: the case of the parity breaking pair density wave
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Domain wall Skyrmions
• Matryoshka Skyrmions
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Creating vortons and three-dimensional skyrmions from domain wall annihilation with stretched vortices in Bose-Einstein condensates
• Incarnations of Skyrmions
• Statistical Mechanics of Vortices from D-branes and T-duality
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Relations among topological solitons
• Emergence of Transient Domain Wall Skyrmions after Ultrafast Demagnetisation
• Effective Action of Domain Wall Networks
• D-brane Configurations for Domain Walls and Their Webs
• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• Wigner solids of domain wall skyrmions
• Quantum nucleation of topological solitons
• Formation of Chiral Soliton Lattice
• Defect formation from defect--anti-defect annihilations
• Knots from wall--anti-wall annihilations with stretched strings
• Supersymmetry Breaking in Spatially Modulated Vacua
• Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-dimensional Subspace

Cited by in corpus (13)

• Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Skyrmion crystal phase on a magnetic domain wall in chiral magnets
• Solitonic ground state in supersymmetric theory in background
• Manipulation and trapping of magnetic skyrmions with domain walls in chiral magnetic thin films
• Creation of domain-wall Skyrmions in chiral magnets
• Domain Wall Networks as Skyrmion Crystals in Chiral Magnets
• Magnetic D-brane solitons: skyrmion strings ending on a Néel wall in chiral magnets
• Demagnetization in micromagnetics: magnetostatic self-interactions of bulk chiral magnetic skyrmions
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Creation of domain-wall skyrmions in chiral magnets with Landau-Lifshitz-Gilbert dynamics and demagnetization
• Chiral non-Abelian domain walls in the Ginzburg-Landau theory
• Fermionic domain-wall Skyrmions of QCD in a magnetic field